Qtl Manual

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Package ‘qtl’
February 16, 2018
Version 1.42-7
Date 2018-02-16
Title Tools for Analyzing QTL Experiments
Author Karl W Broman  and Hao Wu, with
ideas from Gary Churchill and Saunak Sen and contributions from
Danny Arends, Robert Corty, Timothee Flutre, Ritsert Jansen, Pjotr
Prins, Lars Ronnegard, Rohan Shah, Laura Shannon, Quoc Tran, Aaron
Wolen, and Brian Yandell
Maintainer Karl W Broman 
Description Analysis of experimental crosses to identify genes
(called quantitative trait loci, QTLs) contributing to variation in
quantitative traits.
Depends R (>= 2.14.0)
Imports parallel, graphics, stats, utils, grDevices
Suggests testthat
License GPL-3
URL https://rqtl.org, https://github.com/kbroman/qtl
BugReports https://github.com/kbroman/qtl/issues
Encoding UTF-8

R topics documented:
A starting point
add.cim.covar .
add.threshold .
addcovarint . .
addint . . . . .
addloctocross .
addmarker . . .
addpair . . . .
addqtl . . . . .
addtoqtl . . . .
allchrsplits . . .
argmax.geno . .
arithscan . . . .

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26

R topics documented:

2
arithscanperm . . .
badorder . . . . . .
bayesint . . . . . .
bristle3 . . . . . .
bristleX . . . . . .
c.cross . . . . . . .
c.scanone . . . . .
c.scanoneperm . .
c.scantwo . . . . .
c.scantwoperm . .
calc.errorlod . . . .
calc.genoprob . . .
calc.penalties . . .
cbind.scanoneperm
cbind.scantwoperm
checkAlleles . . . .
chrlen . . . . . . .
chrnames . . . . .
cim . . . . . . . .
clean.cross . . . . .
clean.scantwo . . .
cleanGeno . . . . .
comparecrosses . .
comparegeno . . .
compareorder . . .
condense.scantwo .
convert.map . . . .
convert.scanone . .
convert.scantwo . .
convert2riself . . .
convert2risib . . .
convert2sa . . . . .
countXO . . . . . .
drop.dupmarkers .
drop.markers . . .
drop.nullmarkers .
dropfromqtl . . . .
droponemarker . .
effectplot . . . . .
effectscan . . . . .
est.map . . . . . .
est.rf . . . . . . . .
fake.4way . . . . .
fake.bc . . . . . . .
fake.f2 . . . . . . .
fill.geno . . . . . .
find.flanking . . . .
find.marker . . . .
find.markerindex .
find.markerpos . .
find.pheno . . . . .
find.pseudomarker

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27
28
29
30
31
32
33
34
35
36
37
38
40
41
42
43
44
45
45
47
48
49
50
50
51
52
53
54
55
56
57
58
59
60
60
61
62
63
64
67
69
71
72
73
74
75
76
77
78
78
79
80

R topics documented:
findDupMarkers . . . . . .
fitqtl . . . . . . . . . . . .
fitstahl . . . . . . . . . . .
flip.order . . . . . . . . . .
formLinkageGroups . . . .
formMarkerCovar . . . . .
geno.crosstab . . . . . . .
geno.image . . . . . . . .
geno.table . . . . . . . . .
getid . . . . . . . . . . . .
groupclusteredheatmap . .
hyper . . . . . . . . . . .
inferFounderHap . . . . .
inferredpartitions . . . . .
interpPositions . . . . . .
jittermap . . . . . . . . . .
listeria . . . . . . . . . . .
locateXO . . . . . . . . .
locations . . . . . . . . . .
lodint . . . . . . . . . . .
makeqtl . . . . . . . . . .
map10 . . . . . . . . . . .
map2table . . . . . . . . .
mapthis . . . . . . . . . .
markerlrt . . . . . . . . .
markernames . . . . . . .
max.scanone . . . . . . . .
max.scanPhyloQTL . . . .
max.scantwo . . . . . . .
movemarker . . . . . . . .
MQM . . . . . . . . . . .
mqmaugment . . . . . . .
mqmautocofactors . . . . .
mqmextractmarkers . . . .
mqmfind.marker . . . . . .
mqmgetmodel . . . . . . .
mqmpermutation . . . . .
mqmplot.circle . . . . . .
mqmplot.cistrans . . . . .
mqmplot.clusteredheatmap
mqmplot.cofactors . . . .
mqmplot.directedqtl . . . .
mqmplot.heatmap . . . . .
mqmplot.multitrait . . . .
mqmplot.permutations . .
mqmplot.singletrait . . . .
mqmprocesspermutation .
mqmscan . . . . . . . . .
mqmscanall . . . . . . . .
mqmscanfdr . . . . . . . .
mqmsetcofactors . . . . .
mqmtestnormal . . . . . .

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81
82
85
87
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90
91
92
93
94
95
96
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98
99
100
101
102
103
104
105
106
107
108
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109
110
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113
114
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119
120
121
122
124
126
127
129
130
131
132
133
134
135
136
138
140
141
143

R topics documented:

4
multitrait . . . . .
nchr . . . . . . . .
nind . . . . . . . .
nmar . . . . . . . .
nmissing . . . . . .
nphe . . . . . . . .
nqrank . . . . . . .
nqtl . . . . . . . .
ntyped . . . . . . .
nullmarkers . . . .
orderMarkers . . .
phenames . . . . .
pickMarkerSubset .
plot.cross . . . . .
plot.qtl . . . . . . .
plot.rfmatrix . . . .
plot.scanone . . . .
plot.scanoneboot .
plot.scanoneperm .
plot.scanPhyloQTL
plot.scantwo . . . .
plot.scantwoperm .
plotErrorlod . . . .
plotGeno . . . . .
plotInfo . . . . . .
plotLodProfile . . .
plotMap . . . . . .
plotMissing . . . .
plotModel . . . . .
plotPheno . . . . .
plotPXG . . . . . .
plotRF . . . . . . .
pull.argmaxgeno .
pull.draws . . . . .
pull.geno . . . . .
pull.genoprob . . .
pull.map . . . . . .
pull.markers . . . .
pull.pheno . . . . .
pull.rf . . . . . . .
qtlversion . . . . .
read.cross . . . . .
readMWril . . . . .
reduce2grid . . . .
refineqtl . . . . . .
reorderqtl . . . . .
replace.map . . . .
replacemap.scanone
replacemap.scantwo
replaceqtl . . . . .
rescalemap . . . .
ripple . . . . . . .

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144
145
146
146
147
148
148
149
150
151
151
153
154
155
156
157
158
160
161
162
163
166
167
168
170
171
173
175
176
177
178
180
181
182
183
184
185
186
186
187
188
188
195
196
197
199
200
201
202
203
204
205

R topics documented:
scanone . . . . . . . . .
scanoneboot . . . . . . .
scanonevar . . . . . . . .
scanonevar.meanperm . .
scanonevar.varperm . . .
scanPhyloQTL . . . . .
scanqtl . . . . . . . . . .
scantwo . . . . . . . . .
scantwopermhk . . . . .
shiftmap . . . . . . . . .
sim.cross . . . . . . . .
sim.geno . . . . . . . . .
sim.map . . . . . . . . .
simFounderSnps . . . .
simPhyloQTL . . . . . .
simulatemissingdata . . .
stepwiseqtl . . . . . . .
strip.partials . . . . . . .
subset.cross . . . . . . .
subset.map . . . . . . .
subset.scanone . . . . .
subset.scanoneperm . . .
subset.scantwo . . . . .
subset.scantwoperm . . .
summary.cross . . . . .
summary.fitqtl . . . . . .
summary.qtl . . . . . . .
summary.ripple . . . . .
summary.scanone . . . .
summary.scanoneboot . .
summary.scanoneperm .
summary.scanPhyloQTL
summary.scantwo . . . .
summary.scantwoperm .
summaryMap . . . . . .
summaryScantwoOld . .
switch.order . . . . . . .
switchAlleles . . . . . .
table2map . . . . . . . .
top.errorlod . . . . . . .
totmar . . . . . . . . . .
transformPheno . . . . .
tryallpositions . . . . . .
typingGap . . . . . . . .
write.cross . . . . . . . .
xaxisloc.scanone . . . .
Index

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6

A starting point

A starting point

Introductory comments on R/qtl

Description
A brief introduction to the R/qtl package, with a walk-through of an analysis.
New to R and/or R/qtl?
• In order to use the R/qtl package, you must type (within R) library(qtl). You may wish to
include this in a .Rprofile file.
• Documention and several tutorials are available at the R archive (https://cran.r-project.
org).
• Use the help.start function to start the html version of the R help.
• Type library(help=qtl) to get a list of the functions in R/qtl.
• Use the example function to run examples of the various functions in R/qtl.
• A tutorial on the use of R/qtl is distributed with the package and is also available at https:
//rqtl.org/rqtltour.pdf.
• Download the latest version of R/qtl from the R archive or from https://rqtl.org.
Walk-through of an analysis
Here we briefly describe the use of R/qtl to analyze an experimental cross. A more extensive tutorial
on its use is distributed with the package and is also available at https://rqtl.org/rqtltour.
pdf.
A difficult first step in the use of most data analysis software is the import of data. With R/qtl,
one may import data in several different formats by use of the function read.cross. The internal
data structure used by R/qtl is rather complicated, and is described in the help file for read.cross.
We won’t discuss data import any further here, except to say that the comma-delimited format
("csv") is recommended. If you have trouble importing data, send an email to Karl Broman,
, perhaps attaching examples of your data files. (Such data will
be kept confidential.) Also see the sample data files and code at https://rqtl.org/sampledata.
We consider the example data hyper, an experiment on hypertension in the mouse, kindly provided
by Bev Paigen and Gary Churchill. Use the data function to load the data.
data(hyper)
The hyper data set has class "cross". The function summary.cross gives summary information
on the data, and checks the data for internal consistency. A number of other utility functions are
available; hopefully these are self-explanatory.
summary(hyper)
nind(hyper)
nphe(hyper)
nchr(hyper)
nmar(hyper)
totmar(hyper)
The function plot.cross gives a graphical summary of the data; it calls plotMissing (to plot a
matrix displaying missing genotypes) and plotMap (to plot the genetic maps), and also displays
histograms or barplots of the phenotypes. The plotMissing function can plot individuals ordered

A starting point

7

by their phenotypes; you can see that for most markers, only individuals with extreme phenotypes
were genotyped.
plot(hyper)
plotMissing(hyper)
plotMissing(hyper, reorder=TRUE)
plotMap(hyper)
Note that one marker (on chromosome 14) has no genotype data. The function drop.nullmarkers
removes such markers from the data.
hyper <- drop.nullmarkers(hyper)
totmar(hyper)
The function est.rf estimates the recombination fraction between each pair of markers, and calculates a LOD score for the test of r = 1/2. This is useful for identifying markers that are placed on the
wrong chromosome. Note that since, for these data, many markers were typed only on recombinant
individuals, the pairwise recombination fractions show rather odd patterns.
hyper <- est.rf(hyper)
plotRF(hyper)
plotRF(hyper, chr=c(1,4))
To re-estimate the genetic map for an experimental cross, use the function est.map. The function
plotMap, in addition to plotting a single map, can plot the comparison of two genetic maps (as long
as they are composed of the same numbers of chromosomes and markers per chromosome). The
function replace.map map be used to replace the genetic map in a cross with a new one.
newmap <- est.map(hyper, error.prob=0.01, verbose=TRUE)
plotMap(hyper, newmap)
hyper <- replace.map(hyper, newmap)
The function calc.errorlod may be used to assist in identifying possible genotyping errors; it
calculates the error LOD scores described by Lincoln and Lander (1992). The calc.errorlod
function return a modified version of the input cross, with error LOD scores included. The function
top.errorlod prints the genotypes with values above a cutoff (by default, the cutoff is 4.0).
hyper <- calc.errorlod(hyper, error.prob=0.01)
top.errorlod(hyper)
The function plotGeno may be used to inspect the observed genotypes for a chromosome, with
likely genotyping errors flagged.
plotGeno(hyper, chr=16, ind=c(24:34, 71:81))
Before doing QTL analyses, some intermediate calculations need to be performed. The function
calc.genoprob calculates conditional genotype probabilities given the multipoint marker data.
sim.geno simulates sequences of genotypes from their joint distribution, given the observed marker
data.
As with calc.errorlod, these functions return a modified version of the input cross, with the intermediate calculations included. The step argument indicates the density of the grid on which the
calculations will be performed, and determines the density at which LOD scores will be calculated.
hyper <- calc.genoprob(hyper, step=2.5, error.prob=0.01)
hyper <- sim.geno(hyper, step=2.5, n.draws=64, error.prob=0.01)
The function scanone performs a genome scan with a single QTL model. By default, it performs
standard interval mapping (Lander and Botstein 1989): use of a normal model and the EM algorithm. If one specifies method="hk", Haley-Knott regression is performed (Haley and Knott 1992).
These two methods require the results from calc.genoprob.
out.em <- scanone(hyper)
out.hk <- scanone(hyper, method="hk")

8

A starting point
If one specifies method="imp", a genome scan is performed by the multiple imputation method of
Sen and Churchill (2001). This method requires the results from sim.geno.
out.imp <- scanone(hyper, method="imp")
The output of scanone is a data.frame with class "scanone". The function plot.scanone may be
used to plot the results, and may plot up to three sets of results against each other, as long as they
conform appropriately.
plot(out.em)
plot(out.hk, col="blue", add=TRUE)
plot(out.imp, col="red", add=TRUE)
plot(out.hk, out.imp, out.em, chr=c(1,4), lty=1,
col=c("blue","red","black"))
The function summary.scanone may be used to list information on the peak LOD for each chromosome for which the LOD exceeds a specified threshold.
summary(out.em)
summary(out.em, threshold=3)
summary(out.hk, threshold=3)
summary(out.imp, threshold=3)
The function max.scanone returns the maximum LOD score, genome-wide.
max(out.em)
max(out.hk)
max(out.imp)
One may also use scanone to perform a permutation test to get a genome-wide LOD significance
threshold.
operm.hk <- scanone(hyper, method="hk", n.perm=1000)
The result has class "scanoneperm". The summary.scanoneperm function may be used to calculate
LOD thresholds.
summary(operm.hk, alpha=0.05)
The permutation results may also be used in the summary.scanone function to calculate LOD
thresholds and genome-scan-adjusted p-values.
summary(out.hk, perms=operm.hk, alpha=0.05, pvalues=TRUE)
We should say at this point that the function save.image will save your workspace to disk. You’ll
wish you had used this if R crashes.
save.image()
The function scantwo performs a two-dimensional genome scan with a two-QTL model. Methods
"em", "hk" and "imp" are all available. scantwo is considerably slower than scanone, and can
require a great deal of memory. Thus, you may wish to re-run calc.genoprob and/or sim.geno
with a more coarse grid.
hyper <- calc.genoprob(hyper, step=10, err=0.01)
hyper <- sim.geno(hyper, step=10, n.draws=64, err=0.01)
out2.hk <- scantwo(hyper, method="hk")
out2.em <- scantwo(hyper)
out2.imp <- scantwo(hyper, method="imp")
The output is an object with class scantwo. The function plot.scantwo may be used to plot the
results. The upper triangle contains LOD scores for tests of epistasis, while the lower triangle
contains LOD scores for the full model.

A starting point

9

plot(out2.hk)
plot(out2.em)
plot(out2.imp)
The function summary.scantwo lists the interesting aspects of the output. For each pair of chromosomes (k, l), it calculates the maximum LOD score for the full model, Mf (k, l); a LOD score
indicating evidence for a second QTL, allowing for epistasis), Mf v1 (k, l); a LOD score indicating
evidence for epistasis, Mi (k, l); the LOD score for the additive QTL model, Ma (k, l); and a LOD
score indicating evidence for a second QTL, assuming no epistasis, Mav1 (k, l).
You must provide five LOD thresholds, corresponding to the above five LOD scores, and in that
order. A chromosome pair is printed if either (a) Mf (k, l) ≥ Tf and (Mf v1 (k, l) ≥ Tf v1 or
Mi (k, l) ≥ Ti ), or (b) Ma (k, l) ≥ Ta and Mav1 (k, l) ≥ Tav1 .
summary(out2.em, thresholds=c(6.2, 5.0, 4.6, 4.5, 2.3))
summary(out2.em, thresholds=c(6.2, 5.0, Inf, 4.5, 2.3))
In the latter case, the interaction LOD score will be ignored.
The function max.scantwo returns the maximum joint and additive LODs for a two-dimensional
genome scan.
max(out2.em)
Permutation tests may also performed with scantwo; it may take a few days of CPU time. The
output is a list containing the maxima of the above five LOD scores for each of the imputations.
operm2 <- scantwo(hyper, method="hk", n.perm=100)
summary(operm2, alpha=0.05)
Citing R/qtl
To cite R/qtl in publications, use the Broman et al. (2003) reference listed below.
Author(s)
Karl W Broman, 
References
Broman, K. W. and Sen, Ś. (2009) A guide to QTL mapping with R/qtl. Springer. https://rqtl.
org/book
Broman, K. W., Wu, H., Sen, Ś. and Churchill, G. A. (2003) R/qtl: QTL mapping in experimental
crosses. Bioinformatics 19, 889–890.
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
Lander, E. S. and Botstein, D. (1989) Mapping Mendelian factors underlying quantitative traits
using RFLP linkage maps. Genetics 121, 185–199.
Lincoln, S. E. and Lander, E. S. (1992) Systematic detection of errors in genetic linkage data.
Genomics 14, 604–610.
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.

10

add.cim.covar

add.cim.covar

Indicate marker covariates from composite interval mapping

Description
Add dots at the locations of the selected marker covariates, for a plot of composite interval mapping
results.
Usage
add.cim.covar(cimresult, chr, gap=25, ...)
Arguments
cimresult

Composite interval mapping results, as output from cim.

chr

Optional vector specifying which chromosomes to plot. (The chromosomes
must be specified by name.) This should be identical to that used in the call
to plot.scanone.

gap

Gap separating chromosomes (in cM). This should be identical to that used in
the call to plot.scanone.

...

Additional plot arguments, passed to the function points.

Details
One must first have used the function plot.scanone to plot the composite interval mapping results.
The arguments chr and gap must be identical to the values used in the call to plot.scanone.
Dots indicating the locations of the selected marker covariates are displayed on the x-axis. (By
default, solid red circles are plotted; this may be modified by specifying the graphics parameters
pch and col.)
Value
A data frame indicating the marker covariates that were plotted.
Author(s)
Karl W Broman, 
See Also
cim, plot.scanone
Examples
## Not run: data(hyper)
hyper <- calc.genoprob(hyper, step=2.5)
out <- scanone(hyper)
out.cim <- cim(hyper, n.marcovar=3)
plot(out, out.cim, chr=c(1,4,6,15), col=c("blue", "red"))

add.threshold

11

add.cim.covar(out.cim, chr=c(1,4,6,15))
## End(Not run)

add.threshold

Add significance threshold to plot

Description
Add a significance threshold to a plot created by plot.scanone), using the permutation results.
Usage
add.threshold(out, chr, perms, alpha=0.05, lodcolumn=1, gap=25, ...)
Arguments
out

An object of class "scanone", as output by scanone. This must be identical to
what was used in the call to plot.scanone.

chr

Optional vector specifying which chromosomes to plot. If a selected subset of
chromosomes were plotted, they must be specified here.

perms

Permutation results from scanone, used to calculate the significance threshold.

alpha

Significance level of the threshold.

lodcolumn

An integer indicating which of column in the permutation results should be used.

gap

Gap separating chromosomes (in cM). This must be identical to what was used
in the call to plot.scanone.

...

Passed to the function abline when it is called.

Details
This function allows you to add a horizontal line at the significance threshold to genome scan results
plotted by plot.scanone.
The arguments out, chr, and gap must match what was used in the call to plot.scanone.
The argument perms must be specified. If X-chromosome-specific permutations were performed
(via the argument perm.Xsp in the call to scanone), separate thresholds will be plotted for the
autosomes and the X chromosome. These are calculated via the summary.scanoneperm function.
Value
None.
Author(s)
Karl W Broman, 
See Also
scanone, plot.scanone, summary.scanoneperm, xaxisloc.scanone

12

addcovarint

Examples
data(hyper)
hyper <- calc.genoprob(hyper)
out <- scanone(hyper, method="hk")
operm <- scanone(hyper, method="hk", n.perm=100, perm.Xsp=TRUE)
plot(out, chr=c(1,4,6,15,"X"))
add.threshold(out, chr=c(1,4,6,15,"X"), perms=operm, alpha=0.05)
add.threshold(out, chr=c(1,4,6,15,"X"), perms=operm, alpha=0.1,
col="green", lty=2)

addcovarint

Add QTL x covariate interaction to a multiple-QTL model

Description
Try adding all QTL x covariate interactions, one at a time, to a multiple QTL model, for a given set
of covariates.
Usage
addcovarint(cross, pheno.col=1, qtl, covar=NULL, icovar, formula,
method=c("imp","hk"), model=c("normal", "binary"),
verbose=TRUE, pvalues=TRUE, simple=FALSE, tol=1e-4,
maxit=1000, require.fullrank=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype.
One may also give a character string matching a phenotype name. Finally, one
may give a numeric vector of phenotypes, in which case it must have the length
equal to the number of individuals in the cross, and there must be either nonintegers or values < 1 or > no. phenotypes; this last case may be useful for
studying transformations.

qtl

An object of class qtl, as output from makeqtl.

covar

A matrix or data.frame of covariates. These must be strictly numeric.

icovar

Vector of character strings indicating the columns in covar to be considered for
QTL x covariate interactions.

formula

An object of class formula indicating the model to be fitted. (It can also be the
character string representation of a formula.) QTLs are referred to as Q1, Q2, etc.
Covariates are referred to by their names in the data frame covar.

method

Indicates whether to use multiple imputation or Haley-Knott regression.

model

The phenotype model: the usual model or a model for binary traits

verbose

If TRUE, will print a message if there are no interactions to test.

pvalues

If FALSE, p-values will not be included in the results.

simple

If TRUE, don’t include p-values or sums of squares in the summary.

tol

Tolerance for convergence for the binary trait model.

addcovarint

13

maxit
Maximum number of iterations for fitting the binary trait model.
require.fullrank
If TRUE, give LOD=0 when covariate matrix in the linear regression is not of
full rank.
Details
The formula is used to specified the model to be fit. In the formula, use Q1, Q2, etc., or q1, q2, etc.,
to represent the QTLs, and the column names in the covariate data frame to represent the covariates.
We enforce a hierarchical structure on the model formula: if a QTL or covariate is in involved in an
interaction, its main effect must also be included.
Value
An object of class addcovarint, with results as in the drop-one-term analysis from fitqtl. This
is a data frame (given class "addcovarint", with the following columns: degrees of freedom (df),
Type III sum of squares (Type III SS), LOD score(LOD), percentage of variance explained (%var),
F statistics (F value), and P values for chi square (Pvalue(chi2)) and F distribution (Pvalue(F)).
Note that the degree of freedom, Type III sum of squares, the LOD score and the percentage of
variance explained are the values comparing the full to the sub-model with the term dropped. Also
note that for imputation method, the percentage of variance explained, the the F values and the P
values are approximations calculated from the LOD score.
QTL x covariate interactions already included in the input formula are not tested.
Author(s)
Karl W Broman, 
References
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.
See Also
addint, fitqtl, makeqtl, scanqtl, refineqtl, addqtl, addpair
Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c(1, 8, 13)
qp <- c(26, 56, 28)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
# use the sex phenotype as the covariate
covar <- data.frame(sex=fake.f2$pheno$sex)

14

addint

# try all possible QTL x sex interactions, one at a time
addcovarint(fake.f2, pheno.col=1, qtl, covar, "sex", y~Q1+Q2+Q3,
method="hk")

addint

Add pairwise interaction to a multiple-QTL model

Description
Try adding all possible pairwise interactions, one at a time, to a multiple QTL model.
Usage
addint(cross, pheno.col=1, qtl, covar=NULL, formula, method=c("imp","hk"),
model=c("normal", "binary"), qtl.only=FALSE, verbose=TRUE,
pvalues=TRUE, simple=FALSE, tol=1e-4, maxit=1000, require.fullrank=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

pheno.col

Column number in the phenotype matrix to be used as the phenotype. One may
also give a character string matching a phenotype name. Finally, one may give
a numeric vector of phenotypes, in which case it must have the length equal to
the number of individuals in the cross, and there must be either non-integers
or values < 1 or > no. phenotypes; this last case may be useful for studying
transformations.

qtl

An object of class qtl, as output from makeqtl.

covar

A matrix or data.frame of covariates. These must be strictly numeric.

formula

An object of class formula indicating the model to be fitted. (It can also be the
character string representation of a formula.) QTLs are referred to as Q1, Q2, etc.
Covariates are referred to by their names in the data frame covar. If the new
QTL is not included in the formula, its main effect is added.

method

Indicates whether to use multiple imputation or Haley-Knott regression.

model

The phenotype model: the usual model or a model for binary traits

qtl.only

If TRUE, only test QTL:QTL interactions (and not interactions with covariates).

verbose

If TRUE, will print a message if there are no interactions to test.

pvalues

If FALSE, p-values will not be included in the results.

simple

If TRUE, don’t include p-values or sums of squares in the summary.

tol

Tolerance for convergence for the binary trait model.

maxit

Maximum number of iterations for fitting the binary trait model.

require.fullrank
If TRUE, give LOD=0 when covariate matrix in the linear regression is not of
full rank.

addint

15

Details
The formula is used to specified the model to be fit. In the formula, use Q1, Q2, etc., or q1, q2, etc.,
to represent the QTLs, and the column names in the covariate data frame to represent the covariates.
We enforce a hierarchical structure on the model formula: if a QTL or covariate is in involved in an
interaction, its main effect must also be included.
Value
An object of class addint, with results as in the drop-one-term analysis from fitqtl. This is a data
frame (given class "addint", with the following columns: degrees of freedom (df), Type III sum
of squares (Type III SS), LOD score(LOD), percentage of variance explained (%var), F statistics (F
value), and P values for chi square (Pvalue(chi2)) and F distribution (Pvalue(F)).
Note that the degree of freedom, Type III sum of squares, the LOD score and the percentage of
variance explained are the values comparing the full to the sub-model with the term dropped. Also
note that for imputation method, the percentage of variance explained, the the F values and the P
values are approximations calculated from the LOD score.
Pairwise interactions already included in the input formula are not tested.
Author(s)
Karl W Broman, 
References
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.
See Also
addcovarint, fitqtl, makeqtl, scanqtl, refineqtl, addqtl, addpair
Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c(1, 8, 13)
qp <- c(26, 56, 28)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
# try all possible pairwise interactions, one at a time
addint(fake.f2, pheno.col=1, qtl, formula=y~Q1+Q2+Q3, method="hk")

16

addloctocross

addloctocross

Add phenotype location into a cross object

Description
Add phenotype location(s) into a cross object (with eQTL/pQTL studies)
Usage
addloctocross(cross, locations=NULL, locfile="locations.txt", verbose=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

locations

R variable holding location information

locfile

load from a file, see the details section for the layout of the file.

verbose

If TRUE, give verbose output

Details
inputfile layout: Num Name Chr cM 1 X3.Hydroxypropyl 4 50.0 Num is the number of the phenotype in the cross object Name is the name of the phenotype (will be checked against the name
already in the cross object at position num Chr Chromosome cM postion from start of chromosome
in cM
Value
The input cross object, with the locations added as an aditional component locations
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
See Also
• mqmplot.cistrans - Cis/trans plot
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning

addmarker

17

Examples
## Not run:
data(multitrait)
data(locations)
multiloc <- addloctocross(multitrait,locations)
results <- scanall(multiloc)
mqmplot.cistrans(results, multiloc, 5, FALSE, TRUE)
## End(Not run)

addmarker

Add a marker to a cross

Description
Add a marker to a cross object.
Usage
addmarker(cross, genotypes, markername, chr, pos)
Arguments
cross

An object of class cross. See read.cross for details.

genotypes

Vector of numeric genotypes.

markername

Marker name as character string.

chr

Chromosome ID as character string.

pos

Position of marker, as numeric value.

Details
Use this function with caution. It would be best to incorporate new data into a single file to be
imported with read.cross.
But if you have genotypes on one or two additional markers that you want to add, you might load
them with read.csv and incorporate them with this function.
Value
The input cross object with the single marker added.
Author(s)
Karl W Broman, 
See Also
pull.markers, drop.markers

18

addpair

Examples
data(fake.f2)
# genotypes for new marker
gi <- pull.geno(fill.geno(fake.f2))[,"D5M197"]
# add marker to cross
fake.f2 <- addmarker(fake.f2, gi, "D5M197imp", "5", 11)

addpair

Scan for an additional pair of QTL in a multiple-QTL model

Description
Scan for an additional pair of QTL in the context of a multiple QTL model.
Usage
addpair(cross, chr, pheno.col=1, qtl, covar=NULL, formula,
method=c("imp","hk"), model=c("normal", "binary"),
incl.markers=FALSE, verbose=TRUE, tol=1e-4, maxit=1000,
forceXcovar=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to be scanned. If missing, all chromosomes are scanned. Refer to chromosomes by name. Refer to chromosomes
with a preceding - to have all chromosomes but those considered. A logical
(TRUE/FALSE) vector may also be used.

pheno.col

Column number in the phenotype matrix to be used as the phenotype. One may
also give a character string matching a phenotype name. Finally, one may give
a numeric vector of phenotypes, in which case it must have the length equal to
the number of individuals in the cross, and there must be either non-integers
or values < 1 or > no. phenotypes; this last case may be useful for studying
transformations.

qtl

An object of class qtl, as output from makeqtl.

covar

A matrix or data.frame of covariates. These must be strictly numeric.

formula

An object of class formula indicating the model to be fitted. (It can also be the
character string representation of a formula.) QTLs are referred to as Q1, Q2, etc.
Covariates are referred to by their names in the data frame covar. If the new
QTL are not included in the formula, a two-dimensional scan as in scantwo is
performed.

method

Indicates whether to use multiple imputation or Haley-Knott regression.

model

The phenotype model: the usual model or a model for binary traits

incl.markers

If FALSE, do calculations only at points on an evenly spaced grid. If calc.genoprob
or sim.geno were run with stepwidth="variable" or stepwidth="max", we
force incl.markers=TRUE.

addpair

19

verbose

If TRUE, display information about the progress of calculations. If verbose is
an integer > 1, further messages from scanqtl are also displayed.

tol

Tolerance for convergence for the binary trait model.

maxit

Maximum number of iterations for fitting the binary trait model.

forceXcovar

If TRUE, force inclusion of X-chr-related covariates (like sex and cross direction).

Details
The formula is used to specified the model to be fit. In the formula, use Q1, Q2, etc., or q1, q2, etc.,
to represent the QTLs, and the column names in the covariate data frame to represent the covariates.
We enforce a hierarchical structure on the model formula: if a QTL or covariate is in involved in an
interaction, its main effect must also be included.
If neither of the two new QTL are indicated in the formula, we perform a two-dimensional scan as
in scantwo. That is, for each pair of QTL positions, we fit two models: two additive QTL added to
the formula, and two interacting QTL added to the formula.
If the both of the new QTL are indicated in the formula, that particular model is fit, with the positions of the new QTL allowed to vary across the genome. If just one of the QTL is indicated
in the formula, a main effect for the other is added, and that particular model is fit, again with the
positions of both QTL varying. Note that in this case the LOD scores are not analogous to those produced by scantwo. Thus, there slightly modified forms for the plots (produced by plot.scantwo)
and summaries (produced by summary.scantwo and max.scantwo). In the plot, the x-axis is to
be interpreted as the position of the first of the new QTL, and the y-axis is to be interpreted as the
position of the second of the new QTL. In the summaries, we give the single best pair of positions
on each pair of chromosomes, and give LOD scores comparing that pair of positions to the base
model (without each of these QTL), and to the base model plus one additional QTL on one or the
other of the chromosomes.
Value
An object of class scantwo, as produced by scantwo.
If neither of the new QTL were indicated in the formula, the result is just as in scantwo, though
with LOD scores relative to the base model (omitting the new QTL).
Otherwise, the results are contained in what would ordinarily be in the full and additive LOD scores,
with the additive LOD scores corresponding to the case that the first of the new QTL is to the
left of the second of the new QTL, and the full LOD scores corresponding to the case that the
first of the new QTL is to the right of the second of the new QTL. Because the structure of the
LOD scores in this case is different from those output by scantwo, we include, in this case, an attribute "addpair"=TRUE. (We also require results of single-dimensional scans, omitting each of the
two new QTL from the formula, one at a time; these are included as attributes "lod.minus1"
and "lod.minus2".) The results are then treated somewhat differently by summary.scantwo,
max.scantwo, and plot.scantwo. See the Details section.
Author(s)
Karl W Broman, 
References
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.

20

addqtl
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.

See Also
addint, addqtl, fitqtl, makeqtl, scanqtl, refineqtl, makeqtl, scantwo, addtoqtl
Examples
# A totally contrived example to show some of what you can do
# simulate backcross data with 3 chromosomes (names "17", "18", "19")
# one QTL on chr 17 at 40 cM
# one QTL on chr 18 at 30 cM
# two QTL on chr 19, at 10 and 40 cM
data(map10)
model <- rbind(c(1,40,0), c(2,30,0), c(3,10,0), c(3,40,0))
## Not run: fakebc <- sim.cross(map10[17:19], model=model, type="bc", n.ind=250)
# het at QTL on 17 and 1st QTL on 19 increases phenotype by 1 unit
# het at QTL on 18 and 2nd QTL on 19 decreases phenotype by 1 unit
qtlgeno <- fakebc$qtlgeno
phe <- rnorm(nind(fakebc))
w <- qtlgeno[,1]==2 & qtlgeno[,3]==2
phe[w] <- phe[w] + 1
w <- qtlgeno[,2]==2 & qtlgeno[,4]==2
phe[w] <- phe[w] - 1
fakebc$pheno[,1] <- phe
## Not run: fakebc <- calc.genoprob(fakebc, step=2, err=0.001)
# base model has QTLs on chr 17 and 18
qtl <- makeqtl(fakebc, chr=c("17", "18"), pos=c(40,30), what="prob")
# scan for an additional pair of QTL, one interacting with the locus
#
on 17 and one interacting with the locus on 18
out.ap <- addpair(fakebc, qtl=qtl, formula = y~Q1*Q3 + Q2*Q4, method="hk")
max(out.ap)
summary(out.ap)
plot(out.ap)

addqtl

Scan for an additional QTL in a multiple-QTL model

Description
Scan for an additional QTL in the context of a multiple QTL model.

addqtl

21

Usage
addqtl(cross, chr, pheno.col=1, qtl, covar=NULL, formula,
method=c("imp","hk"), model=c("normal", "binary"),
incl.markers=TRUE, verbose=FALSE, tol=1e-4, maxit=1000,
forceXcovar=FALSE, require.fullrank=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to be scanned. If missing, all chromosomes are scanned. Refer to chromosomes by name. Refer to chromosomes
with a preceding - to have all chromosomes but those considered. A logical
(TRUE/FALSE) vector may also be used.

pheno.col

Column number in the phenotype matrix to be used as the phenotype. One may
also give a character string matching a phenotype name. Finally, one may give
a numeric vector of phenotypes, in which case it must have the length equal to
the number of individuals in the cross, and there must be either non-integers
or values < 1 or > no. phenotypes; this last case may be useful for studying
transformations.

qtl

An object of class qtl, as output from makeqtl.

covar

A matrix or data.frame of covariates. These must be strictly numeric.

formula

An object of class formula indicating the model to be fitted. (It can also be the
character string representation of a formula.) QTLs are referred to as Q1, Q2, etc.
Covariates are referred to by their names in the data frame covar. If the new
QTL is not included in the formula, its main effect is added.

method

Indicates whether to use multiple imputation or Haley-Knott regression.

model

The phenotype model: the usual model or a model for binary traits

incl.markers

If FALSE, do calculations only at points on an evenly spaced grid. If calc.genoprob
or sim.geno were run with stepwidth="variable" or stepwidth="max", we
force incl.markers=TRUE.

verbose

If TRUE, display information about the progress of calculations. If verbose is
an integer > 1, further messages from scanqtl are also displayed.

tol

Tolerance for convergence for the binary trait model.

maxit

Maximum number of iterations for fitting the binary trait model.

forceXcovar

If TRUE, force inclusion of X-chr-related covariates (like sex and cross direction).
require.fullrank
If TRUE, give LOD=0 when covariate matrix in the linear regression is not of
full rank.
Details
The formula is used to specified the model to be fit. In the formula, use Q1, Q2, etc., or q1, q2, etc.,
to represent the QTLs, and the column names in the covariate data frame to represent the covariates.
We enforce a hierarchical structure on the model formula: if a QTL or covariate is in involved in an
interaction, its main effect must also be included.
If one wishes to scan for QTL that interact with another QTL, include it in the formula (with an
index of one more than the number of QTL in the input qtl object).

22

addtoqtl

Value
An object of class scanone, as produced by the scanone function. LOD scores are relative to the
base model (with any terms that include the new QTL omitted).
Author(s)
Karl W Broman, 
References
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.
See Also
scanone, fitqtl, scanqtl, refineqtl, makeqtl, addtoqtl, addpair, addint
Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c(1, 8, 13)
qp <- c(26, 56, 28)
fake.f2 <- subset(fake.f2, chr=c(1,2,3,8,13))
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
# scan for an additional QTL
out1 <- addqtl(fake.f2, qtl=qtl, formula=y~Q1+Q2+Q3, method="hk")
max(out1)
# scan for an additional QTL that interacts with the locus on chr 1
out2 <- addqtl(fake.f2, qtl=qtl, formula=y~Q1*Q4+Q2+Q3, method="hk")
max(out2)
# plot interaction LOD scores
plot(out2-out1)

addtoqtl

Add to a qtl object

Description
Add a QTL or multiple QTL to a qtl object.

addtoqtl

23

Usage
addtoqtl(cross, qtl, chr, pos, qtl.name, drop.lod.profile=TRUE)

Arguments
cross

An object of class cross. See read.cross for details.

qtl

The qtl object to which additional QTL are to be added.

chr

Vector indicating the chromosome for each new QTL. (These should be character strings referring to the chromosomes by name.)

pos

Vector (of same length as chr) indicating the positions on the chromosome for
each new QTL. If there is no marker or pseudomarker at a position, the nearest
position is used.

qtl.name

Optional user-specified name for each new QTL, used in the drop-one-term
ANOVA table in fitqtl. If unspecified, the names will be of the form "Chr1@10"
for a QTL on Chromsome 1 at 10 cM.

drop.lod.profile
If TRUE, remove any LOD profiles from the object.

Value
An object of class qtl, just like the input qtl object, but with additional QTL added. See makeqtl
for details.

Author(s)
Karl W Broman, 

See Also
makeqtl, fitqtl, dropfromqtl, replaceqtl, reorderqtl

Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c(1, 6, 13)
qp <- c(25.8, 33.6, 18.63)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
qtl <- addtoqtl(fake.f2, qtl, 14, 35)

24

allchrsplits

allchrsplits

Test all possible splits of a chromosome into two pieces

Description
In order to assess the support for a linkage group, this function splits the linkage groups into two
pieces at each interval and in each case calculates a LOD score comparing the combined linkage
group to the two pieces.
Usage
allchrsplits(cross, chr, error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
m=0, p=0, maxit=4000, tol=1e-6, sex.sp=TRUE,
verbose=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

A vector specifying which chromosomes to study. This should be a vector of
character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi, Carter-Falconer, or Morgan map
function when converting genetic distances into recombination fractions. (Ignored if m > 0.)

m

Interference parameter for the chi-square model for interference; a non-negative
integer, with m=0 corresponding to no interference. This may be used only for
a backcross or intercross.

p

Proportion of chiasmata from the NI mechanism, in the Stahl model; p=0 gives
a pure chi-square model. This may be used only for a backcross or intercross.

maxit

Maximum number of EM iterations to perform.

tol

Tolerance for determining convergence.

sex.sp

Indicates whether to estimate sex-specific maps; this is used only for the 4-way
cross.

verbose

If TRUE, print information on progress.

Value
A data frame (actually, an object of class "scanone", so that one may use plot.scanone, summary.scanone,
etc.) with each row being an interval at which a split is made. The first two columns are the chromosome ID and midpoint of the interval. The third column is a LOD score comparing the combined
linkage group to the split into two linkage groups. A fourth column (gap) indicates the length of
each interval.
The row names indicate the flanking markers for each interval.

argmax.geno

25

Author(s)
Karl W Broman, 
See Also
est.map, ripple, est.rf, switch.order, movemarker
Examples
data(fake.bc)
allchrsplits(fake.bc, 7, error.prob=0, verbose=FALSE)

argmax.geno

Reconstruct underlying genotypes

Description
Uses the Viterbi algorithm to identify the most likely sequence of underlying genotypes, given the
observed multipoint marker data, with possible allowance for genotyping errors.
Usage
argmax.geno(cross, step=0, off.end=0, error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
stepwidth=c("fixed", "variable", "max"))
Arguments
cross

An object of class cross. See read.cross for details.

step

Maximum distance (in cM) between positions at which the genotypes are reconstructed, though for step=0, genotypes are reconstructed only at the marker
locations.

off.end

Distance (in cM) past the terminal markers on each chromosome to which the
genotype reconstructions will be carried.

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi, Carter-Falconer or Morgan map
function when converting genetic distances into recombination fractions.

stepwidth

Indicates whether the intermediate points should with fixed or variable step
sizes. We recommend using "fixed"; "variable" is included for the qtlbim
package (http://www.ssg.uab.edu/qtlbim). The "max" option inserts the
minimal number of intermediate points so that the maximum distance between
points is step.

Details
We use the Viterbi algorithm to calculate arg maxv Pr(g = v|O) where g is the underlying sequence of genotypes and O is the observed marker genotypes.
This is done by calculating γk (vk ) = maxv1 ,...,vk−1 Pr(g1 = v1 , . . . , gk = vk , O1 , . . . , Ok ) for
k = 1, . . . , n and then tracing back through the sequence.

26

arithscan

Value
The input cross object is returned with a component, argmax, added to each component of cross$geno.
The argmax component is a matrix of size [n.ind x n.pos], where n.pos is the number of positions
at which the reconstructed genotypes were obtained, containing the most likely sequences of underlying genotypes. Attributes "error.prob", "step", and "off.end" are set to the values of the
corresponding arguments, for later reference.
Warning
The Viterbi algorithm can behave badly when step is small but positive. One may observe quite
different results for different values of step.
The problem is that, in the presence of data like A----H, the sequences AAAAAA and HHHHHH may be
more likely than any one of the sequences AAAAAH, AAAAHH, AAAHHH, AAHHHH, AHHHHH, AAAAAH. The
Viterbi algorithm produces a single "most likely" sequence of underlying genotypes.
Author(s)
Karl W Broman, 
References
Lange, K. (1999) Numerical analysis for statisticians. Springer-Verlag. Sec 23.3.
Rabiner, L. R. (1989) A tutorial on hidden Markov models and selected applications in speech
recognition. Proceedings of the IEEE 77, 257–286.
See Also
sim.geno, calc.genoprob, fill.geno
Examples
data(fake.f2)
fake.f2 <- argmax.geno(fake.f2, step=2, off.end=5, err=0.01)

arithscan

Arithmetic operators for scanone and scantwo results

Description
Add or subtract LOD scores in results from scanone or scantwo.
Usage
scan1+scan2
scan1-scan2
Arguments
scan1, scan2

Genome scan results on the same set of chromosomes and markers, as output by
scanone or scantwo.

arithscanperm

27

Details
This is used to calculate the sum or difference of LOD scores of two genome scan results. It
is particularly useful for calculating the LOD scores for QTL-by-covariate interactions (see the
example, below). Note that the degrees of freedom are also added or subtracted.
Value
The same type of data structure as the input objects, with LOD scores added or subtracted.
Author(s)
Karl W Broman, 
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=2.5)
# covariates
ac <- pull.pheno(fake.bc, c("sex","age"))
ic <- pull.pheno(fake.bc, "sex")
# scan with additive but not the interactive covariate
out.acovar <- scanone(fake.bc, addcovar=ac)
# scan with interactive covariate
out.icovar <- scanone(fake.bc, addcovar=ac, intcovar=ic)
# plot the difference of with and without the interactive covariate
#
This is a LOD score for a test of QTL x covariate interaction
plot(out.icovar-out.acovar)

arithscanperm

Arithmetic Operators for permutation results

Description
Add or subtract LOD scores in permutation results from scanone or scantwo.
Usage
perm1+perm2
perm1-perm2
Arguments
perm1, perm2

Permutation results from scanone or scantwo, on the same set of chromosomes
and markers.

28

badorder

Details
This is used to calculate the sum or difference of LOD scores of two sets of permutation results
from scanone or scantwo. One must be careful to ensure that the permutations are perfectly linked,
which will require the use of set.seed.
Value
The same data structure as the input objects, with LOD scores added or subtracted.
Author(s)
Karl W Broman, 
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=2.5)
# covariates
ac <- pull.pheno(fake.bc, c("sex","age"))
ic <- pull.pheno(fake.bc, "sex")
# set seed
theseed <- round(runif(1, 1, 10^8))
set.seed(theseed)
# permutations with additive but not the interactive covariate
## Not run: operm.acovar <- scanone(fake.bc, addcovar=ac, n.perm=1000)
# re-set the seed
set.seed(theseed)
# permutations with interactive covariate
## Not run: operm.icovar <- scanone(fake.bc, addcovar=ac, intcovar=ic,
n.perm=1000)
## End(Not run)
# permutation results for the QTL x covariate interaction
operm.gxc <- operm.icovar - operm.acovar
# LOD thresholds
summary(operm.gxc)

badorder

An intercross with misplaced markers

Description
Simulated data for an intercross with some markers out of order.

bayesint

29

Usage
data(badorder)
Format
An object of class cross. See read.cross for details.
Details
There are 250 F2 individuals typed at a total of 36 markers on four chromosomes. The data were
simulated with QTLs at the center of chromosomes 1 and 3.
The order of several markers on chromosome 1 is incorrect. Markers on chromosomes 2 and 3 are
switched.
Author(s)
Karl W Broman, 
See Also
est.rf, ripple, est.map, sim.cross
Examples
data(badorder)
# estimate recombination fractions
badorder <- est.rf(badorder)
plotRF(badorder)
# re-estimate map
newmap <- est.map(badorder)
plotMap(badorder, newmap)
# assess marker order on chr 1
rip3 <- ripple(badorder, chr=1, window=3)
summary(rip3)

bayesint

Bayesian credible interval

Description
Calculate an approximate Bayesian credible interval for a particular chromosome, using output from
scanone.
Usage
bayesint(results, chr, qtl.index, prob=0.95, lodcolumn=1, expandtomarkers=FALSE)

30

bristle3

Arguments
results

Output from scanone, or a qtl object as output from refineqtl.

chr

A chromosome ID (if input results are from scanone (should have length 1).

qtl.index

Numeric index for a QTL (if input results are from refineqtl (should have
length 1).

prob

Probability coverage of the interval.

lodcolumn

An integer indicating which of the LOD score columns should be considered (if
input results are from scanone).

expandtomarkers
If TRUE, the interval is expanded to the nearest flanking markers.
Details
We take 10LOD , rescale it to have area 1, and then calculate the connected interval with density
above some threshold and having coverage matching the target probability.
Value
An object of class scanone indicating the estimated QTL position and the approximate endpoints
for the Bayesian credible interval.
Author(s)
Karl W Broman, 
See Also
scanone, lodint
Examples
data(hyper)
hyper <- calc.genoprob(hyper, step=0.5)
out <- scanone(hyper, method="hk")
bayesint(out, chr=1)
bayesint(out, chr=4)
bayesint(out, chr=4, prob=0.99)
bayesint(out, chr=4, expandtomarkers=TRUE)

bristle3

Data on bristle number in Drosophila

Description
Data from bristle number in chromosome 3 recombinant isogenic lines of Drosophila melanogaster.
Usage
data(bristle3)

bristleX

31

Format
An object of class cross. See read.cross for details.
Details
There are 66 chromosome 3 recombinant isogenic lines, derived from inbred lines that were selected
for low (A) and high (B) abdominal bristle numbers. A recombinant chromosome 3 was placed in
an isogenic low background.
There are eight phenotypes: the average and SD of the number of abdominal and sternopleural
bristles in males and females for each line.
Each line is typed at 29 genetic markers on chromosome 3.
References
Long, A. D., Mullaney, S. L., Reid, L. A., Fry, J. D., Langley, C. H. and MacKay, T. F. C.
(1995) High resolution mapping of genetic factors affecting abdominal bristle number in Drosophila
melanogaster. Genetics 139, 1273–1291.
See Also
bristleX, listeria, fake.bc, fake.f2, fake.4way, hyper
Examples
data(bristle3)
# Summaries
summary(bristle3)
plot(bristle3)
# genome scan for each of the average phenotypes
bristle3 <- calc.genoprob(bristle3, step=2)
out <- scanone(bristle3, pheno.col=c(1,3,5,7))
# Plot the results
# maximum LOD score among four phenotypes
ym <- max(apply(out[,-(1:2)], 2, max))
plot(out, lod=1:3, ylim=c(0,ym))
plot(out, lod=4, add=TRUE, col="green")

bristleX

Data on bristle number in Drosophila

Description
Data from bristle number in chromosome X recombinant isogenic lines of Drosophila melanogaster.
Usage
data(bristleX)
Format
An object of class cross. See read.cross for details.

32

c.cross

Details
There are 92 chromosome X recombinant isogenic lines, derived from inbred lines that were selected for low (A) and high (B) abdominal bristle numbers. A recombinant chromosome X was
placed in an isogenic low background.
There are eight phenotypes: the average and SD of the number of abdominal and sternopleural
bristles in males and females for each line.
Each line is typed at 17 genetic markers on chromosome 3.
References
Long, A. D., Mullaney, S. L., Reid, L. A., Fry, J. D., Langley, C. H. and MacKay, T. F. C.
(1995) High resolution mapping of genetic factors affecting abdominal bristle number in Drosophila
melanogaster. Genetics 139, 1273–1291.
See Also
bristleX, listeria, fake.bc, fake.f2, fake.4way, hyper
Examples
data(bristleX)
# Summaries
summary(bristleX)
plot(bristleX)
# genome scan for each of the average phenotypes
bristleX <- calc.genoprob(bristleX, step=2)
out <- scanone(bristleX, pheno.col=c(1,3,5,7))
# Plot the results
# maximum LOD score among four phenotypes
ym <- max(apply(out[,-(1:2)], 2, max))
plot(out, lod=1:3, ylim=c(0,ym))
plot(out, lod=4, add=TRUE, col="green")

c.cross

Combine data for QTL experiments

Description
Concatenate the data for multiple QTL experiments.
Usage
## S3 method for class 'cross'
c(...)

c.scanone

33

Arguments
...

A set of objects of class cross. See read.cross for details. These must all
either be of the same cross type or be a combination of backcrosses and intercrosses. All crosses must have the same number of chromosomes and chromosome names, and the same marker orders and positions, though the set of
markers need not be precisely the same.

Value
The concatenated input, as a cross object. Additional columns are added to the phenotype data indicating which cross an individual comes from; another column indicates cross type (0=BC, 1=intercross), if there are crosses of different types. The crosses are not required to have exactly the
same set of phenotypes; phenotypes with the same names are assumed to be the same.
If the crosses have different sets of markers, we interpolate marker order, but the cM positions of
markers that are in common between crosses must be precisely the same in the different crosses.
Author(s)
Karl W Broman, 
See Also
subset.cross
Examples
data(fake.f2)
junk <- fake.f2
junk <- c(fake.f2,junk)

c.scanone

Combine columns from multiple scanone results

Description
Concatenate the columns from different runs of scanone.
Usage
## S3 method for class 'scanone'
c(..., labels)
## S3 method for class 'scanone'
cbind(..., labels)
Arguments
...

labels

A set of objects of class scanone. (This can also be a list of scanone objects.)
These are the results from scanone (with n.perm=0), generally run with different phenotypes or methods. All must conform with each other, meaning that
calc.genoprob and/or sim.geno were run with the same values for step and
off.end and with data having the same genetic map.
A vector of character strings, of length 1 or of the same length as the input, to
be appended to the column names in the output.

34

c.scanoneperm

Details
The aim of this function is to concatenate the results from multiple runs scanone, generally for
different phenotypes and/or methods, to be used in parallel with summary.scanone.
Value
The concatenated input, as a scanone object.
Author(s)
Karl W Broman, 
See Also
summary.scanone, scanone, cbind.scanoneperm
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2)
out.hk <- scanone(fake.f2, method="hk")
out.np <- scanone(fake.f2, model="np")
out <- c(out.hk, out.np, labels=c("hk","np"))
plot(out, lod=1:2, col=c("blue", "red"))

c.scanoneperm

Combine data from scanone permutations

Description
Concatenate the data for multiple runs of scanone with n.perm > 0.
Usage
## S3 method for class 'scanoneperm'
c(...)
## S3 method for class 'scanoneperm'
rbind(...)
Arguments
...

A set of objects of class scanoneperm. (This can also be a list of scanoneperm
objects.) These are the permutation results from scanone (that is, when n.perm > 0).
These must all have the same number of columns. (That is, they must have been
created with the same number of phenotypes, and it is assumed that they were
generated in precisely the same way.)

Details
The aim of this function is to concatenate the results from multiple runs of a permutation test
scanone, to assist with the case that such permutations are done on multiple processors in parallel.

c.scantwo

35

Value
The concatenated input, as a scanoneperm object.
Author(s)
Karl W Broman, 
See Also
summary.scanoneperm, scanone, cbind.scanoneperm, c.scantwoperm
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2)
operm1 <- scanone(fake.f2, method="hk", n.perm=100, perm.Xsp=TRUE)
operm2 <- scanone(fake.f2, method="hk", n.perm=50, perm.Xsp=TRUE)
operm <- c(operm1, operm2)

c.scantwo

Combine columns from multiple scantwo results

Description
Concatenate the columns from different runs of scantwo.
Usage
## S3 method for class 'scantwo'
c(...)
## S3 method for class 'scantwo'
cbind(...)
Arguments
...

A set of objects of class scantwo. (This can also be a list of scantwo objects.)
These are the results from scantwo (with n.perm=0), generally run with different phenotypes or methods. All must conform with each other, meaning that
calc.genoprob and/or sim.geno were run with the same values for step and
off.end and with data having the same genetic map.

Details
The aim of this function is to concatenate the results from multiple runs scantwo, generally for
different phenotypes and/or methods.
Value
The concatenated input, as a scantwo object.

36

c.scantwoperm

Author(s)
Karl W Broman, 
See Also
summary.scantwo, scantwo, c.scanone
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc)
out2a <- scantwo(fake.bc, method="hk")
out2b <- scantwo(fake.bc, pheno.col=2, method="hk")
out2 <- c(out2a, out2b)

c.scantwoperm

Combine data from scantwo permutations

Description
Concatenate the data for multiple runs of scantwo with n.perm > 0.
Usage
## S3 method for class 'scantwoperm'
c(...)
## S3 method for class 'scantwoperm'
rbind(...)
Arguments
...

A set of objects of class scantwoperm. (This can also be a list of scantwoperm
objects.) These are the permutation results from scantwo (that is, when n.perm > 0).
These must all concern the same number of LOD columns. (That is, they must
have been created with the same number of phenotypes, and it is assumed that
they were generated in precisely the same way.)

Details
The aim of this function is to concatenate the results from multiple runs of a permutation test
scantwo, to assist with the case that such permutations are done on multiple processors in parallel.
Value
The concatenated input, as a scantwoperm object.
Author(s)
Karl W Broman, 

calc.errorlod

37

See Also
summary.scantwoperm, scantwo, cbind.scantwoperm
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2)
## Not run: operm1 <- scantwo(fake.f2, method="hk", n.perm=50)
operm2 <- scantwo(fake.f2, method="hk", n.perm=50)
## End(Not run)
operm <- c(operm1, operm2)

calc.errorlod

Identify likely genotyping errors

Description
Calculates a LOD score for each genotype, measuring the evidence for genotyping errors.
Usage
calc.errorlod(cross, error.prob=0.01,
map.function=c("haldane","kosambi","c-f","morgan"),
version=c("new","old"))
Arguments
cross
error.prob
map.function
version

An object of class cross. See read.cross for details.
Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype)
Indicates whether to use the Haldane, Kosambi, Carter-Falconer, or Morgan map
function when converting genetic distances into recombination fractions.
Specifies whether to use the original version of this function or the current (preferred) version.

Details
Calculates, for each individual at each marker, a LOD score measuring the strength of evidence for
a genotyping error, as described by Lincoln and Lander (1992).
In the latest version, evidence for a genotype being in error is considered assuming that all other
genotypes (for that individual, on that chromosome) are correct. The argument version allows one
to specify whether this new version is used, or whether the original (old) version of the calculation
is performed.
Note that values below 4 are generally not interesting. Also note that if markers are extremely
tightly linked, recombination events can give large error LOD scores. The error LOD scores should
not be trusted blindly, but should be viewed as a tool for identifying genotypes deserving further
study.
Use top.errorlod to print all genotypes with error LOD scores above a specified threshold,
plotErrorlod to plot the error LOD scores for specified chromosomes, and plotGeno to view
the observed genotype data with likely errors flagged.

38

calc.genoprob

Value
The input cross object is returned with a component, errorlod, added to each component of
cross$geno. The errorlod component is a matrix of size (n.ind x n.mar). An attribute "error.prob"
is set to the value of the corresponding argument, for later reference.
Author(s)
Karl W Broman, 
References
Lincoln, S. E. and Lander, E. S. (1992) Systematic detection of errors in genetic linkage data.
Genomics 14, 604–610.
See Also
plotErrorlod, top.errorlod, cleanGeno
Examples
data(hyper)
hyper <- calc.errorlod(hyper,error.prob=0.01)
# print those above a specified cutoff
top.errorlod(hyper, cutoff=4)
# plot genotype data, flagging genotypes with error LOD > cutoff
plotGeno(hyper, chr=1, ind=160:200, cutoff=7, min.sep=2)

calc.genoprob

Calculate conditional genotype probabilities

Description
Uses the hidden Markov model technology to calculate the probabilities of the true underlying genotypes given the observed multipoint marker data, with possible allowance for genotyping errors.
Usage
calc.genoprob(cross, step=0, off.end=0, error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
stepwidth=c("fixed", "variable", "max"))
Arguments
cross

An object of class cross. See read.cross for details.

step

Maximum distance (in cM) between positions at which the genotype probabilities are calculated, though for step = 0, probabilities are calculated only at the
marker locations.

off.end

Distance (in cM) past the terminal markers on each chromosome to which the
genotype probability calculations will be carried.

calc.genoprob

39

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi or Carter-Falconer map function
when converting genetic distances into recombination fractions.

stepwidth

Indicates whether the intermediate points should with fixed or variable step
sizes. We recommend using "fixed"; "variable" is included for the qtlbim
package (http://www.ssg.uab.edu/qtlbim). The "max" option inserts the
minimal number of intermediate points so that the maximum distance between
points is step.

Details
Let Ok denote the observed marker genotype at position k, and gk denote the corresponding true
underlying genotype.
We use the forward-backward equations to calculate αkv = log P r(O1 , . . . , Ok , gk = v) and βkv =
log P r(Ok+1 , . . . , On |gk = v)
P
We then obtain P r(gk |O1 , . . . , On ) = exp(αkv + βkv )/s where s = v exp(αkv + βkv )
In the case of the 4-way cross, with a sex-specific map, we assume a constant ratio of female:male
recombination rates within the inter-marker intervals.
Value
The input cross object is returned with a component, prob, added to each component of cross$geno.
prob is an array of size [n.ind x n.pos x n.gen] where n.pos is the number of positions at which the
probabilities were calculated and n.gen = 3 for an intercross, = 2 for a backcross, and = 4 for a 4-way
cross. Attributes "error.prob", "step", "off.end", and "map.function" are set to the values of
the corresponding arguments, for later reference (especially by the function calc.errorlod).
Author(s)
Karl W Broman, 
References
Lange, K. (1999) Numerical analysis for statisticians. Springer-Verlag. Sec 23.3.
Rabiner, L. R. (1989) A tutorial on hidden Markov models and selected applications in speech
recognition. Proceedings of the IEEE 77, 257–286.
See Also
sim.geno, argmax.geno, calc.errorlod
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=2, off.end=5)
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=0, off.end=0, err=0.01)

40

calc.penalties

calc.penalties

Calculate LOD penalties

Description
Derive penalties for the penalized LOD scores (used by stepwiseqtl) on the basis of permutation
results from a two-dimensional, two-QTL scan (obtained by scantwo).
Usage
calc.penalties(perms, alpha=0.05, lodcolumn)
Arguments
perms

Permutation results from scantwo.

alpha

Significance level.

lodcolumn

If the scantwo permutation results contain LOD scores for multiple phenotypes,
this argument indicates which to use in the summary. This may be a vector. If
missing, penalties for all phenotypes are calculated.

Details
Thresholds derived from scantwo permutations (that is, for a two-dimensional, two-QTL genome
scan) are used to calculate penalties on main effects and interactions.
The main effect penalty is the 1-alpha quantile of the null distribution of the genome-wide maximum LOD score from a single-QTL genome scan (as with scanone).
The "heavy" interaction penalty is the 1-alpha quantile of the null distribution of the maximum
interaction LOD score (that is, the log10 likelihood ratio comparing the best model with two interacting QTL to the best model with two additive QTL) from a two-dimensional, two-QTL genome
scan (as with scantwo).
The "light" interaction penality is the difference between the "fv1" threshold from the scantwo
permutations (that is, the 1-alpha quantile of the LOD score comparing the best model with two
interacting QTL to the best single-QTL model) and the main effect penalty.
If the permutations results were obtained with perm.Xsp=TRUE, to give X-chr-specific results, six
penalties are calculated: main effect for autosomes, main effect for X chr, heavy penalty on A:A
interactions, light penalty on A:A interactions, penalty on A:X interactions, and penalty on X:X
interactions.
Value
Vector of three values indicating the penalty on main effects and heavy and light penalties on interactions, or a matrix of such results, with each row corresponding to a different phenotype.
If the input permutations are X-chromosome-specific, the result has six values: main effect for autosomes, main effect for X chr, heavy penalty on A:A interactions, light penalty on A:A interactions,
penalty on A:X interactions, and penalty on X:X interactions.
Author(s)
Karl W Broman, 

cbind.scanoneperm

41

References
Manichaikul, A., Moon, J. Y., Sen, Ś, Yandell, B. S. and Broman, K. W. (2009) A model selection
approach for the identification of quantitative trait loci in experimental crosses, allowing epistasis.
Genetics, 181, 1077–1086.
See Also
scantwo, stepwiseqtl
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=5)
out.2dim <- scantwo(fake.f2, method="hk")
# permutations
## Not run: permo.2dim <- scantwo(fake.f2, method="hk", n.perm=1000)
summary(permo.2dim, alpha=0.05)
# penalties
calc.penalties(permo.2dim)

cbind.scanoneperm

Combine columns from multiple scanone permutation results

Description
Concatenate the columns from different runs of scanone with n.perm > 0.
Usage
## S3 method for class 'scanoneperm'
cbind(..., labels)
Arguments
...

A set of objects of class scanoneperm. These are the permutation results from
scanone (that is, when n.perm > 0), generally run with different phenotypes or
methods.

labels

A vector of character strings, of length 1 or of the same length as the input ...,
to be appended to the column names in the output.

Details
The aim of this function is to concatenate the results from multiple runs of a permutation test
scanone, generally for different phenotypes and/or methods, to be used in parallel with c.scanone.
Value
The concatenated input, as a scanoneperm object. If different numbers of permutation replicates
were used, those columns with fewer replicates are padded with missing values (NA).

42

cbind.scantwoperm

Author(s)
Karl W Broman, 
See Also
summary.scanoneperm, scanone, c.scanoneperm, c.scanone
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2)
operm1 <- scanone(fake.f2, method="hk", n.perm=10, perm.Xsp=TRUE)
operm2 <- scanone(fake.f2, method="em", n.perm=5, perm.Xsp=TRUE)
operm <- cbind(operm1, operm2, labels=c("hk","em"))
summary(operm)

cbind.scantwoperm

Combine scantwo permutations by column

Description
Column-bind permutations results from scantwo for multiple phenotypes or models.
Usage
## S3 method for class 'scantwoperm'
cbind(...)
Arguments
...

A set of objects of class scantwoperm. (This can also be a list of scantwoperm
objects.) These are the permutation results from scantwo (that is, when n.perm > 0).
These must all concern the same number of permutations.

Value
The column-binded input, as a scantwoperm object.
Author(s)
Karl W Broman, 
See Also
scantwo, c.scantwoperm, summary.scantwoperm

checkAlleles

43

Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc)
## Not run: operm1 <- scantwo(fake.bc, pheno.col=1, method="hk", n.perm=50)
operm2 <- scantwo(fake.bc, pheno.col=2, method="hk", n.perm=50)
## End(Not run)
operm <- cbind(operm1, operm2)

checkAlleles

Identify markers with switched alleles

Description
Identify markers whose alleles might have been switched by comparing the LOD score for linkage
to all other autosomal markers with the original data to that when the alleles have been switched.
Usage
checkAlleles(cross, threshold=3, verbose)
Arguments
cross

An object of class cross. See read.cross for details.

threshold

Only an increase in maximum 2-point LOD of at least this amount will lead to
a marker being flagged.

verbose

If TRUE and there are no markers above the threshold, print a message.

Details
For each marker, we compare the maximum LOD score for the cases where the estimated recombination fraction > 0.5 to those where r.f. < 0.5. The function est.rf must first be run.
Note: Markers that are tightly linked to a marker whose alleles are switched are likely to also be
flagged by this method. The real problem markers are likely those with the biggest difference in
LOD scores.
Value
A data frame containing the flagged markers, having four columns: the marker name, chromosome
ID, numeric index within chromosome, and the difference between the maximum two-point LOD
score with the alleles switched to that from the original data.
Author(s)
Karl W Broman, 
See Also
est.rf, geno.crosstab, switchAlleles

44

chrlen

Examples
data(fake.f2)
# switch homozygotes at marker D5M391
fake.f2 <- switchAlleles(fake.f2, "D5M391")
fake.f2 <- est.rf(fake.f2)
checkAlleles(fake.f2)

chrlen

Chromosome lengths in QTL experiment

Description
Obtain the chromosome lengths in a cross or map object.
Usage
chrlen(object)
Arguments
object

An object of class map or of class cross.

Value
Returns a vector of chromosome lengths. If the cross has sex-specific maps, it returns a 2-row
matrix with the two lengths for each chromosome.
Author(s)
Karl W Broman, 
See Also
summaryMap, pull.map, summary.cross
Examples
data(fake.f2)
chrlen(fake.f2)
map <- pull.map(fake.f2)
chrlen(map)

chrnames

45

chrnames

Pull out the chromosome names from a cross

Description
Pull out the chromosome names from a cross object as one big vector.
Usage
chrnames(cross)
Arguments
cross

An object of class cross. See read.cross for details.

Value
A vector of character strings (the chromosome names).
Author(s)
Karl W Broman, 
See Also
markernames, phenames
Examples
data(listeria)
chrnames(listeria)

cim

Composite interval mapping

Description
Composite interval mapping by a scheme from QTL Cartographer: forward selection at the markers (here, with filled-in genotype data) to a fixed number, followed by interval mapping with the
selected markers as covariates, dropping marker covariates if they are within some fixed window
size of the location under test.
Usage
cim(cross, pheno.col=1, n.marcovar=3, window=10,
method=c("em", "imp", "hk", "ehk"),
imp.method=c("imp", "argmax"), error.prob=0.0001,
map.function=c("haldane", "kosambi", "c-v", "morgan"),
n.perm)

46

cim

Arguments
cross

An object of class cross. See read.cross for details.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype.
One may also give a character string matching a phenotype name. Finally, one
may give a numeric vector of phenotypes, in which case it must have the length
equal to the number of individuals in the cross, and there must be either nonintegers or values < 1 or > no. phenotypes; this last case may be useful for
studying transformations.

n.marcovar

Number of marker covariates to use.

window

Window size, in cM.

method

Indicates whether to use the EM algorithm, imputation, Haley-Knott regression,
or the extended Haley-Knott method.

imp.method

Method used to impute any missing marker genotype data.

error.prob

Genotyping error probability assumed when imputing the missing marker genotype data.

map.function

Map function used when imputing the missing marker genotype data.

n.perm

If specified, a permutation test is performed rather than an analysis of the observed data. This argument defines the number of permutation replicates.

Details
We first use fill.geno to impute any missing marker genotype data, either via a simple random
imputation or using the Viterbi algorithm.
We then perform forward selection to a fixed number of markers. These will be used (again, with
any missing data filled in) as covariates in the subsequent genome scan.
Value
The function returns an object of the same form as the function scanone:
If n.perm is missing, the function returns the scan results as a data.frame with three columns: chromosome, position, LOD score. Attributes indicate the names and positions of the chosen marker
covariates.
If n.perm > 0, the function results the results of a permutation test: a vector giving the genome-wide
maximum LOD score in each of the permutations.
Author(s)
Karl W Broman, 
References
Jansen, R. C. (1993) Interval mapping of multiple quantitative trait loci. Genetics, 135, 205–211.
Jansen, R. C. and Stam, P. (1994) High resolution of quantitative traits into multiple loci via interval
mapping. Genetics, 136, 1447-1455.
Zeng, Z. B. (1993) Theoretical basis for separation of multiple linked gene effects in mapping
quantitative trait loci. Proc. Natl. Acad. Sci. USA, 90, 10972–10976.
Zeng, Z. B. (1994) Precision mapping of quantitative trait loci. Genetics, 136, 1457–1468.

clean.cross

47

See Also
add.cim.covar, scanone, summary.scanone, plot.scanone, fill.geno
Examples
data(hyper)
hyper <- calc.genoprob(hyper, step=2.5)
out <- scanone(hyper)
out.cim <- cim(hyper, n.marcovar=3)
plot(out, out.cim, chr=c(1,4,6,15), col=c("blue", "red"))
add.cim.covar(out.cim, chr=c(1,4,6,15))

clean.cross

Remove derived data

Description
Remove any intermediate calculations from a cross object.
Usage
## S3 method for class 'cross'
clean(object, ...)
Arguments
object

An object of class cross. See read.cross for details.

...

Ignored at this point.

Value
The input object, with any intermediate calculations (such as is produced by calc.genoprob,
argmax.geno and sim.geno) removed.
Author(s)
Karl W Broman, 
See Also
drop.nullmarkers, drop.markers, clean.scantwo
Examples
data(fake.f2)
names(fake.f2$geno)
fake.f2 <- calc.genoprob(fake.f2)
names(fake.f2$geno)
fake.f2 <- clean(fake.f2)
names(fake.f2$geno)

48

clean.scantwo

clean.scantwo

Clean up scantwo output

Description
In an object output from scantwo, replaces negative and missing LOD scores with 0, and replaces
LOD scores for pairs of positions that are not separated by n.mar markers, or that are less than
distance cM apart, with 0. Further, if the LOD for full model is less than the LOD for the additive
model, the additive LOD is pasted over the full LOD.
Usage
## S3 method for class 'scantwo'
clean(object, n.mar=1, distance=0, ...)
Arguments
object

An object of class scantwo. See scantwo for details.

n.mar

Pairs of positions not separated by at least this many markers have LOD scores
set to 0.

distance

Pairs of positions not separated by at least this distance have LOD scores set to
0.

...

Ignored at this point.

Value
The input scantwo object, with any negative or missing LOD scores replaced by 0, and LOD scores
for pairs of positions separated by fewer than n.mar markers, or less than distance cM, are set to
0. Also, if the LOD for the full model is less than the LOD for the additive model, the additive LOD
is used in place of the full LOD.
Author(s)
Karl W Broman, 
See Also
scantwo, summary.scantwo
Examples
data(fake.f2)
fake.f2
out2 
See Also
locateXO, countXO, calc.errorlod
Examples
data(hyper)
sum(ntyped(hyper))
hyperc <- cleanGeno(hyper, chr=4, maxdist=c(2.5, 10), maxmark=c(2, 1))
sum(ntyped(hyperc))

50

comparegeno

comparecrosses

Compare two cross objects

Description
Verify that two objects of class cross have identical classes, chromosomes, markers, genotypes,
genetic maps, and phenotypes.
Usage
comparecrosses(cross1, cross2, tol=1e-5)
Arguments
cross1

An object of class cross (must be an intercross). See read.cross for details.

cross2

An object of class cross (must be an intercross). See read.cross for details.

tol

Tolerance value for comparing genetic map positions and numeric phenotypes.

Value
None.
Author(s)
Karl W Broman, 
See Also
summary.cross
Examples
data(listeria)
comparecrosses(listeria, listeria)

comparegeno

Compare individuals’ genotype data

Description
Count proportion of matching genotypes between all pairs of individuals, to look for unusually
closely related individuals.
Usage
comparegeno(cross, what=c("proportion","number","both"))

compareorder

51

Arguments
cross

An object of class cross. See read.cross for details.

what

Indicates whether to return the proportion or number of matching genotypes (or
both).

Value
A matrix whose (i,j)th element is the proportion or number of matching genotypes for individuals i
and j.
If called with what="both", the lower triangle contains the proportion and the upper triangle contains the number.
If called with what="proportion", the diagonal contains missing values. Otherwise, the diagonal
contains the number of typed markers for each individual.
Author(s)
Karl W Broman, 
See Also
nmissing
Examples
data(listeria)
output <- comparegeno(listeria)
# image of the proportions
n.ind <- nind(listeria)
image(1:n.ind, 1:n.ind, output, col=gray((0:99)/99),
breaks=seq(0,1,len=101))
# histogram
hist(output, breaks=150, prob=TRUE,
xlab="Proportion of matching genotypes")
rug(output)

compareorder

Compare two orderings of markers on a chromosome

Description
Compare the likelihood of an alternative order for markers on a chromosome to the current order.
Usage
compareorder(cross, chr, order, error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
maxit=4000, tol=1e-6, sex.sp=TRUE)

52

condense.scantwo

Arguments
cross

An object of class cross. See read.cross for details.

chr

The chromosome to investigate. Only one chromosome is allowed. (This should
be a character string referring to the chromosomes by name.)

order

The alternate order of markers on the chromosome: a numeric vector that is a
permutation of the integers from 1 to the number of markers on the chromosome.

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi, Carter-Falconer, or Morgan map
function when converting genetic distances into recombination fractions.

maxit

Maximum number of EM iterations to perform.

tol

Tolerance for determining convergence.

sex.sp

Indicates whether to estimate sex-specific maps; this is used only for the 4-way
cross.

Value
A data frame with two rows: the current order in the input cross object, and the revised order. The
first column is the log10 likelihood of the new order relative to the original one (positive values
indicate that the new order is better supported). The second column is the estimated genetic length
of the chromosome for each order. In the case of sex-specific maps, there are separate columns for
the female and male genetic lengths.
Author(s)
Karl W Broman, 
See Also
ripple, switch.order, movemarker
Examples
data(badorder)
compareorder(badorder, chr=1, order=c(1:8,11,10,9,12))

condense.scantwo

Condense the output from a 2-d genome scan

Description
Produces a very condensed version of the output of scantwo.
Usage
## S3 method for class 'scantwo'
condense(object)

convert.map

53

Arguments
object

An object of class scantwo, the output of the function scantwo.

Details
This produces a very reduced version of the output of scantwo, for which a summary may still be
created via summary.scantwo, though plots can no longer be made.
Value
An object of class scantwocondensed, containing just the maximum full, additive and interactive
LOD scores, and the positions where they occured, on each pair of chromosomes.
Author(s)
Karl W Broman, 
See Also
scantwo, summary.scantwo, max.scantwo
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2)
out2 <- scantwo(fake.f2, method="hk")
out2c <- condense(out2)
summary(out2c, allpairs=FALSE)
max(out2c)

convert.map

Change map function for a genetic map

Description
Convert a genetic map from using one map function to another.
Usage
## S3 method for class 'map'
convert(object, old.map.function=c("haldane", "kosambi", "c-f", "morgan"),
new.map.function=c("haldane", "kosambi", "c-f", "morgan"), ...)

54

convert.scanone

Arguments
object

A genetic map object, of class "map": A list whose components are vectors of
marker locations.
old.map.function
The map function used in forming the map in object.
new.map.function
The new map function to be used.
...

Ignored at this point.

Details
The location of the first marker on each chromosome is left unchanged. Inter-marker distances are
converted to recombination fractions with the inverse of the old.map.function, and then back to
distances with the new.map.function.
Value
The same as the input, but with inter-marker distances changed to reflect a different map function.
Author(s)
Karl W Broman, 
See Also
est.map, replace.map
Examples
data(listeria)
map <- pull.map(listeria)
map <- convert(map, "haldane", "kosambi")
listeria <- replace.map(listeria, map)

convert.scanone

Convert output from scanone for R/qtl version 0.98

Description
Convert the output from scanone from the format used in R/qtl version 0.97 and earlier to that used
in version 0.98 and later.
Usage
## S3 method for class 'scanone'
convert(object, ...)
Arguments
object

Output from the function scanone, for R/qtl version 0.97 and earlier.

...

Ignored at this point.

convert.scantwo

55

Details
Previously, inter-marker locations were named as, for example, loc7.5.c3; these were changed to
c3.loc7.5.
Value
The same scanone output, but revised for use with R/qtl version 0.98 and later.
Author(s)
Karl W Broman, 
See Also
scanone, convert.scantwo
Examples
## Not run: out.new <- convert(out.old)

convert.scantwo

Convert output from scantwo for R/qtl version 1.03 and earlier

Description
Convert the output from scantwo from the format used in R/qtl version 1.03 and earlier to that used
in version 1.04 and later.
Usage
## S3 method for class 'scantwo'
convert(object, ...)
Arguments
object

Output from the function scantwo, for R/qtl version 1.03 and earlier.

...

Ignored at this point.

Details
Previously, the output from scantwo contained the full and interaction LOD scores. In R/qtl version
1.04 and later, the output contains the LOD scores from the full and additive QTL models.
Value
The same scanone output, but revised for use with R/qtl version 1.03 and later.
Author(s)
Karl W Broman, 

56

convert2riself

See Also
scantwo, convert.scanone
Examples
## Not run: out2.new <- convert(out2.old)

convert2riself

Convert a cross to RIL by selfing

Description
Convert a cross to type "riself" (RIL by selfing).
Usage
convert2riself(cross)
Arguments
cross

An object of class cross. See read.cross for details.

Details
If there are more genotypes with code 3 (BB) than code 2 (AB), we omit the genotypes with
code==2 and call those with code==3 the BB genotypes.
If, instead, there are more genotypes with code 2 than code 3, we omit the genotypes with code==3
and call those with code==2 the BB genotypes.
Any chromosomes with class "X" (X chromosome) are changed to class "A" (autosomal).
Value
The input cross object, with genotype codes possibly changed and cross type changed to "riself".
Author(s)
Karl W Broman, 
See Also
convert2risib
Examples
data(hyper)
hyper.as.riself <- convert2riself(hyper)

convert2risib

57

convert2risib

Convert a cross to RIL by sib mating

Description
Convert a cross to type "risib" (RIL by sib mating).

Usage
convert2risib(cross)

Arguments
cross

An object of class cross. See read.cross for details.

Details
If there are more genotypes with code 3 (BB) than code 2 (AB), we omit the genotypes with
code==2 and call those with code==3 the BB genotypes.
If, instead, there are more genotypes with code 2 than code 3, we omit the genotypes with code==3
and call those with code==2 the BB genotypes.

Value
The input cross object, with genotype codes possibly changed and cross type changed to "risib".

Author(s)
Karl W Broman, 

See Also
convert2riself

Examples
data(hyper)
hyper.as.risib <- convert2risib(hyper)

58

convert2sa

convert2sa

Convert a sex-specific map to a sex-averaged one

Description
Convert a sex-specific map to a sex-averaged one, assuming that the female and male maps are
actually the same (that is, that the map was estimated assuming a common recombination rate in
females and males).
Usage
convert2sa(map, tol=1e-4)
Arguments
map

A map object with sex-specific locations (but assuming that the female and male
maps are the same), as output by the function est.map for a 4-way cross, with
argument sex.sp=FALSE.

tol

Tolerance value for inspecting the differences between the female and male
maps; if they differ by more than this tolerance, a warning is issued.

Details
We pull out just the female marker locations, and give a warning if there are large differences
between the female and male maps.
Value
A map object, with sex-averaged distances.
Author(s)
Karl W Broman, 
See Also
est.map, plotMap
Examples
data(fake.4way)
## Not run: fake.4way <- subset(fake.4way, chr="-X")
nm <- est.map(fake.4way, sex.sp=FALSE)
plot(convert2sa(nm))

countXO

59

countXO

Count number of obligate crossovers for each individual

Description
Count the number of obligate crossovers for each individual in a cross, either by chromosome or
overall.
Usage
countXO(cross, chr, bychr=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to investigate. This should be a
vector of character strings referring to chromosomes by name; numeric values
are converted to strings. Refer to chromosomes with a preceding - to have all
chromosomes but those considered. A logical (TRUE/FALSE) vector may also
be used.

bychr

If TRUE, return counts for each individual chromosome; if FALSE, return the
overall number across the selected chromosomes.

Details
For each individual we count the minimal number of crossovers that explain the observed genotype
data.
Value
If bychr=TRUE, a matrix of counts is returned, with rows corresponding to individuals and columns
corresponding to chromosomes.
If bychr=FALSE, a vector of counts (the total number of crossovers across all selected chromosomes)
is returned.
Author(s)
Karl W Broman, 
See Also
ripple, locateXO, cleanGeno
Examples
data(hyper)
plot(countXO(hyper))

60

drop.markers

drop.dupmarkers

Drop duplicate markers

Description
Drop markers with duplicate names; retaining the first of each set, with consensus genotyps
Usage
drop.dupmarkers(cross, verbose=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

verbose

If TRUE, print information on the numbers of genotypes and markers omitted.
If > 1, give more detailed information on genotypes omitted.

Value
The input cross object, with any duplicate markers omitted (except for one). The marker retained
will have consensus genotypes; if multiple versions of a marker have different genotypes for an
individual, they will be replaced by NA.
Any derived data (such as produced by calc.genoprob) will be stripped off.
Author(s)
Karl W Broman, 
See Also
drop.nullmarkers, pull.markers, drop.markers, summary.cross, clean.cross
Examples
data(listeria)
listeria <- drop.dupmarkers(listeria)

drop.markers

Drop a set of markers

Description
Drop a vector of markers from the data matrices and genetic maps.
Usage
drop.markers(cross, markers)

drop.nullmarkers

61

Arguments
cross

An object of class cross. See read.cross for details.

markers

A character vector of marker names.

Value
The input object, with any markers in the vector markers removed from the genotype data matrices,
genetic maps, and, if applicable, any derived data (such as produced by calc.genoprob). (It might
be a good idea to re-derive such things after using this function.)
Author(s)
Karl W Broman, 
See Also
drop.nullmarkers, pull.markers, geno.table, clean.cross
Examples
data(listeria)
listeria2 <- drop.markers(listeria, c("D10M44","D1M3","D1M75"))

drop.nullmarkers

Drop markers without any genotype data

Description
Drop markers, from the data matrices and genetic maps, that have no genotype data.
Usage
drop.nullmarkers(cross)
Arguments
cross

An object of class cross. See read.cross for details.

Value
The input object, with any markers lacking genotype data removed from the genotype data matrices,
genetic maps, and, if applicable, any derived data (such as produced by calc.genoprob). (It might
be a good idea to re-derive such things after using this function.)
Author(s)
Karl W Broman, 
See Also
nullmarkers, drop.markers, clean.cross, geno.table

62

dropfromqtl

Examples
# removes one marker from hyper
data(hyper)
hyper <- drop.nullmarkers(hyper)
# shouldn't do anything to listeria
data(listeria)
listeria <- drop.nullmarkers(listeria)

dropfromqtl

Drop a QTL from a qtl object

Description
Drop a QTL or multiple QTL from a QTL object
Usage
dropfromqtl(qtl, index, chr, pos, qtl.name, drop.lod.profile=TRUE)
Arguments
qtl

A qtl object, as created by makeqtl.

index

Vector specifying the numeric indices of the QTL to be dropped.

chr

Vector indicating the chromosome for each QTL to drop.

pos

Vector (of same length as chr) indicating the positions of the QTL to be dropped.

qtl.name

Vector specifying the names of the QTL to be dropped.

drop.lod.profile
If TRUE, remove any LOD profiles from the object.
Details
Provide either chr and pos, or one of qtl.name or index.
Value
The input qtl object with the specified QTL omitted. See makeqtl for details on the format.
Author(s)
Karl W Broman, kbroman@biostat.wisc.edu
See Also
makeqtl, fitqtl, addtoqtl, replaceqtl , reorderqtl

droponemarker

63

Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c(1, 6, 13)
qp <- c(25.8, 33.6, 18.63)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
newqtl <- dropfromqtl(qtl, chr=1, pos=25.8)
altqtl <- dropfromqtl(qtl, index=1)

droponemarker

Drop one marker at a time and determine effect on genetic map

Description
Drop one marker at a time from a genetic map and calculate the change in log likelihood and in the
chromosome length, in order to identify problematic markers.
Usage
droponemarker(cross, chr, error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
m=0, p=0, maxit=4000, tol=1e-6, sex.sp=TRUE,
verbose=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

A vector specifying which chromosomes to test for the position of the marker.
This should be a vector of character strings referring to chromosomes by name;
numeric values are converted to strings. Refer to chromosomes with a preceding
- to have all chromosomes but those considered. A logical (TRUE/FALSE)
vector may also be used.

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi, Carter-Falconer, or Morgan map
function when converting genetic distances into recombination fractions. (Ignored if m > 0.)

m

Interference parameter for the chi-square model for interference; a non-negative
integer, with m=0 corresponding to no interference. This may be used only for
a backcross or intercross.

p

Proportion of chiasmata from the NI mechanism, in the Stahl model; p=0 gives
a pure chi-square model. This may be used only for a backcross or intercross.

maxit

Maximum number of EM iterations to perform.

tol

Tolerance for determining convergence.

64

effectplot
sex.sp

Indicates whether to estimate sex-specific maps; this is used only for the 4-way
cross.

verbose

If TRUE, print information on progress; if > 1, print even more information.

Value
A data frame (actually, an object of class "scanone", so that one may use plot.scanone, summary.scanone,
etc.) with each row being a marker. The first two columns are the chromosome ID and position.
The third column is a LOD score comparing the hypothesis that the marker is not linked to the
hypothesis that it belongs at that position.
In the case of a 4-way cross, with sex.sp=TRUE, there are two additional columns with the change
in the estimated female and male genetic lengths of the respective chromosome, upon deleting that
marker. With sex.sp=FALSE, or for other types of crosses, there is one additional column, with the
change in estimated genetic length of the respective chromosome, when the marker is omitted.
A well behaved marker will have a negative LOD score and a small change in estimated genetic
length. A poorly behaved marker will have a large positive LOD score and a large change in
estimated genetic length. But note that dropping the first or last marker on a chromosome could
result in a large change in estimated length, even if they are not badly behaved; for these markers
one should focus on the LOD scores, with a large positive LOD score being bad.
Author(s)
Karl W Broman, 
See Also
tryallpositions, est.map, ripple, est.rf, switch.order, movemarker, drop.markers
Examples
data(fake.bc)
droponemarker(fake.bc, 7, error.prob=0, verbose=FALSE)

effectplot

Plot phenotype means against genotypes at one or two markers

Description
Plot the phenotype means for each group defined by the genotypes at one or two markers (or the
values at a discrete covariate).
Usage
effectplot(cross, pheno.col=1, mname1, mark1, geno1, mname2, mark2,
geno2, main, ylim, xlab, ylab, col, add.legend=TRUE,
legend.lab, draw=TRUE, var.flag=c("pooled","group"))

effectplot

65

Arguments
cross

An object of class cross.

pheno.col

Column number in the phenotype matrix to be drawn in the plot. One may also
give a character string matching a phenotype name. Finally, one may give a
numeric vector of phenotypes, in which case it must have the length equal to
the number of individuals in the cross, and there must be either non-integers
or values < 1 or > no. phenotypes; this last case may be useful for studying
transformations.

mname1

Name for the first marker or pseudomarker. Pseudomarkers (that is, non-marker
positions on the imputation grid) may be referred to in a form like "5@30.3",
for position 30.3 on chromosome 5.

mark1

Genotype data for the first marker. If unspecified, genotypes will be taken from
the data in the input cross object, using the name specified in mname1.

geno1

Optional labels for the genotypes (or classes in a covariate).

mname2

Name for the second marker or pseudomarker (optional).

mark2

Like mark1 (optional).

geno2

Optional labels for the genotypes (or classes in a covariate).

main

Optional figure title.

ylim

Optional y-axis limits.

xlab

Optional x-axis label.

ylab

Optional y-axis label.

col

Optional vector of colors for the different line segments.

add.legend

A logical value to indicate whether to add a legend.

legend.lab

Optional title for the legend.

draw

A logical value to indicate generate the plot or not. If FALSE, no figure will be
plotted and this function can be used to calculate the group means and standard
errors.

var.flag

The method to calculate the group variance. "pooled" means to use the pooled
variance and "group" means to calculate from individual group.

Details
In the plot, the y-axis is the phenotype. In the case of one marker, the x-axis is the genotype for that
marker. In the case of two markers, the x-axis is for different genotypes of the second marker, and
the genotypes of first marker are represented by lines in different colors. Error bars are plotted at ±
1 SE.
The results of sim.geno are used; if they are not available, sim.geno is run with n.draws=16. The
average phenotype for each genotype group takes account of missing genotype data by averaging
across the imputations. The SEs take account of both the residual phenotype variation and the
imputation error.
Value
A data.frame containing the phenotype means and standard errors for each group.
Author(s)
Hao Wu; Karl W Broman, 

66

effectplot

See Also
plotPXG, find.marker, effectscan, find.pseudomarker
Examples
data(fake.f2)
# impute genotype data
## Not run: fake.f2 <- sim.geno(fake.f2, step=5, n.draws=64)
########################################
# one marker plots
########################################
### plot of genotype-specific phenotype means for 1 marker
mname <- find.marker(fake.f2, 1, 37) # marker D1M437
effectplot(fake.f2, pheno.col=1, mname1=mname)
### output of the function contains the means and SEs
output <- effectplot(fake.f2, mname1=mname)
output
### plot a phenotype
# Plot of sex-specific phenotype means,
# note that "sex" must be a phenotype name here
effectplot(fake.f2, mname1="sex", geno1=c("F","M"))
# alternatively:
sex <- pull.pheno(fake.f2, "sex")
effectplot(fake.f2, mname1="Sex", mark1=sex, geno1=c("F","M"))
########################################
# two markers plots
########################################
### plot two markers
# plot of genotype-specific phenotype means for 2 markers
mname1 <- find.marker(fake.f2, 1, 37) # marker D1M437
mname2 <- find.marker(fake.f2, 13, 24) # marker D13M254
effectplot(fake.f2, mname1=mname1, mname2=mname2)
### plot two pseudomarkers
##### refer to pseudomarkers by their positions
effectplot(fake.f2, mname1="1@35", mname2="13@25")
##### alternatively, find their names via find.pseudomarker
pmnames <- find.pseudomarker(fake.f2, chr=c(1, 13), c(35, 25))
effectplot(fake.f2, mname1=pmnames[1], mname2=pmnames[2])
### Plot of sex- and genotype-specific phenotype means
mname <- find.marker(fake.f2, 13, 24) # marker D13M254
# sex and a marker
effectplot(fake.f2, mname1=mname, mname2="Sex",
mark2=sex, geno2=c("F","M"))
# Same as above, switch role of sex and the marker

effectscan

67

# sex and marker
effectplot(fake.f2, mname1="Sex", mark1=sex,
geno1=c("F","M"), mname2=mname)
# X chromosome marker
mname <- find.marker(fake.f2, "X", 14) # marker DXM66
effectplot(fake.f2, mname1=mname)
# Two markers, including one on the X
mnames <- find.marker(fake.f2, c(13, "X"), c(24, 14))
effectplot(fake.f2, mname1=mnames[1], mname2=mnames[2])

effectscan

Plot estimated QTL effects across the whole genome

Description
This function is used to plot the estimated QTL effects along selected chromosomes. For a backcross, there will be only one line, representing the additive effect. For an intercross, there will be
two lines, representing the additive and dominance effects.
Usage
effectscan(cross, pheno.col=1, chr, get.se=FALSE, draw=TRUE,
gap=25, ylim, mtick=c("line","triangle"),
add.legend=TRUE, alternate.chrid=FALSE, ...)
Arguments
cross

An object of class cross.

pheno.col

Column number in the phenotype matrix which to be drawn in the plot. One
may also give a character string matching a phenotype name.

chr

Optional vector indicating the chromosomes to be drawn in the plot. This should
be a vector of character strings referring to chromosomes by name; numeric
values are converted to strings. Refer to chromosomes with a preceding - to
have all chromosomes but those considered. A logical (TRUE/FALSE) vector
may also be used.

get.se

If TRUE, estimated standard errors are calculated.

draw

If TRUE, draw the figure.

gap

Gap separating chromosomes (in cM).

ylim

Y-axis limits (optional).

mtick

Tick mark type for markers.

add.legend
If TRUE, add a legend.
alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
...

Passed to the function plot when it is called.

68

effectscan

Details
The results of sim.geno are required for taking account of missing genotype information.
For a backcross, the additive effect is estimated as the difference between the phenotypic averages
for heterozygotes and homozygotes.
For recombinant inbred lines, the additive effect is estimated as half the difference between the
phenotypic averages for the two homozygotes.
For an intercross, the additive and dominance effects are estimated from linear regression on a and
d with a = -1, 0, 1, for the AA, AB and BB genotypes, respectively, and d = 0, 1, 0, for the AA, AB
and BB genotypes, respectively.
As usual, the X chromosome is a bit more complicated. We estimate separate additive effects for
the two sexes, and for the two directions within females.
There is an internal function plot.effectscan that creates the actual plot by calling plot.scanone.
In the case get.se=TRUE, colored regions indicate ± 1 SE.
Value
The results are returned silently, as an object of class "effectscan", which is the same as the form
returned by the function scanone, though with estimated effects where LOD scores might be. That
is, it is a data frame with the first two columns being chromosome ID and position (in cM), and
subsequent columns being estimated effects, and (if get.se=TRUE) standard errors.
Author(s)
Karl W. Broman, 
References
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.
See Also
effectplot, plotPXG, sim.geno
Examples
data(fake.f2)
fake.f2 <- sim.geno(fake.f2, step=2.5, n.draws=16)
# allelic effect on whole genome
effectscan(fake.f2)
# on chromosome 13, include standard errors
effectscan(fake.f2, chr="13", mtick="triangle", get.se=TRUE)

est.map

est.map

69

Estimate genetic maps

Description
Uses the Lander-Green algorithm (i.e., the hidden Markov model technology) to re-estimate the
genetic map for an experimental cross.
Usage
est.map(cross, chr, error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
m=0, p=0, maxit=10000, tol=1e-6, sex.sp=TRUE,
verbose=FALSE, omit.noninformative=TRUE, offset, n.cluster=1)
Arguments
cross
chr

An object of class cross. See read.cross for details.
Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.
error.prob
Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).
map.function
Indicates whether to use the Haldane, Kosambi, Carter-Falconer, or Morgan map
function when converting genetic distances into recombination fractions. (Ignored if m > 0.)
m
Interference parameter for the chi-square model for interference; a non-negative
integer, with m=0 corresponding to no interference. This may be used only for
a backcross or intercross.
p
Proportion of chiasmata from the NI mechanism, in the Stahl model; p=0 gives
a pure chi-square model. This may be used only for a backcross or intercross.
maxit
Maximum number of EM iterations to perform.
tol
Tolerance for determining convergence.
sex.sp
Indicates whether to estimate sex-specific maps; this is used only for the 4-way
cross.
verbose
If TRUE, print tracing information.
omit.noninformative
If TRUE, on each chromosome, omit individuals with fewer than two typed
markers, since they are not informative for linkage.
offset
Defines the starting position for each chromosome. If missing, we use the starting positions that are currently present in the input cross object. This should be
a single value (to be used for all chromosomes) or a vector with length equal
to the number of chromosomes, defining individual starting positions for each
chromosome. For a sex-specific map (as in a 4-way cross), we use the same
offset for both the male and female maps.
n.cluster
If the package snow is available calculations for multiple chromosomes are run
in parallel using this number of nodes.

70

est.map

Details
By default, the map is estimated assuming no crossover interference, but a map function is used to
derive the genetic distances (though, by default, the Haldane map function is used).
For a backcross or intercross, inter-marker distances may be estimated using the Stahl model for
crossover interference, of which the chi-square model is a special case.
In the chi-square model, points are tossed down onto the four-strand bundle according to a Poisson
process, and every (m + 1)st point is a chiasma. With the assumption of no chromatid interference,
crossover locations on a random meiotic product are obtained by thinning the chiasma process. The
parameter m (a non-negative integer) governs the strength of crossover interference, with m = 0
corresponding to no interference.
In the Stahl model, chiasmata on the four-strand bundle are a superposition of chiasmata from two
mechanisms, one following a chi-square model and one exhibiting no interference. An additional
parameter, p, gives the proportion of chiasmata from the no interference mechanism.
Value
A map object; a list whose components (corresponding to chromosomes) are either vectors of marker
positions (in cM) or matrices with two rows of sex-specific marker positions. The maximized log
likelihood for each chromosome is saved as an attribute named loglik. In the case that estimation
was under an interference model (with m > 0), allowed only for a backcross, m and p are also
included as attributes.
Author(s)
Karl W Broman, 
References
Armstrong, N. J., McPeek, M. J. and Speed, T. P. (2006) Incorporating interference into linkage
analysis for experimental crosses. Biostatistics 7, 374–386.
Lander, E. S. and Green, P. (1987) Construction of multilocus genetic linkage maps in humans.
Proc. Natl. Acad. Sci. USA 84, 2363–2367.
Lange, K. (1999) Numerical analysis for statisticians. Springer-Verlag. Sec 23.3.
Rabiner, L. R. (1989) A tutorial on hidden Markov models and selected applications in speech
recognition. Proceedings of the IEEE 77, 257–286.
Zhao, H., Speed, T. P. and McPeek, M. S. (1995) Statistical analysis of crossover interference using
the chi-square model. Genetics 139, 1045–1056.
See Also
map2table, plotMap, replace.map, est.rf, fitstahl
Examples
data(fake.f2)
newmap <- est.map(fake.f2)
logliks <- sapply(newmap, attr, "loglik")
plotMap(fake.f2, newmap)
fake.f2 <- replace.map(fake.f2, newmap)

est.rf

est.rf

71

Estimate pairwise recombination fractions

Description
Estimate the sex-averaged recombination fraction between all pairs of genetic markers.
Usage
est.rf(cross, maxit=10000, tol=1e-6)
Arguments
cross

An object of class cross. See read.cross for details.

maxit

Maximum number of iterations for the EM algorithm (not used with backcrosses).

tol

Tolerance for determining convergence (not used with backcrosses).

Details
For a backcross, one can simply count recombination events. For an intercross or 4-way cross, a
version of the EM algorithm must be used to estimate recombination fractions. (Since, for example,
in an intercross individual that is heterozygous at two loci, it is not known whether there were 0 or
2 recombination events.) Note that, for the 4-way cross, we estimate sex-averaged recombination
fractions.
Value
The input cross object is returned with a component, rf, added. This is a matrix of size (tot.mar x
tot.mar). The diagonal contains the number of typed meioses per marker, the lower triangle contains
the estimated recombination fractions, and the upper triangle contains the LOD scores (testing rf =
0.5).
Author(s)
Karl W Broman, 
See Also
plotRF, pull.rf, plot.rfmatrix, est.map, badorder, checkAlleles
Examples
data(badorder)
badorder <- est.rf(badorder)
plotRF(badorder)

72

fake.4way

fake.4way

Simulated data for a 4-way cross

Description
Simulated data for a phase-known 4-way cross, obtained using sim.cross.
Usage
data(fake.4way)
Format
An object of class cross. See read.cross for details.
Details
There are 250 individuals typed at 157 markers, including 8 on the X chromosome.
There are two phenotypes (including sex, for which 0=female and 1=male). The quantitative phenotype is affected by three QTLs: two on chromosome 2 at positions 10 and 25 cM on the female
genetic map, and one on chromosome 7 at position 40 cM on the female map.
Author(s)
Karl W Broman, 
See Also
sim.cross, fake.bc, fake.f2, listeria, hyper, bristle3, bristleX
Examples
data(fake.4way)
plot(fake.4way)
summary(fake.4way)
# estimate recombination fractions
fake.4way <- est.rf(fake.4way)
plotRF(fake.4way)
# estimate genetic maps
ssmap <- est.map(fake.4way, verbose=TRUE)
samap <- est.map(fake.4way, sex.sp=FALSE, verbose=TRUE)
plot(ssmap, samap)
# error lod scores
fake.4way <- calc.genoprob(fake.4way, err=0.01)
fake.4way <- calc.errorlod(fake.4way, err=0.01)
top.errorlod(fake.4way, cutoff=2.5)
# genome scan
fake.4way <- calc.genoprob(fake.4way, step=2.5)

fake.bc

73

out.hk <- scanone(fake.4way, method="hk")
out.em <- scanone(fake.4way, method="em")
plot(out.em,out.hk,chr=c(2,7))

fake.bc

Simulated data for a backcross

Description
Simulated data for a backcross, obtained using sim.cross.
Usage
data(fake.bc)
Format
An object of class cross. See read.cross for details.
Details
There are 400 backcross individuals typed at 91 markers and with two phenotypes and two covariates (sex and age).
The two phenotypes are due to four QTLs, with no epistasis. There is one on chromosome 2 (at 30
cM), two on chromosome 5 (at 10 and 50 cM), and one on chromosome 10 (at 30 cM). The QTL on
chromosome 2 has an effect only in the males (sex=1); the two QTLs on chromosome 5 have effect
in coupling for the first phenotype and in repulsion for the second phenotype. Age has an effect of
increasing the phenotypes.
Author(s)
Karl W Broman, 
See Also
sim.cross, fake.4way, fake.f2, listeria, hyper, bristle3, bristleX
Examples
data(fake.bc)
summary(fake.bc)
plot(fake.bc)
# genome scans without covariates
fake.bc <- calc.genoprob(fake.bc, step=2.5)
out.nocovar <- scanone(fake.bc, pheno.col=1:2)
# genome scans with covariates
ac <- pull.pheno(fake.bc, c("sex","age"))
ic <- pull.pheno(fake.bc, "sex")
out.covar <- scanone(fake.bc, pheno.col=1:2,
addcovar=ac, intcovar=ic)

74

fake.f2

# summaries
summary(out.nocovar, thr=3, format="allpeaks")
summary(out.covar, thr=3, format="allpeaks")
# plots
plot(out.nocovar, out.covar, chr=c(2,5,10), lod=1, col="blue",
lty=1:2, ylim=c(0,13))
plot(out.nocovar, out.covar, chr=c(2,5,10), lod=2, col="red",
lty=1:2, add=TRUE)

fake.f2

Simulated data for an F2 intercross

Description
Simulated data for an F2 intercross, obtained using sim.cross.
Usage
data(fake.f2)
Format
An object of class cross. See read.cross for details.
Details
There are 200 F2 individuals typed at 94 markers, including 3 on the X chromosome. There is one
quantitative phenotype, along with an indication of sex (0=female, 1=male) and the direction of the
cross (pgm = paternal grandmother, 0=A, meaning the cross was (AxB)x(AxB), and 1=B, meaning
the cross was (AxB)x(BxA)).
Note that the X chromosome genotypes are coded in a special way (see read.cross). For the
individuals with pgm=0, sex=0, 1=AA and 2=AB; for individuals with pgm=0, sex=1, 1=A and 2=B
(hemizygous); for individuals with pgm=1, sex=0, 1=BB and 2=AB; for individuals with pgm=1,
sex=1, 1=A and 2=B. This requires special care!
The data were simulated using an additive model with three QTLs on chromosome 1 (at 30, 50 and
70 cM), one QTL on chromosome 13 (at 30 cM), and one QTL on the X chromosome (at 10 cM).
Author(s)
Karl W Broman, 
See Also
sim.cross, fake.bc, fake.4way, listeria, hyper, bristle3, bristleX
Examples
data(fake.f2)
summary(fake.f2)
plot(fake.f2)

fill.geno

fill.geno

75

Fill holes in genotype data

Description
Replace the genotype data for a cross with a version imputed either by simulation with sim.geno,
by the Viterbi algorithm with argmax.geno, or simply filling in genotypes between markers that
have matching genotypes.
Usage
fill.geno(cross, method=c("imp","argmax", "no_dbl_XO", "maxmarginal"),
error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
min.prob=0.95)
Arguments
cross

An object of class cross. See read.cross for details.

method

Indicates whether to impute using a single simulation replicate from sim.geno,
using the Viterbi algorithm, as implemented in argmax.geno, by simply filling
in missing genotypes between markers with matching genotypes, or by choosing
(at each marker) the genotype with maximal marginal probability.

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi or Carter-Falconer map function
when converting genetic distances into recombination fractions.

min.prob

For method="maxmarginal", genotypes with probability greater than this value
will be imputed; those less than this value will be made missing.

Details
This function is written so that one may perform rough genome scans by marker regression without
having to drop individuals with missing genotype data. We must caution the user that little trust
should be placed in the results.
With method="imp", a single random imputation is performed, using sim.geno.
With method="argmax", for each individual the most probable sequence of genotypes, given the
observed data (via argmax.geno), is used.
With method="no_dbl_XO", non-recombinant intervals are filled in; recombinant intervals are left
missing. For example, a sequence of genotypes like A---A---H---H---A (with A and H corresponding to genotypes AA and AB, respectively, and with - being a missing value) will be filled in as
AAAAA---HHHHH---A.
With method="maxmarginal", the conditional genotype probabilities are calculated with calc.genoprob,
and then at each marker, the most probable genotype is determined. This is taken as the imputed
genotype if it has probability greater than min.prob; otherwise it is made missing.
With method="no_dbl_XO" and method="maxmarginal", some missing genotypes likely remain.
With method="maxmarginal", some observed genotypes may be made missing.

76

find.flanking

Value
The input cross object with the genotype data replaced by an imputed version. Any intermediate
calculations (such as is produced by calc.genoprob, argmax.geno and sim.geno) are removed.
Author(s)
Karl W Broman, 
See Also
sim.geno, argmax.geno
Examples
data(hyper)
out.mr <- scantwo(fill.geno(hyper,method="argmax"), method="mr")
plot(out.mr)

find.flanking

Find flanking markers for a specified position

Description
Find the genetic markers flanking a specified position on a chromosome, as well as the marker that
is closest to the specified position.
Usage
find.flanking(cross, chr, pos)
Arguments
cross

An object of class cross. See read.cross for details.

chr

A vector of chromosome identifiers, or a single such.

pos

A vector of cM positions.

Value
A data.frame, each row corresponding to one of the input positions. The first column contains the
left-flanking markers, the second column contains the right-flanking markers, and the third column
contains the markers closest to the specified positions.
Author(s)
Brian Yandell
See Also
find.marker, plotPXG, find.markerpos, find.pseudomarker

find.marker

77

Examples
data(listeria)
find.flanking(listeria, 5, 28)
find.flanking(listeria, c(1, 5, 13), c(81, 28, 26))

find.marker

Find marker closest to a specified position

Description
Find the genetic marker closest to a specified position on a chromosome.
Usage
find.marker(cross, chr, pos, index)
Arguments
cross
chr
pos
index

An object of class cross. See read.cross for details.
A vector of chromosome identifiers, or a single such.
A vector of cM positions.
A vector of numeric indices of the markers within chromosomes.

Details
Provide one of pos or index.
If the input chr has length one, it is expanded to the same length as the input pos or index.
If pos is specified and multiple markers are exactly the same distance from the specified position,
one is chosen at random from among those with the most genotype data.
For a cross with sex-specific maps, positions specified by pos are assumed to correspond to the
female genetic map.
Value
A vector of marker names (of the same length as the input pos), corresponding to the markers
nearest to the specified chromosomes/positions (if pos is specified) or to the input numeric indices
(in index is specified).
Author(s)
Karl W Broman, 
See Also
find.flanking, plotPXG, find.pseudomarker, effectplot, find.markerpos
Examples
data(listeria)
find.marker(listeria, 5, 28)
find.marker(listeria, 5, index=6)
find.marker(listeria, c(1, 5, 13), c(81, 28, 26))

78

find.markerpos

find.markerindex

Determine the numeric index for a marker

Description
Determine the numeric index for a marker in a cross object, when all markers on all chromosomes
are pasted together.
Usage
find.markerindex(cross, name)
Arguments
cross

An object of class cross. See read.cross for details.

name

A vector of marker names.

Value
A vector of numeric indices, from 1, 2, . . . , totmar(cross), with NA for markers not found.
Author(s)
Danny Arends; Karl W Broman 
See Also
find.markerpos
Examples
data(hyper)
mar <- find.marker(hyper, 4, 30)
find.markerindex(hyper, mar)

find.markerpos

Find position of a marker

Description
Find the chromosome and cM position of a set of genetic markers.
Usage
find.markerpos(cross, marker)
Arguments
cross

An object of class cross. See read.cross for details.

marker

A vector of marker names.

find.pheno

79

Value
A data frame with two columns: the chromosome and position of the markers.
Author(s)
Karl W Broman, 
See Also
find.flanking, find.marker, find.pseudomarker
Examples
data(hyper)
find.markerpos(hyper, "D4Mit164")
find.markerpos(hyper, c("D4Mit164", "D1Mit94"))

find.pheno

Find column number for a particular phenotype

Description
Find the column number corresponding to a particular phenotype name.
Usage
find.pheno(cross, pheno)
Arguments
cross

An object of class cross. See read.cross for details.

pheno

Vector of phenotype names (as character strings).

Value
A vector of numbers, corresponding to the column numbers of the phenotype in the input cross with
the specified names.
Author(s)
Brian Yandell
Examples
data(fake.bc)
find.pheno(fake.bc, "sex")

80

find.pseudomarker

find.pseudomarker

Find the pseudomarker closest to a specified position

Description
Find the pseudomarker closest to a specified position on a chromosome.
Usage
find.pseudomarker(cross, chr, pos, where=c("draws", "prob"), addchr=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

A vector of chromosome identifiers, or a single such.

pos

A vector of cM positions.

where

Indicates whether to look in the draws or prob components of the input cross.

addchr

If TRUE, include something like "c5." at the beginning of the names of nonpseudomarker locations, as in the output of scanone; if FALSE, don’t include
this sort of string, as in the genotype probabilities from calc.genoprob.

Details
If the input chr has length one, it is expanded to the same length as the input pos.
If multiple markers are exactly the same distance from the specified position, one is chosen at
random from among those with the most genotype data.
For a cross with sex-specific maps, the input positions are assumed to correspond to the female
genetic map.
Value
A vector of pseudomarker names (of the same length as the input pos), corresponding to the markers
nearest to the specified chromosomes/positions.
Author(s)
Karl W Broman, 
See Also
find.flanking, plotPXG, effectplot, find.marker, find.markerpos
Examples
data(listeria)
listeria <- calc.genoprob(listeria, step=2.5)
find.pseudomarker(listeria, 5, 28, "prob")
find.pseudomarker(listeria, c(1, 5, 13), c(81, 28, 26), "prob")

findDupMarkers

findDupMarkers

81

Find markers with identical genotype data

Description
Identify sets of markers with identical genotype data.

Usage
findDupMarkers(cross, chr, exact.only=TRUE, adjacent.only=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector specifying which chromosomes to consider. This may be a logical, numeric, or character string vector.

exact.only

If TRUE, look only for markers that have matching genotypes and the same
pattern of missing data; if FALSE, also look for cases where one the observed
genotypes at marker match those at another, and where the first marker has missing genotype whenever the genotype for the second marker is missing.

adjacent.only

If TRUE, look only for sets of markers that are adjacent to each other.

Details
If exact.only=TRUE, we look only for groups of markers whose pattern of missing data and observed genotypes match exactly. One marker (chosen at random) is selected as the name of the
group (in the output of the function).
If exact.only=FALSE, we look also for markers whose observed genotypes are contained in the
observed genotypes of another marker. We use a pair of nested loops, working from the markers
with the most observed genotypes to the markers with the fewest observed genotypes.

Value
A list of marker names; each component is a set of markers whose genotypes match one other
marker, and the name of the component is the name of the marker that they match.

Author(s)
Karl W Broman, 
See Also
drop.nullmarkers, drop.markers

82

fitqtl

Examples
data(hyper)
hyper <- drop.nullmarkers(hyper)
dupmar <- findDupMarkers(hyper) # finds 4 pairs
dupmar.adjonly <- findDupMarkers(hyper, adjacent.only=TRUE) # finds 4 pairs
dupmar.nexact <- findDupMarkers(hyper, exact.only=FALSE, adjacent.only=TRUE) # finds 6 pairs
# one might consider dropping the extra markers
totmar(hyper) # 173 markers
hyper <- drop.markers(hyper, unlist(dupmar.adjonly))
totmar(hyper) # 169 markers

fitqtl

Fit a multiple-QTL model

Description
Fits a user-specified multiple-QTL model. If specified, a drop-one-term analysis will be performed.
Usage
fitqtl(cross, pheno.col=1, qtl, covar=NULL, formula, method=c("imp", "hk"),
model=c("normal", "binary"), dropone=TRUE, get.ests=FALSE,
run.checks=TRUE, tol=1e-4, maxit=1000, forceXcovar=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype.
One may also give a character string matching a phenotype name. Finally, one
may give a numeric vector of phenotypes, in which case it must have the length
equal to the number of individuals in the cross, and there must be either nonintegers or values < 1 or > no. phenotypes; this last case may be useful for
studying transformations.

qtl

An object of class qtl, as output from makeqtl.

covar

A matrix or data.frame of covariates. These must be strictly numeric.

formula

An object of class formula indicating the model to be fitted. (It can also be the
character string representation of a formula.) QTLs are referred to as Q1, Q2, etc.
Covariates are referred to by their names in the data frame covar.

method

Indicates whether to use multiple imputation or Haley-Knott regression.

model

The phenotype model: the usual model or a model for binary traits

dropone

If TRUE, do drop-one-term analysis.

get.ests

If TRUE, return estimated QTL effects and their estimated variance-covariance
matrix.

run.checks

If TRUE, check the input formula and check for individuals with missing phenotypes or covariates.

fitqtl

83

tol

Tolerance for convergence for the binary trait model.

maxit

Maximum number of iterations for fitting the binary trait model.

forceXcovar

If TRUE, force inclusion of X-chr-related covariates (like sex and cross direction).

Details
The formula is used to specified the model to be fit. In the formula, use Q1, Q2, etc., or q1, q2, etc.,
to represent the QTLs, and the column names in the covariate data frame to represent the covariates.
We enforce a hierarchical structure on the model formula: if a QTL or covariate is in involved in an
interaction, its main effect must also be included.
In the drop-one-term analysis, for a given QTL/covariate model, all submodels will be analyzed.
For each term in the input formula, when it is dropped, all higher order terms that contain it will
also be dropped. The comparison between the new model and the full (input) model will be output.
The estimated percent variances explained for the QTL are simplify transformations of the conditional LOD scores by the formula h2 = 1 − 10−(2/n)LOD . While these may be reasonable for
unlinked, additive QTL, they can be completely wrong in the case of linked QTL, but we don’t
currently have any alternative.
For model="binary", a logistic regression model is used.
The part to get estimated QTL effects is not complete for the case of the X chromosome and 4way crosses. The values returned in these cases are based on a design matrix that is convenient
for calculations but not easily interpreted.
The estimated QTL effects for a backcross are derived by the coding scheme ± 1/2 for AA and
AB, so that the additive effect corresponds to the difference between phenotype averages for the
two genotypes. For doubled haploids and RIL, the coding scheme is ± 1 for AA and BB, so that
the additive effect corresponds to half the difference between the phenotype averages for the two
homozygotes.
For an intercross, the additive effect is derived from the coding scheme -1/0/+1 for genotypes
AA/AB/BB, and so is half the difference between the phenotype averages for the two homozygotes.
The dominance deviation is derived from the coding scheme 0/+1/0 for genotypes AA/AB/BB, and
so is the difference between the phenotype average for the heterozygotes and the midpoint between
the phenotype averages for the two homozygotes.
Epistatic effects and QTL × covariate interaction effects are obtained through the products of the
corresponding additive/dominant effect columns.
Value
An object of class fitqtl. It may contains as many as four components:
• result.full is the ANOVA table as a matrix for the full model result. It contains the degree
of freedom (df), Sum of squares (SS), mean square (MS), LOD score (LOD), percentage of
variance explained (%var) and P value (Pvalue).
• lod is the LOD score from the fit of the full model.
• result.drop is a drop-one-term ANOVA table as a matrix. It contains degrees of freedom
(df), Type III sum of squares (Type III SS), LOD score(LOD), percentage of variance explained (%var), F statistics (F value), and P values for chi square (Pvalue(chi2)) and F distribution (Pvalue(F)). Note that the degree of freedom, Type III sum of squares, the LOD score
and the percentage of variance explained are the values comparing the full to the sub-model
with the term dropped. Also note that for imputation method, the percentage of variance explained, the the F values and the P values are approximations calculated from the LOD score.

84

fitqtl
• ests contains the estimated QTL effects and standard errors.
When method="normal", residuals are saved as an attribute of the output, named "residuals" and
accessible via the attr function.
The part to get estimated QTL effects is fully working only for the case of autosomes in a
backcross, intercross, RIL or doubled haploids. In other cases the values returned are based
on a design matrix that is convenient for calculations but not easily interpreted.

Author(s)
Hao Wu; Karl W Broman, 
References
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.
See Also
summary.fitqtl, makeqtl, scanqtl, refineqtl, addtoqtl , dropfromqtl, replaceqtl, reorderqtl
Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c(1, 8, 13)
qp <- c(26, 56, 28)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
# fit model with 3 interacting QTLs interacting
# (performing a drop-one-term analysis)
lod <- fitqtl(fake.f2, pheno.col=1, qtl, formula=y~Q1*Q2*Q3, method="hk")
summary(lod)
## Not run:
# fit an additive QTL model
lod.add <- fitqtl(fake.f2, pheno.col=1, qtl, formula=y~Q1+Q2+Q3, method="hk")
summary(lod.add)
# fit the model including sex as an interacting covariate
Sex <- data.frame(Sex=pull.pheno(fake.f2, "sex"))
lod.sex <- fitqtl(fake.f2, pheno.col=1, qtl, formula=y~Q1*Q2*Q3*Sex,
cov=Sex, method="hk")
summary(lod.sex)
# fit the same with an additive model
lod.sex.add <- fitqtl(fake.f2, pheno.col=1, qtl, formula=y~Q1+Q2+Q3+Sex,
cov=Sex, method="hk")
summary(lod.sex.add)

fitstahl

85

# residuals
residuals <- attr(lod.sex.add, "residuals")
plot(residuals)
## End(Not run)

fitstahl

Fit Stahl interference model

Description
Fit the Stahl model for crossover inference (or the chi-square model, which is a special case).
Usage
fitstahl(cross, chr, m, p, error.prob=0.0001, maxit=4000, tol=1e-4,
maxm=15, verbose=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

m

Interference parameter (a non-negative integer); if unspecified, this is estimated.

p

The proportion of chiasmata coming from the no interference mechanism in the
Stahl model (0 <= p <= 1). p=0 gives the chi-square model. If unspecified, this
is estimated.

error.prob

The genotyping error probability. If = NULL, it is estimated.

maxit

Maximum number of iterations to perform.

tol

Tolerance for determining convergence.

maxm

Maximum value of m to consider, if m is unspecified.

verbose

Logical; indicates whether to print tracing information.

Details
This function is currently only available for backcrosses and intercrosses.
The Stahl model of crossover interference (of which the chi-square model is a special case) is fit.
In the chi-square model, points are tossed down onto the four-strand bundle according to a Poisson
process, and every (m + 1)st point is a chiasma. With the assumption of no chromatid interference,
crossover locations on a random meiotic product are obtained by thinning the chiasma process. The
parameter m (a non-negative integer) governs the strength of crossover interference, with m = 0
corresponding to no interference.
In the Stahl model, chiasmata on the four-strand bundle are a superposition of chiasmata from two
mechanisms, one following a chi-square model and one exhibiting no interference. An additional
parameter, p, gives the proportion of chiasmata from the no interference mechanism.

86

fitstahl
If all of m, p, and error.prob are specified, any of them with length > 1 must all have the same
length.
If m is unspecified, we do a grid search starting at 0 and stop when the likelihood decreases (thus
assuming a single mode), or maxm is reached.

Value
A matrix with four columns: m, p, error.prob, and the log likelihood.
If specific values for m, p, error.prob are provided, the log likelihood for each set are given.
If some are left unspecified, the maximum likelihood estimates are provided in the results.
Author(s)
Karl W Broman, 
References
Armstrong, N. J., McPeek, M. J. and Speed, T. P. (2006) Incorporating interference into linkage
analysis for experimental crosses. Biostatistics 7, 374–386.
Zhao, H., Speed, T. P. and McPeek, M. S. (1995) Statistical analysis of crossover interference using
the chi-square model. Genetics 139, 1045–1056.
See Also
est.map, sim.cross
Examples
# Simulate genetic map: one chromosome of length 200 cM with
# a 2 cM marker spacing
mymap <- sim.map(200, 51, anchor.tel=TRUE, include.x=FALSE,
sex.sp=FALSE, eq.spacing=TRUE)
# Simulate data under the chi-square model, no errors
mydata <- sim.cross(mymap, n.ind=250, type="bc",
error.prob=0, m=3, p=0)
# Fit the chi-square model for specified m's
## Not run: output <- fitstahl(mydata, m=1:5, p=0, error.prob=0)
plot(output$m, output$loglik, lwd=2, type="b")
# Find the MLE of m in the chi-square model
## Not run: mle <- fitstahl(mydata, p=0, error.prob=0)
## Not run:
# Simulate data under the Stahl model, no errors
mydata <- sim.cross(mymap, n.ind=250, type="bc",
error.prob=0, m=3, p=0.1)
# Find MLE of m for the Stahl model with known p
mle.stahl <- fitstahl(mydata, p=0.1, error.prob=0)
# Fit the Stahl model with unknown p and m,

flip.order

87

# get results for m=0, 1, 2, ..., 8
output <- fitstahl(mydata, m=0:8, error.prob=0)
plot(output$m, output$loglik, type="b", lwd=2)
## End(Not run)

flip.order

Flip the orders of markers on a set of chromosomes

Description
Flip the orders of markers on a specified set of chromosome, so that the markers will be in the
reverse order.
Usage
flip.order(cross, chr)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Vector indicating the chromosomes to flip. This should be a vector of character
strings referring to chromosomes by name. A logical (TRUE/FALSE) vector
may also be used.

Details
If the cross contains results from calc.genoprob, sim.geno, argmax.geno, or calc.errorlod,
those results are also updated.
Results of est.rf and markerlrt are deleted.
Value
The input cross object, but with the marker order on the specified chromosomes flipped.
Author(s)
Karl W Broman, 
See Also
switch.order
Examples
data(fake.f2)
fake.f2 <- flip.order(fake.f2, c(1, 5, 13))

88

formLinkageGroups

formLinkageGroups

Partition markers into linkage groups

Description
Use pairwise linkage information between markers (as calculated by est.rf to partition markers
into linkage groups.
Usage
formLinkageGroups(cross, max.rf=0.25, min.lod=3, reorgMarkers=FALSE,
verbose=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

max.rf

Maximum recombination fraction for placing two markers in the same linkage
group (see Details).

min.lod

Minimum LOD score for placing two markers in the same linkage group (see
Details).

reorgMarkers

If TRUE, the output is a cross object, like the input, but with the markers organized into the inferred linkage groups. If FALSE, the output is a table indicating
the initial chromosome assignments and the inferred linkage group partitions.

verbose

If TRUE, display information about the progress of the calculations.

Details
Two markers are placed in the same linkage group if the estimated recombination fraction between
them is ≤ max.rf and the LOD score (for the test of the rec. frac. = 1/2) is ≥ min.lod. The
transitive property (if A is linked to B and B is linked to C then A is linked to C) is used to close
the groups.
Value
If reorgMarkers=FALSE (the default), the output is a data frame with rows corresponding to the
markers and with two columns: the initial chromosome assignment and the inferred linkage group.
Linkage groups are ordered by the number of markers they contain (from largest to smallest).
If reorgMarkers=TRUE, the output is a cross object, like the input, but with the markers reorganized
into the inferred linkage groups. The marker order and marker positions within the linkage groups
are arbitrary.
Author(s)
Karl W Broman, 
See Also
est.rf, orderMarkers

formMarkerCovar

89

Examples
data(listeria)
listeria <- est.rf(listeria)
result <- formLinkageGroups(listeria)
tab <- table(result[,1], result[,2])
apply(tab, 1, function(a) sum(a!=0))
apply(tab, 2, function(a) sum(a!=0))

formMarkerCovar

Create matrix of marker covariates for QTL analysis

Description
Pull out a matrix of genotypes or genotype probabilities to use markers as covariates in QTL analysis.
Usage
formMarkerCovar(cross, markers, method=c("prob", "imp", "argmax"), ...)
Arguments
cross

An object of class cross. See read.cross for details.

markers

A vector of character strings of marker or pseudomarker names. Pseudomarker
names may be of the form "5@21.5" (for chr 5 at 21.5 cM), but then all names
must be of this form.

method

If method="prob", the genotype probabilities from calc.genoprob are used;
otherwise we use fill.geno to impute missing data, with this method.

...

Passed to fill.geno, if necessary.

Value
A matrix containing genotype probabilities or genotype indicators, suitable for use as covariates in
scanone.
Author(s)
Karl W Broman, 
See Also
pull.geno, pull.genoprob, fill.geno, scanone
Examples
data(hyper)
hyper <- calc.genoprob(hyper, step=0)
peakMarker <- "D4Mit164"
X <- formMarkerCovar(hyper, peakMarker)
out <- scanone(hyper, addcovar=X)

90

geno.crosstab

geno.crosstab

Create table of two-locus genotypes

Description
Create a cross tabulation of the genotypes at a pair of markers.

Usage
geno.crosstab(cross, mname1, mname2, eliminate.zeros=TRUE)

Arguments
cross

An object of class cross. See read.cross for details.

mname1

The name of the first marker (as a character string). (Alternatively, a vector with
the two character strings, in which case mname2 should not be given.)

mname2

The name of the second marker (as a character string).

eliminate.zeros
If TRUE, don’t show the rows and columns that have no data.

Value
A matrix containing the number of individuals having each possible pair of genotypes. Genotypes
for the first marker are in the rows; genotypes for the second marker are in the columns.

Author(s)
Karl W Broman, 

See Also
geno.table, find.marker

Examples
data(hyper)
geno.crosstab(hyper, "D1Mit123", "D1Mit156")
geno.crosstab(hyper, "DXMit22", "DXMit16")
geno.crosstab(hyper, c("DXMit22", "DXMit16"))

geno.image

91

geno.image

Plot grid of genotype data

Description
Plot a grid showing which the genotype data in a cross.
Usage
geno.image(x, chr, reorder=FALSE, main="Genotype data",
alternate.chrid=FALSE, ...)
Arguments
x

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to be drawn in the plot. This should
be a vector of character strings referring to chromosomes by name; numeric
values are converted to strings. Refer to chromosomes with a preceding - to
have all chromosomes but those considered. A logical (TRUE/FALSE) vector
may also be used.

reorder

Specify whether to reorder individuals according to their phenotypes.
FALSE
TRUE
n

Don’t reorder
Reorder according to the sum of the phenotypes
Reorder according to phenotype n

main
Title to place on plot.
alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
...

Passed to image.

Details
Uses image to plot a grid with the genotype data. The genotypes AA, AB, BB are displayed in the
colors red, blue, and green, respectively. In an intercross, if there are genotypes "not BB" and "not
AA", these are displayed in purple and orange, respectively. White pixels indicate missing data.
Value
None.
Author(s)
Karl W Broman, 
See Also
plot.cross, plotMissing, plotGeno, image

92

geno.table

Examples
data(listeria)
geno.image(listeria)

geno.table

Create table of genotype distributions

Description
Create table showing the observed numbers of individuals with each genotype at each marker, including P-values from chi-square tests for Mendelian segregation.
Usage
geno.table(cross, chr, scanone.output=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

scanone.output If TRUE, give result in the form output by scanone, so that one may use plot.scanone,
etc.
Details
The P-values are obtained from chi-square tests of Mendelian segregation. In the case of the X chromosome, the sexes and cross directions are tested separately, and the chi-square statistics combined,
and so the test is of whether any of the groups show deviation from Mendel’s rules.
Value
If scanone.output=FALSE, the output is a matrix containing, for each marker, the number of individuals with each possible genotype, as well as the number that were not typed. The first column
gives the chromosome ID, and the last column gives P-values from chi-square tests of Mendelian
segregation.
If scanone.output=TRUE, the output is of the form produced by scanone, with the first two
columns being chromosome IDs and cM positions of the markers. The third column is − log10 (P )
from chi-square tests of Mendelian segregation. The fourth column is the proportion of missing
data. The remaining columns are the proportions of the different genotypes (among typed individuals).
Author(s)
Karl W Broman, 

getid

93

See Also
summary.cross, drop.markers, drop.nullmarkers
Examples
data(listeria)
geno.table(listeria)
geno.table(listeria, chr=13)
gt <- geno.table(listeria)
gt[gt$P.value < 0.01,]
out <- geno.table(listeria, scanone.output=TRUE)
plot(out)
plot(out, lod=2)

getid

Pull out the individual identifiers from a cross

Description
Pull out the individual identifiers from a cross object.
Usage
getid(cross)
Arguments
cross

An object of class cross. See read.cross for details.

Value
A vector of individual identifiers, pulled from the phenotype data (a column named id or ID).
If there are no such identifiers in the cross, the function returns NULL.
Author(s)
Karl W Broman, 
See Also
subset.cross, top.errorlod
Examples
data(fake.f2)
# create an ID column
fake.f2$pheno$id <- paste("ind", sample(nind(fake.f2)), sep="")
getid(fake.f2)

94

groupclusteredheatmap

groupclusteredheatmap Retrieving groups of traits after clustering

Description
Retrieving groups of clustered traits from the output of mqmplot.clusteredheatmap.
Usage
groupclusteredheatmap(cross, clusteredheatmapresult, height)
Arguments
cross
An object of class cross. See read.cross for details.
clusteredheatmapresult
Resultint dendrogram object from mqmplot.clusteredheatmap
height
Height at which to ’cut’ the dendrogram, a higher cut-off gives less but larger
groups. Height represents the maximum distance between two traits clustered
together using hclust. the ’normal’ behaviour of bigger groups when using a
higher heigh cut-off depends on the tree stucture and the amount of traits clustered using mqmplot.clusteredheatmap
Value
A list containing groups of traits which were clustered together with a distance less that height
Author(s)
Danny Arends 
See Also
•
•
•
•
•
•
•
•
•

The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
MQM - MQM description and references
mqmscan - Main MQM single trait analysis
mqmscanall - Parallellized traits analysis
mqmaugment - Augmentation routine for estimating missing data
mqmautocofactors - Set cofactors using marker density
mqmsetcofactors - Set cofactors at fixed locations
mqmpermutation - Estimate significance levels
scanone - Single QTL scanning

Examples
data(multitrait)
multitrait <- fill.geno(multitrait) # impute missing genotype data
result <- mqmscanall(multitrait, logtransform=TRUE)
cresults <- mqmplot.clusteredheatmap(multitrait,result)
groupclusteredheatmap(multitrait,cresults,10)

hyper

hyper

95

Data on hypertension

Description
Data from an experiment on hypertension in the mouse.
Usage
data(hyper)
Format
An object of class cross. See read.cross for details.
Details
There are 250 male backcross individuals typed at 174 markers (actually one contains only missing
values), including 4 on the X chromosome, with one phenotype.
The phenotype is the blood pressure. See the reference below. Note that, for most markers, genotypes are available on only the individuals with extreme phenotypes. At many markers, only recombinant individuals were typed.
Source
Bev Paigen and Gary Churchill (The Jackson Laboratory, Bar Harbor, Maine) http://phenome.
jax.org/db/q?rtn=projects/projdet&reqprojid=119
References
Sugiyama, F., Churchill, G. A., Higgens, D. C., Johns, C., Makaritsis, K. P., Gavras, H. and Paigen,
B. (2001) Concordance of murine quantitative trait loci for salt-induced hypertension with rat and
human loci. Genomics 71, 70–77.
See Also
fake.bc, fake.f2, fake.4way, listeria, bristle3, bristleX
Examples
data(hyper)
summary(hyper)
plot(hyper)
# Note the selective genotyping
## Not run: plotMissing(hyper, reorder=TRUE)
# A marker on c14 has no data; remove it
hyper <- drop.nullmarkers(hyper)

96

inferFounderHap

inferFounderHap

Crude reconstruction of founder haplotypes in multi-parent RIL

Description
Uses groups of adjacent markers to infer the founder haplotypes in SNP data on multi-parent recombinant inbred lines.
Usage
inferFounderHap(cross, chr, max.n.markers=15)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Indicator of chromosome to consider. If multiple chromosomes are selected,
only the first is used.

max.n.markers

Maximum number of adjacent markers to consider.

Details
We omit SNPs for which any of the founders are missing.
We then consider groups of adjacent SNPs, looking for founder haplotypes that are unique; RIL
sharing such a unique haplotype are then inferred to have that founder’s DNA.
We consider each marker as the center of a haplotype, and consider haplotypes of size 1, 3, 5,
. . . , max.n.markers. We end the extension of the haplotypes when all founders have a unique
haplotype.
Value
A matrix of dimension nind(cross) × no. markers, with the inferred founder origin for each line
at each marker.
Author(s)
Karl W Broman, 
See Also
sim.geno, calc.genoprob, fill.geno, argmax.geno
Examples
map <- sim.map(100, n.mar=101, include.x=FALSE, eq.spacing=TRUE)
founderGeno <- simFounderSnps(map, "8")
ril <- sim.cross(map, n.ind=10, type="ri8sib", founderGeno=founderGeno)
h <- inferFounderHap(ril, max.n.markers=11)
mean(!is.na(h)) # proportion inferred
plot(map[[1]], h[1,], ylim=c(0.5, 8.5), xlab="Position", ylab="Genotype")

inferredpartitions

97

inferredpartitions

Identify inferred partitions in mapping QTL to a phylogenetic tree

Description
Identify the inferred partitions for a chromosome from the results of scanPhyloQTL.
Usage
inferredpartitions(output, chr, lodthreshold, probthreshold=0.9)
Arguments
output

An object output by the function scanPhyloQTL.

chr

A character string indicating the chromosome to consider. (It can also be a
number, but it’s then converted to a character string.)

lodthreshold

LOD threshold; if maximum LOD score is less than this, the null model is considered.

probthreshold

Threshold on posterior probabilities. See Details below.

Details
We consider a single chromosome, and take the maximum LOD score for each partition on that
chromosome. The presence of a QTL is inferred if at least one partition has LOD score greater
than lodthreshold. In this case, we then convert the LOD scores for the partitions to approximate
posterior probabilities by taking 10LOD and then rescaling them to sum to 1. These are sorted
from largest to smallest, and we then take as the inferred partitions the smallest set whose posterior
probabilities cumulatively add up to at least probthreshold.
Value
A vector of character strings. If the null model (no QTL) is inferred, the output is "null". Otherwise, it is the set of inferred partitions.
Author(s)
Karl W Broman, 
References
Broman, K. W., Kim, S., An\’e, C. and Payseur, B. A. Mapping quantitative trait loci to a phylogenetic tree. In preparation.
See Also
scanPhyloQTL, plot.scanPhyloQTL, summary.scanPhyloQTL, max.scanPhyloQTL, simPhyloQTL

98

interpPositions

Examples
# example map; drop X chromosome
data(map10)
map10 <- map10[1:19]
# simulate data
x <- simPhyloQTL(4, partition="AB|CD", crosses=c("AB", "AC", "AD"),
map=map10, n.ind=150,
model=c(1, 50, 0.5, 0))
# run calc.genoprob on each cross
## Not run: x <- lapply(x, calc.genoprob, step=2)
# scan genome, at each position trying all possible partitions
out <- scanPhyloQTL(x, method="hk")
# inferred partitions
inferredpartitions(out, chr=3, lodthreshold=3)
# inferred partitions with prob'y threshold = 0.95
inferredpartitions(out, chr=3, lodthreshold=3, probthreshold=0.95)

interpPositions

Interpolate positions from one map to another

Description
On the basis of a pair of marker maps with common markers, take positions along one map and
interpolate (or, past the terminal markers on a chromosome, extrapolate) their positions on the
second map.
Usage
interpPositions(oldpositions, oldmap, newmap)
Arguments
oldpositions

A data frame with two columns: chr (chromosome identifiers) and pos (positions, along oldmap).

oldmap

An object of class "map"; see sim.map for details.

newmap

An object of class "map", with the same chromosomes and markers as oldmap.

Details
In this explanation, take oldmap and newmap to be the physical and genetic maps, respectively.
We use linear interpolation within each interval, assuming a constant recombination rate within
the interval. Past the terminal markers, we use linear extrapolation, using the chromosome-wide
average recombination rate.

jittermap

99

Value
The input data frame, oldpositions, with an additional column newpos with the interpolated positions along newmap.
Author(s)
Karl W Broman, 
See Also
shiftmap, rescalemap, pull.map
Examples
data(hyper)
# hyper genetic map
gmap <- pull.map(hyper)
# a fake physical map, with each chromosome starting at 0.
pmap <- shiftmap(rescalemap(gmap, 2))
# positions on pmap to determine location on gmap
tofind <- data.frame(chr=c(1, 5, 17, "X"), pos=c(220, 20, 105, 10))
rownames(tofind) <- paste("loc", 1:nrow(tofind), sep="")
interpPositions(tofind, pmap, gmap)

jittermap

Jitter marker positions in a genetic map

Description
Jitter the marker positions in a genetic map so that no two markers are on top of each other.
Usage
jittermap(object, amount=1e-6)
Arguments
object

Either a cross (an object of class cross; see read.cross for details) or a map
(an object of class map; see pull.map for details).

amount

The amount by which markers should be moved.

Value
Either the input cross object or the input map, but with marker positions slightly jittered. If the input
was a cross, the function clean is run to strip off any intermediate calculations.
Author(s)
Karl W Broman, 

100

listeria

See Also
pull.map, replace.map, summary.cross
Examples
data(hyper)
hyper <- jittermap(hyper)

listeria

Data on Listeria monocytogenes susceptibility

Description
Data from an experiment on susceptibility to Listeria monocytogenes infection in the mouse.
Usage
data(listeria)
Format
An object of class cross. See read.cross for details.
Details
There are 120 F2 individuals typed at 133 markers, including 2 on the X chromosome, with one
phenotype.
The phenotype is the survival time (in hours) following infection. Mice with phenotype 264 hours
may be considered to have recovered from the infection. See the references below.
Source
Victor Boyartchuk and William Dietrich (Department of Genetics, Harvard Medical School and
Howard Hughes Medical Institute)
References
Boyartchuk, V. L., Broman, K. W., Mosher, R. E., D’Orazio S. E. F., Starnbach, M. N. and Dietrich,
W. F. (2001) Multigenic control of Listeria monocytogenes susceptibility in mice. Nature Genetics
27, 259–260.
Broman, K. W. (2003) Mapping quantitative trait loci in the case of a spike in the phenotype distribution. Genetics 163, 1169–1175.
See Also
fake.bc, fake.f2, fake.4way, hyper, bristle3, bristleX

locateXO

101

Examples
data(listeria)
# Summaries
summary(listeria)
plot(listeria)
# Take log of phenotype
listeria$pheno[,1] <- log2(listeria$pheno[,1])
plot(listeria)
# Genome scan with a two-part model, using log survival
listeria <- calc.genoprob(listeria, step=2)
out <- scanone(listeria, model="2part", method="em",
upper=TRUE)
# Summary of the results
summary(out, thr=c(5,3,3), format="allpeaks")
# Plot LOD curves for interesting chromosomes
#
(The two-part model gives three LOD scores)
plot(out, chr=c(1,5,6,13,15), lodcolumn=1:3,
lty=1, col=c("black","red","blue"))

locateXO

Estimate locations of crossovers

Description
Estimate the locations of crossovers for each individual on a given chromosome.
Usage
locateXO(cross, chr, full.info=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Chromosome to investigate (if unspecified, the first chromosome is considered).
This should be a character string referring to a chromosome by name; numeric
values are converted to strings.

full.info

If TRUE, output will include information on the left and right endpoints of the
intervals to which recombination events are known, as well as the corresponding
marker indices.

Details
For each individual we detemine the locations of obligate crossovers, and estimate their location to
be at the midpoint between the nearest flanking typed markers.
The function currently only works for a backcross, intercross, or recombinant inbred line.

102

locations

Value
A list with one component per individual. Each component is either NULL or is a numeric vector
with the estimated crossover locations.
If full.info=TRUE, in place of a numeric vector with estimated locations, there is a matrix that
includes those locations, the left and right endpoints of the intervals to which crossovers can be
placed, the marker indices corresponding to those endpoint, and genotype codes for the genotypes
to the left and right of each crossover. The final column indicates the number of typed markers
between the current crossover and the next one (useful for identifying potential genotyping errors).
Author(s)
Karl W Broman, 
See Also
countXO, cleanGeno
Examples
data(hyper)
xoloc <- locateXO(hyper, chr=4)
table(sapply(xoloc, length))

locations

Genetic locations of traits for the multitrait dataset

Description
A table with genetic locations of the traits in the multitrait dataset
Usage
data(locations)
Format
Each row is a trait with the following information: Name, Name of the trait (will be checked against
the name in the cross object Chr, Chromosome of the trait cM, Location in cM from the start of the
chromosome
Source
Additional information from the Arabidopsis RIL selfing experiment with Landsberg erecta (Ler)
and Cape Verde Islands (Cvi) with 162 individuals scored (with errors at) 117 markers. Dataset
obtained from GBIC - Groningen BioInformatics Centre
References
• Keurentijes JJB, Fu J, de Vos CHR,Lommen A, Jansen RC et al (2006), The genetics of plant
metabolism. Nature Genetics 38, 842–849.
• Alonso-Blanco C., Peeters, A. J. and Koornneef, M. (2006) Development of an AFLP based
linkage map of Ler, Col and Cvi Arabidopsis thaliana ecotypes and construction of a Ler/Cvi
recombinant inbred line population. Plant J. 14(2), 259–271.

lodint

103

See Also
multitrait
Examples
## Not run:
data(multitrait)
data(locations)
multiloc <- addloctocross(multitrait,locations)
results <- scanall(multiloc)
mqmplot.cistrans(results,multiloc, 5, FALSE, TRUE)
## End(Not run)

lodint

LOD support interval

Description
Calculate a LOD support interval for a particular chromosome, using output from scanone.
Usage
lodint(results, chr, qtl.index, drop=1.5, lodcolumn=1, expandtomarkers=FALSE)
Arguments
results

Output from scanone, or a qtl object as output from refineqtl.

chr

A chromosome ID (if input results are from scanone (should have length 1).

qtl.index

Numeric index for a QTL (if input results are from refineqtl (should have
length 1).

drop

LOD units to drop to form the interval.

lodcolumn

An integer indicating which of the LOD score columns should be considered (if
input results are from scanone).

expandtomarkers
If TRUE, the interval is expanded to the nearest flanking markers.
Value
An object of class scanone indicating the estimated QTL position and the approximate endpoints
for the LOD support interval.
Author(s)
Karl W Broman, 
See Also
scanone, bayesint

104

makeqtl

Examples
data(hyper)
hyper <- calc.genoprob(hyper, step=0.5)
out <- scanone(hyper, method="hk")
lodint(out, chr=1)
lodint(out, chr=4)
lodint(out, chr=4, drop=2)
lodint(out, chr=4, expandtomarkers=TRUE)

makeqtl

Make a qtl object

Description
This function takes a cross object and specified chromosome numbers and positions and pulls out
the genotype probabilities or imputed genotypes at the nearest pseudomarkers, for later use by the
function fitqtl.
Usage
makeqtl(cross, chr, pos, qtl.name, what=c("draws","prob"))
Arguments
cross

An object of class cross. See read.cross for details.

chr

Vector indicating the chromosome for each QTL. (These should be character
strings referring to the chromosomes by name.)

pos

Vector (of same length as chr) indicating the positions on the chromosome to be
taken. If there is no marker or pseudomarker at a position, the nearest position
is used.

qtl.name

Optional user-specified name for each QTL, used in the drop-one-term ANOVA
table in fitqtl. If unspecified, the names will be of the form "Chr1@10" for a
QTL on Chromsome 1 at 10 cM.

what

Indicates whether to pull out the imputed genotypes or the genotype probabilities.

Details
This function will take out the genotype probabilities and imputed genotypes if they are present in
the input cross object. If both fields are missing in the input object, the function will report an error.
Before running this function, the user must have first run either sim.geno (for what="draws") or
calc.genoprob (for what="prob").
Value
An object of class qtl with the following elements (though only one of geno and prob will be
included, according to whether what is given as "draws" or "prob"):
geno

Imputed genotypes.

map10

105

prob

Genotype probabilities.

name

User-defined name for each QTL, or a name of the form "Chr1@10".

altname

QTL names of the form "Q1", "Q2", etc.

chr

Input vector of chromosome numbers.

pos

Input vector of chromosome positions.

n.qtl

Number of QTLs.

n.ind

Number of individuals.

n.gen

A vector indicating the number of genotypes for each QTL.

Author(s)
Hao Wu; Karl W Broman, 
See Also
fitqtl, calc.genoprob, sim.geno, dropfromqtl, replaceqtl, addtoqtl, summary.qtl, reorderqtl
Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c("1", "6", "13")
qp <- c(25.8, 33.6, 18.63)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- sim.geno(fake.f2, n.draws=8, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="draws")
summary(qtl)

map10

An example genetic map

Description
A genetic map corresponding approximately to the mouse genome with a 10 cM marker spacing.
Usage
data(map10)
Format
An object of class map: a list whose components are vectors of marker locations. This map approximates the mouse genome, with 20 chromosomes (including the X chromosome) and 187 markers
at an approximately 10 cM spacing. The markers are equally spaced on each chromosome, but the
spacings are a bit above or below 10 cM, so that the lengths match those in the Mouse Genome
Database.

106

map2table

See Also
sim.map, plotMap, pull.map
Examples
data(map10)
plot(map10)
mycross <- sim.cross(map10, type="f2", n.ind=100)

map2table

Convert genetic map from list to table.

Description
Convert a map object (as a list) to a table (as a data frame).
Usage
map2table(map, chr)
Arguments
map

A map object: a list whose components (corresponding to chromosomes) are either vectors of marker positions or matrices with two rows of sex-specific marker
positions.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

Value
A data frame with two or three columns: chromosome and sex-averaged position, or chromosome,
female position, and male position.
The row names are the marker names.
Author(s)
Karl W Broman, 
See Also
table2map, pull.map, est.map
Examples
data(fake.f2)
map <- pull.map(fake.f2)
map_as_tab <- map2table(map)

mapthis

mapthis

107

Simulated data for illustrating genetic map construction

Description
Simulated data for an F2 intercross, obtained using sim.cross, useful for illustrating the process
of constructing a genetic map.
Usage
data(mapthis)
Format
An object of class cross. See read.cross for details.
Details
These are simulated data, consisting of 300 F2 individuals typed at 100 markers on five chromosomes. There are no real phenotypes, just a set of individual identifiers. The data were simulated for
the purpose of illustrating the process of constructing a genetic map. The markers are all assigned
to a single chromosome and in a random order, and there are a number of problematic markers and
individuals.
See https://rqtl.org/tutorials/geneticmaps.pdf for a tutorial on how to construct a genetic
map with these data.
Author(s)
Karl W Broman, 
References
Broman, K. W. (2010) Genetic map construction with R/qtl. Technical report #214, Department of
Biostatistics and Medical Informatics, University of Wisconsin–Madison
See Also
fake.f2, est.rf, est.map, formLinkageGroups, orderMarkers
Examples
data(mapthis)
summary(mapthis)
plot(mapthis)

108

markernames

markerlrt

General likelihood ratio test for association between marker pairs

Description
Calculate a LOD score for a general likelihood ratio test for each pair of markers, to assess their
association.
Usage
markerlrt(cross)
Arguments
cross

An object of class cross. See read.cross for details.

Value
The input cross object is returned with a component, rf, added. This is a matrix of size (tot.mar
x tot.mar). The diagonal contains the number of typed meioses per marker, the upper and lower
triangles each contain the LOD scores.
Author(s)
Karl W Broman, 
See Also
plotRF, est.rf, badorder
Examples
data(badorder)
badorder <- markerlrt(badorder)
plotRF(badorder)

markernames

Pull out the marker names from a cross

Description
Pull out the marker names from a cross object as one big vector.
Usage
markernames(cross, chr)

max.scanone

109

Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

Value
A vector of character strings (the marker names).
Author(s)
Karl W Broman, 
See Also
pull.map, phenames, chrnames
Examples
data(listeria)
markernames(listeria, chr=5)

max.scanone

Maximum peak in genome scan

Description
Print the row of the output from scanone that corresponds to the maximum LOD, genome-wide.
Usage
## S3 method for class 'scanone'
max(object, chr, lodcolumn=1, na.rm=TRUE, ...)
Arguments
object

An object of the form output by the function scanone: a data.frame whose third
column is the LOD score.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

lodcolumn

An integer, indicating which of the LOD score columns should be considered in
pulling out the peak (these are indexed 1, 2, . . . ).

na.rm

A logical indicating whether missing values should be removed.

...

Ignored.

110

max.scanPhyloQTL

Value
An object of class summary.scanone, to be printed by print.summary.scanone. This is a data.frame
with one row, corresponding to the maximum LOD peak either genome-wide or for the particular
chromosome specified.

Author(s)
Karl W Broman, 
See Also
scanone, plot.scanone, summary.scanone
Examples
data(listeria)
listeria <- calc.genoprob(listeria, step=2.5)
out <- scanone(listeria, model="2part", upper=TRUE)
# Maximum peak for LOD(p,mu)
max(out)
# Maximum peak for LOD(p,mu) on chr 5
max(out,chr=5)
# Maximum peak for LOD(p,mu) on chromosomes other than chr 13
max(out,chr="-13")
# Maximum peak for LOD(p)
max(out, lodcolumn=2)
# Maximum peak for LOD(mu)
max(out, lodcolumn=3)

max.scanPhyloQTL

Maximum peak in genome scan to map a QTL to a phylogenetic tree

Description
Print the chromosome with the maximum LOD score across partitions, from the results of scanPhyloQTL.
Usage
## S3 method for class 'scanPhyloQTL'
max(object, chr, format=c("postprob", "lod"),
...)

max.scanPhyloQTL

111

Arguments
object

An object output by the function scanPhyloQTL.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

format

Indicates whether to provide LOD scores or approximate posterior probabilities;
see the help file for summary.scanPhyloQTL.

...

Ignored at this point.

Details
The output, and the use of the argument format, is as in summary.scanPhyloQTL.
Value
An object of class summary.scanPhyloQTL, to be printed by print.summary.scanPhyloQTL.
Author(s)
Karl W Broman, 
References
Broman, K. W., Kim, S., An\’e, C. and Payseur, B. A. Mapping quantitative trait loci to a phylogenetic tree. In preparation.
See Also
scanPhyloQTL, plot.scanPhyloQTL, summary.scanPhyloQTL, max.scanone, inferredpartitions,
simPhyloQTL
Examples
## Not run:
# example map; drop X chromosome
data(map10)
map10 <- map10[1:19]
# simulate data
x <- simPhyloQTL(4, partition="AB|CD", crosses=c("AB", "AC", "AD"),
map=map10, n.ind=150,
model=c(1, 50, 0.5, 0))
# run calc.genoprob on each cross
x <- lapply(x, calc.genoprob, step=2)
# scan genome, at each position trying all possible partitions
out <- scanPhyloQTL(x, method="hk")
# maximum peak
max(out, format="lod")

112

max.scantwo
# approximate posterior probabilities at peak
max(out, format="postprob")
# all peaks above a threshold for LOD(best) - LOD(2nd best)
summary(out, threshold=1, format="lod")
# all peaks above a threshold for LOD(best), showing approx post'r prob
summary(out, format="postprob", threshold=3)
# plot of results
plot(out)
## End(Not run)

max.scantwo

Maximum peak in two-dimensional genome scan

Description
Print the pair of loci with the largest LOD score in the results of scantwo.
Usage
## S3 method for class 'scantwo'
max(object, lodcolumn=1,
what=c("best", "full", "add", "int"),
na.rm=TRUE, ...)
Arguments
object

An object of class scantwo, the output of the function scantwo.

lodcolumn

If the scantwo results contain LOD scores for multiple phenotypes, this argument indicates which to use.

what

Indicates for which LOD score the maximum should be reported.

na.rm

Ignored.

...

Ignored.

Details
This is very similar to the summary.scantwo function, though this pulls out one pair of positions.
If what="best", we find the pair of positions at which the LOD score for the full model (2 QTL
+ interaction) is maximized, and then also print the positions on that same pair of chromosomes at
which the additive LOD score is maximized.
In the other cases, we pull out the pair of positions with the largest LOD score; which LOD score
is considered is indicated by the what argument.
Value
An object of class summary.scantwo, to be printed by print.summary.scantwo, with the pair of
positions with the maximum LOD score. (Which LOD score is considered is indicated by the what
argument.)

movemarker

113

Output of addpair
Note that, for output from addpair in which the new loci are indicated explicitly in the formula,
the summary provided by max.scantwo is somewhat special.
All arguments (except, of course, the input object) are ignored.
If the formula is symmetric in the two new QTL, the output has just two LOD score columns:
lod.2v0 comparing the full model to the model with neither of the new QTL, and lod.2v1 comparing the full model to the model with just one new QTL.
If the formula is not symmetric in the two new QTL, the output has three LOD score columns:
lod.2v0 comparing the full model to the model with neither of the new QTL, lod.2v1b comparing
the full model to the model in which the first of the new QTL is omitted, and lod.2v1a comparing
the full model to the model with the second of the new QTL omitted.
Author(s)
Karl W Broman, 
See Also
scantwo, plot.scantwo, summary.scantwo
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=10)
out.2dim <- scantwo(fake.f2, method="hk")
max(out.2dim)

movemarker

Move a marker to a new chromosome

Description
Move a specified marker to a different chromosome.
Usage
movemarker(cross, marker, newchr, newpos)
Arguments
cross

An object of class cross. See read.cross for details.

marker

The name of the marker to be moved (a character string).

newchr

The chromosome to which the marker should be moved.

newpos

The position (in cM) at which the marker should be placed. If missing, the
marker is placed at the end of the chromosome.

Value
The input cross object, but with the specified marker moved to the specified chromosome.
All intermediate calculations (such as the results of calc.genoprob and est.rf) are removed.

114

MQM

Author(s)
Karl W Broman, 
See Also
switch.order
Examples
data(badorder)
badorder <- movemarker(badorder, "D2M937", 3, 48.15)
badorder <- movemarker(badorder, "D3M160", 2, 28.83)

MQM

Introduction to Multiple QTL Model (MQM) mapping

Description
Overview of the MQM mapping functions
Introduction
Multiple QTL Mapping (MQM) provides a sensitive approach for mapping quantititive trait loci
(QTL) in experimental populations. MQM adds higher statistical power compared to many other
methods. The theoretical framework of MQM was introduced and explored by Ritsert Jansen,
explained in the ‘Handbook of Statistical Genetics’ (see references), and used effectively in practical
research, with the commercial ‘mapqtl’ software package. Here we present the first free and open
source implementation of MQM, with extra features like high performance parallelization on multiCPU computers, new plots and significance testing.
MQM is an automatic three-stage procedure in which, in the first stage, missing data is ‘augmented’.
In other words, rather than guessing one likely genotype, multiple genotypes are modeled with their
estimated probabilities. In the second stage important markers are selected by multiple regression
and backward elimination. In the third stage a QTL is moved along the chromosomes using these
pre-selected markers as cofactors, except for the markers in the window around the interval under
study. QTL are (interval) mapped using the most ‘informative’ model through maximum likelihood.
A refined and automated procedure for cases with large numbers of marker cofactors is included.
The method internally controls false discovery rates (FDR) and lets users test different QTL models
by elimination of non-significant cofactors.
R/qtl-MQM has the following advantages:
• Higher power to detect linked as well as unlinked QTL, as long as the QTL explain a reasonable amount of variation
• Protection against overfitting, because it fixes the residual variance from the full model. For
this reason more parameters (cofactors) can be used compared to, for example, CIM
• Prevention of ghost QTL (between two QTL in coupling phase)
• Detection of negating QTL (QTL in repulsion phase)

MQM

115

Note
The current implementation of R/qtl-MQM has the following limitations: (1) MQM is limited to
experimental crosses F2, BC, and selfed RIL, (2) MQM does not treat sex chromosomes differently
from autosomal chromosomes - though one can introduce sex as a cofactor. Future versions of
R/qtl-MQM may improve on these points. Check the website and change log (https://rqtl.
org/STATUS.txt) for updates.
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
References
• Arends D, Prins P, Jansen RC. R/qtl: High-throughput multiple QTL mapping. Bioinformatics, to appear
• Jansen RC, (2007) Quantitative trait loci in inbred lines. Chapter 18 of Handbook of Stat.
Genetics 3rd edition. John Wiley & Sons, Ltd.
• Jansen RC, Nap JP (2001), Genetical genomics: the added value from segregation. Trends in
Genetics, 17, 388–391.
• Jansen RC, Stam P (1994), High resolution of quantitative traits into multiple loci via interval
mapping. Genetics, 136, 1447–1455.
• Jansen RC (1993), Interval mapping of multiple quantitative trait loci. Genetics, 135, 205–
211.
• Swertz MA, Jansen RC. (2007), Beyond standardization: dynamic software infrastructures for
systems biology. Nat Rev Genet. 3, 235–243.
• Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977) Maximum likelihood from incomplete
data via the EM algorithm. J. Roy. Statist. Soc. B, 39, 1–38.
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(map10)

# Genetic map modeled after mouse

# simulate a cross (autosomes 1-10)
qtl <- c(3,15,1,0)
# QTL model: chr, pos'n, add've & dom effects
cross <- sim.cross(map10[1:10],qtl,n=100,missing.prob=0.01)

116

mqmaugment
# MQM
crossaug <- mqmaugment(cross) # Augmentation
cat(crossaug$mqm$Nind,'real individuals retained in dataset',
crossaug$mqm$Naug,'individuals augmented\n')
result <- mqmscan(crossaug)

# Scan

# show LOD interval of the QTL on chr 3
lodint(result,chr=3)

mqmaugment

MQM augmentation

Description
Fill in missing genotypes for MQM mapping. For each missing or incomplete marker it fills in (or
‘augments’) all possible genotypes, thus creating new candidate ‘individuals’. The probability of
each indidual is calculated using information on neighbouring markers and recombination frequencies. When a genotype of an augmented genotype is less likely than the minprob parameter it is
dropped from the dataset. The augmented list of individuals is returned in a new cross object. For
a full discussion on augmentation see the MQM tutorial online.
Usage
mqmaugment(cross, maxaugind=82, minprob=0.1,
strategy=c("default","impute","drop"),
verbose=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

maxaugind

Maximum number of augmentations per individual. The default of 82 allows for
six missing markers for an individual in a BC cross (26 = 64) and four missing
markers in an F2 (34 = 81). When a large number of markers are missing this
default number is quickly reached.

minprob

Return individuals with augmented genotypes that have at least this probability
of occurring. minprob is a value between 0 and 1. For example a value of 0.5
will drop all genotypes that are half as likely as the most likely genotype (candidate of the individual). The default value of 0.1 will drop all genotypes that are
less likely of ocurring than 1 in 10, compared against the most likely genotype.
Use a value of 1.0 to return a single filled in genotype for each individual.

strategy

When individuals have too much missing data and augmentation fails three options are provided: 1. "default": Calculate genotypes at missing marker positions, accounting for minprob, and add this individual to the set. 2. "impute":
Calculate the most likely genotypes at missing marker positions and impute
maxaugind individual-variants around the most likely genotype. 3. "drop":
Drop individuals that cannot be augmented from the dataset, this option is not
advised because information from the dropped individuals will be lost.

verbose

If TRUE, give verbose output

mqmaugment

117

Value
Returns the cross object with augmented individuals (many individuals from the data set will be
repeated multiple times). Some individuals may have been dropped completely when the probability
falls below minprob. An added component to the cross object named mqm contains information on
exactly which individuals are retained and repeated.
Note
The sex chromosome ’X’ is treated like autosomes during augmentation. With an F2 the sex chromosome is not considered. This will change in a future version of MQM. Run with verbose=TRUE
to verify how many individuals are augmented versus moved to the second augmentation round.
This could have an effect on the resulting dataset or check the return cross$mqm values. Compare
results by using minprob=1.
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
See Also
• fill.geno - Alternative routine for estimating missing data
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(map10)

# Genetic map modeled after mouse

# simulate a cross (autosomes 1-10)
qtl <- c(3,15,1,0)
# QTL model: chr, pos'n, add've & dom effects
cross <- sim.cross(map10[1:10],qtl,n=100,missing.prob=0.01)
# MQM
crossaug <- mqmaugment(cross) # Augmentation
cat(crossaug$mqm$Nind,'real individuals retained in dataset',
crossaug$mqm$Naug,'individuals augmented\n')
result <- mqmscan(crossaug)

# Scan

# show LOD interval of the QTL on chr 3
lodint(result,chr=3)

118

mqmautocofactors

mqmautocofactors

Automatic setting of cofactors, taking marker density into account

Description
Sets cofactors, taking underlying marker density into account. Together with mqmscan cofactors are
selected through backward elimination.
Usage
mqmautocofactors(cross, num=50, distance=5, dominance=FALSE, plot=FALSE, verbose=FALSE)
Arguments
cross
num
distance
dominance
plot
verbose

An object of class cross. See read.cross for details.
Number of cofactors to set (warns when setting too many cofactors).
Minimal distance between two cofactors, in cM.
If TRUE, create a cofactor list that is safe to use with the dominance scan mode
of MQM. See mqmscan for details.
If TRUE, plots a genetic map displaying the selected markers as cofactors.
If TRUE, give verbose output.

Value
A list of cofactors to be used with mqmscan.
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
See Also
•
•
•
•
•
•
•
•
•

The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
MQM - MQM description and references
mqmscan - Main MQM single trait analysis
mqmscanall - Parallellized traits analysis
mqmaugment - Augmentation routine for estimating missing data
mqmautocofactors - Set cofactors using marker density
mqmsetcofactors - Set cofactors at fixed locations
mqmpermutation - Estimate significance levels
scanone - Single QTL scanning

Examples
data(hyper)

# hyper dataset

hyperfilled <- fill.geno(hyper)
cofactors <- mqmautocofactors(hyperfilled,15) # Set 15 Cofactors
result <- mqmscan(hyperfilled,cofactors) # Backward model selection
mqmgetmodel(result)

mqmextractmarkers

mqmextractmarkers

119

MQM marker extraction

Description
Extract the real markers from a cross object that includes pseudo markers
Usage
mqmextractmarkers(mqmresult)
Arguments
mqmresult

result from mqmscan, including pseudo markers

Value
Returns a scanone object with the pseudo markers removed
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(multitrait)
multitrait <- fill.geno(multitrait)
result <- mqmscan(multitrait)
newresult <- mqmextractmarkers(result)

120

mqmfind.marker

mqmfind.marker

Fetch significant markers after permutation analysis

Description
Fetch significant makers after permutation analysis. These markers can be used as cofactors for
model selection in a forward stepwise approach.
Usage
mqmfind.marker(cross, mqmscan = NULL, perm = NULL, alpha = 0.05, verbose=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

mqmscan

Results from either scanone or mqmscan

perm

a scanoneperm object

alpha

Threshold value, everything with significance < alpha is reported

verbose

Display more output on verbose=TRUE

Value
returns a matrix with at each row a significant marker (determined from the scanoneperm object)
and with columns: markername, chr and pos (cM)
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
See Also
• mqmprocesspermutation - Function called to convert results from an mqmpermutation into
an scanoneperm object
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning

mqmgetmodel

121

Examples
# Use the multitrait dataset
data(multitrait)
# Set cofactors at each 3th marker
cof <- mqmsetcofactors(multitrait,3)
# impute missing genotypes
multitrait <- fill.geno(multitrait)
# log transform the 7th phenotype
multitrait <- transformPheno(multitrait, 7)
# Bootstrap 50 runs in batches of 10
## Not run: result <- mqmpermutation(multitrait,scanfunction=mqmscan,cofactors=cof,
pheno.col=7,n.perm=50,batchsize=10)
## End(Not run)
# Create a permutation object
f2perm <- mqmprocesspermutation(result)
# What LOD score is considered significant ?
summary(f2perm)
# Find markers with a significant QTL effect (First run is original phenotype data)
marker <- mqmfind.marker(multitrait,result[[1]],f2perm)
# Print it to the screen
marker

mqmgetmodel

Retrieve the QTL model used in mapping from the results of an MQM
scan

Description
Retrieves the QTL model used for scanning from the output of an MQM scan. The model only
contains the selected cofactors significant at the specified cofactor.significance from the results of
an mqm scan

Usage
mqmgetmodel(scanresult)
Arguments
scanresult

An object returned by mqmscan, including cofactors and QTL model.

122

mqmpermutation

Value
The function returns the multiple QTL model created, which consists of the cofactors selected
during the modeling phase of the algorithm. This model was used when scanning for additional
QTL in the mqmscan function. The format of the model is compatible with the makeqtl function.
For more information about the format of the model see the makeqtl page. When no cofactor was
selected in the modeling phase no model was created, then this function will return a NULL value.
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
See Also
• mqmsetcofactors - Setting multiple cofactors for backward elimination
• makeqtl - Make a qtl object
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(hyper)
hyperfilled <- fill.geno(hyper)
cofactors <- mqmsetcofactors(hyperfilled,4)
result <- mqmscan(hyperfilled,cofactors)
mqmgetmodel(result)
plot(mqmgetmodel(result))

mqmpermutation

Estimate QTL LOD score significance using permutations or simulations

Description
Two randomization approaches to obtain estimates of QTL significance:
• Random redistribution of traits (method=’permutation’)
• Random redistribution of simulated trait values (method=’simulation’)
Calculations can be parallelized using the SNOW package.

mqmpermutation

123

Usage
mqmpermutation(cross, scanfunction=scanone, pheno.col=1, multicore=TRUE,
n.perm=10, batchsize=10, file="MQM_output.txt",
n.cluster=1, method=c("permutation","simulation"),
cofactors=NULL, plot=FALSE, verbose=FALSE, ...)
Arguments
cross
scanfunction
pheno.col
multicore
n.perm
batchsize
file
n.cluster
method
cofactors
plot
verbose
...

An object of class cross. See read.cross for details.
Function to use when mappingQTL’s (either scanone,cim or mqm)
Column number in the phenotype matrix which should be used as the phenotype.
This can be a vector of integers.
Use multicore (if available)
Number of permutations to perform (DEFAULT=10, should be 1000, or higher,
for publications)
Batch size. The entire set is split in jobs. Each job contains b.size number of
traits per job
Name of the intermediate output file used
Number of child processes to split the job into
What kind permutation should occur: permutation or simulation
cofactors, only used when scanfunction is mqm. List of cofactors to be analysed
in the QTL model. To set cofactors use mqmautocofactors or mqmsetcofactors.
If TRUE, make a plot
If TRUE, print tracing information
Parameters passed through to the scanone, cim or mqmscan functions

Details
Analysis of scanone, cim or mqmscan to scan for QTL in shuffled/randomized data. It is recommended to also install the snow library. The snow library allows calculations to run on multiple
cores or even scale it up to an entire cluster, thus speeding up calculation.
Value
Returns a mqmmulti object. this object is a list of scanone objects that can be plotted using
plot.scanone(result[[trait]])
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
References
• Bruno M. Tesson, Ritsert C. Jansen (2009) Chapter 3.7. Determining the significance threshold eQTL Analysis in Mice and Rats 1, 20–25
• Churchill, G. A. and Doerge, R. W. (1994) Empirical threshold values for quantitative trait
mapping. Genetics 138, 963–971.
• Rossini, A., Tierney, L., and Li, N. (2003), Simple parallel statistical computing. R. UW
Biostatistics working paper series University of Washington. 193
• Tierney, L., Rossini, A., Li, N., and Sevcikova, H. (2004), The snow Package: Simple Network
of Workstations. Version 0.2-1.

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mqmplot.circle

See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
# Use the multitrait dataset
data(multitrait)

multitrait <- calc.genoprob(multitrait)
result <- mqmpermutation(multitrait,pheno.col=7, n.perm=2, batchsize=2)
## Not run: #Set 50 cofactors
cof <- mqmautocofactors(multitrait,50)
## End(Not run)
multitrait <- fill.geno(multitrait)
result <- mqmpermutation(multitrait,scanfunction=mqmscan,cofactors=cof,
pheno.col=7, n.perm=2,batchsize=2,verbose=FALSE)
#Create a permutation object
f2perm <- mqmprocesspermutation(result)
#Get Significant LOD thresholds
summary(f2perm)

mqmplot.circle

Circular genome plot for MQM

Description
Circular genome plot - shows QTL locations and relations.
Usage
mqmplot.circle(cross,result,highlight=0,spacing=25, interactstrength=2,
axis.legend=TRUE, col.legend=FALSE, verbose=FALSE, transparency=FALSE)

mqmplot.circle

125

Arguments
cross

An object of class cross with optionally phenotype locations. See read.cross
for details on reading in cross objects, and optionally addloctocross for adding
phenotype locations.

result

An object of class mqmmulti or scanone. See mqmscanall scanone for details.

highlight

With a mqmmulti object, highlight this phenotype (value between one and the
number of results in the mqmmultiobject)
interactstrength
When highlighting a trait, consider interactions significant they have a change
of more than interactstrength*SEs. A higher value will show less interactions.
However the interactions reported at higher interactstrength values will generaty
be more reliable.
spacing

User defined spacing between chromosomes in cM

axis.legend

When set to FALSE, suppresses the legends. (defaults to plotting legends besides the axis.

col.legend

With a mqmmulti object, plots a legend for the non-highlighed version

transparency

Use transparency when drawing the plots (defaults to no transparency)

verbose

Be verbose

Details
Depending on the input of the result being either scanone or mqmmulti a different plot is drawn.
If model information is present from mqmscan (by setting cofactors) This will be highlighted in red
(see example). If phenotypes have genetic locations (e.g. eQTL) they will be plotted on the genome
otherwise phenotypes will be plotted in the middle of the circle (with a small offset) Locations can
be added by using the addloctocross function.
Value
Plotting routine, no return
Author(s)
Danny Arends 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning

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mqmplot.cistrans

Examples
data(multitrait)
data(locations)
multifilled <- fill.geno(multitrait)
multicof <- mqmsetcofactors(multitrait,10)
multiloc <- addloctocross(multifilled,locations)
#
multires <- mqmscanall(multifilled,cofactors=multicof)

# impute missing genotypes
# create cofactors
add phenotype information to cross
# run mqmscan for all phenotypes

#Basic mqmmulti, color = trait, round circle = significant
mqmplot.circle(multifilled,multires)
#mqmmulti with locations of traits in multiloc
mqmplot.circle(multiloc,multires)
#mqmmulti with highlighting
mqmplot.circle(multitrait,multires,highlight=3)
#mqmmulti with locations of traits in multiloc and highlighting
mqmplot.circle(multiloc,multires,highlight=3)

mqmplot.cistrans

cis-trans plot

Description
Plot results for a genomescan using a multiple-QTL model. With genetic location for the traits it is
possible to show cis- and trans- locations, and detect trans-bands
Usage
mqmplot.cistrans(result, cross, threshold=5, onlyPEAK=TRUE,
highPEAK=FALSE, cisarea=10, pch=22, cex=0.5,
verbose=FALSE, ...)
Arguments
result

An object of class mqmmulti. See mqmscanall for details.

cross

An object of class cross. See read.cross for details.

threshold

Threshold value in LOD, Markers that have a LOD score above this threshold
are plotted as small squares (see pch parameter). The markers with LODscores
below this threshold are not visible

onlyPEAK

Plot only the peak markers ? (TRUE/FALSE) (Peak markers are markers that
have a QTL likelihood above threshold and higher than other markers in the
same region)

highPEAK

Highlight peak markers ? (TRUE/FALSE). When using this option peak markers
(the marker with the highest LOD score in a region above the threshold gets an
25% increase in size and is displayed in red)

cisarea

Adjust the two green lines around the line y=x

mqmplot.clusteredheatmap
pch
cex
verbose
...

What kind of character is used in plotting of the figure (Default: 22, small
square)
Size of the points plotted (default to 0.5 half of the original size)
If TRUE, give verbose output
Extra parameters will be passed to points

Value
Plotting routine, so no return
Author(s)
Danny Arends 
See Also
•
•
•
•
•
•
•
•
•

127

The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
MQM - MQM description and references
mqmscan - Main MQM single trait analysis
mqmscanall - Parallellized traits analysis
mqmaugment - Augmentation routine for estimating missing data
mqmautocofactors - Set cofactors using marker density
mqmsetcofactors - Set cofactors at fixed locations
mqmpermutation - Estimate significance levels
scanone - Single QTL scanning

Examples
data(multitrait)
data(locations)
multiloc <- addloctocross(multitrait,locations)
multiloc <- calc.genoprob(multiloc)
results <- scanall(multiloc, method="hk")
mqmplot.cistrans(results, multiloc, 5, FALSE, TRUE)

mqmplot.clusteredheatmap
Plot clustered heatmap of MQM scan on multiple phenotypes

Description
Plot the results from a MQM scan on multiple phenotypes.
Usage
mqmplot.clusteredheatmap(cross, mqmresult, directed=TRUE, legend=FALSE,
Colv=NA, scale="none", verbose=FALSE,
breaks = c(-100,-10,-3,0,3,10,100),
col = c("darkblue","blue","lightblue","yellow",
"orange","red"), ...)

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mqmplot.clusteredheatmap

Arguments
cross

An object of class cross. See read.cross for details.

mqmresult

Result object from mqmscanall, the object needs to be of class mqmmulti

directed

Take direction of QTLs into account (takes more time because of QTL direction
calculations

legend

If TRUE, add a legend to the plot

Colv

Cluster only the Rows, the columns (Markers) should not be clustered

scale

character indicating if the values should be centered and scaled in either the row
direction or the column direction, or none. The default "none"

verbose

If TRUE, give verbose output.

breaks

Color break points for the LOD scores

col

Colors used between breaks

...

Additional arguments passed to heatmap.

Author(s)
Danny Arends 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(multitrait)
multitrait <- fill.geno(multitrait) # impute missing genotype data
result <- mqmscanall(multitrait, logtransform=TRUE)
cresults <- mqmplot.clusteredheatmap(multitrait,result)
groupclusteredheatmap(multitrait,cresults,10)

mqmplot.cofactors

mqmplot.cofactors

129

Plot cofactors on the genetic map

Description
Plots cofactors as created by mqmsetcofactors or mqmautocofactors on the genetic map.
Usage
mqmplot.cofactors(cross,cofactors, ...)
Arguments
cross

An object of class cross. See read.cross for details.

cofactors

List of cofactors to be analysed in the QTL model. To set cofactors use mqmautocofactors
or mqmsetcofactors.

...

Passed to plot.qtl

Author(s)
Danny Arends 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(multitrait)
cof1 <- mqmsetcofactors(multitrait,20)
cof2 <- mqmsetcofactors(multitrait,10)
op <- par(mfrow=c(2,1))
mqmplot.cofactors(multitrait,cof1,col="blue")
mqmplot.cofactors(multitrait,cof2,col="blue")
op <- par(mfrow=c(1,1))

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mqmplot.directedqtl

mqmplot.directedqtl

Plot LOD*Effect curves of a multiple-QTL model

Description
Plot the LOD*Effect curve for a genome scan with a multiple-QTL model (the output of mqmscan).
Usage
mqmplot.directedqtl(cross, mqmresult, pheno.col=1, draw = TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

mqmresult

Results from mqmscan of type scanone

pheno.col

From which phenotype in the crossobject are the result calculated

draw

If TRUE, draw the figure.

Value
Returns a scanone object, with added the effectsign calculated internally by the function effect.scan.
For more info on the scanone object see: scanone
Author(s)
Danny Arends 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
#Simulated F2 Population
f2qtl <- c(3,15,1,0)
data(map10)
f2cross <- sim.cross(map10,f2qtl,n=100,type="f2")
f2cross <- fill.geno(f2cross)
f2result <- mqmscan(f2cross)
mqmplot.directedqtl(f2cross,f2result)

# QTL at chromosome 3
# Mouse genetic map
# Simulate a F2 Cross
# Fill in missing genotypes
# Do a MQM scan of the genome

mqmplot.heatmap

mqmplot.heatmap

131

Heatmap of a genome of MQM scan on multiple phenotypes

Description
Plotting routine to display a heatmap of results obtained from a multiple-QTL model on multiple
phenotypes (the output of mqmscanall)
Usage
mqmplot.heatmap(cross, result, directed=TRUE, legend=FALSE, breaks =
c(-100,-10,-3,0,3,10,100), col =
c("darkblue","blue","lightblue","yellow","orange","red"), ...)
Arguments
cross

An object of class cross. See read.cross for details.

result

Result object from mqmscanall, the object needs to be of class mqmmulti

directed

Take direction of QTLs into account (takes more time because of QTL direction
calculations

legend

If TRUE, add a legend to the plot

breaks

Color break points for the LOD scores

col

Colors used between breaks

...

Additional arguments passed to the image function

Author(s)
Danny Arends 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(multitrait)
multitrait <- fill.geno(multitrait) # impute missing genotype data
result <- mqmscanall(multitrait, logtransform=TRUE)
mqmplot.heatmap(multitrait,result)

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mqmplot.multitrait

mqmplot.multitrait

Plot the results from a genomescan using a multiple-QTL model on
multiple phenotypes

Description
Plotting routine to display the results from a multiple-QTL model on multiple phenotypes. It supports four different visualizations: a contourmap, heatmap, 3D graph or a multiple QTL plot created
by using plot.scanone on the mqmmulti object
Usage
mqmplot.multitrait(result, type=c("lines","image","contour","3Dplot"),
group=NULL, meanprofile=c("none","mean","median"),
theta=30, phi=15, ...)
Arguments
result

Result object from mqmscanall

type

Selection of the plot method to visualize the data: "lines" (defaut plotting option), "image", "contour" and "3Dplot"

group

A numeric vector indicating which traits to plot. NULL means no grouping

meanprofile

Plot a mean/median profile from the group selected

theta

Horizontal axis rotation in a 3D plot

phi

Vertical axis rotation in a 3D plot

...

Additional arguments passed to plot.

Author(s)
Danny Arends 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning

mqmplot.permutations

133

Examples
data(multitrait)
multitrait <- fill.geno(multitrait) # impute missing genotype data
result <- mqmscanall(multitrait, logtransform=TRUE)
mqmplot.multitrait(result,"lines")
mqmplot.multitrait(result,"contour")
mqmplot.multitrait(result,"image")
mqmplot.multitrait(result,"3Dplot")

mqmplot.permutations

Plot results from mqmpermutation

Description
Plotting routine to display the results from a permutation QTL scan. (the output of mqmpermutation)
Usage
mqmplot.permutations(permutationresult, ...)
Arguments
permutationresult
mqmmulti object returned by mqmpermutation permutation analysis.
...

Extra arguments passed to polyplot

Value
No value returned (plotting routine)
Author(s)
Danny Arends  , Rutger Brouwer
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning

134

mqmplot.singletrait

Examples
# Simulated F2 Population
# QTL at chromosome 3
f2qtl <- c(3,15,1,0)
# Mouse genetic map
data(map10)
# Simulate a F2 Cross
f2cross <- sim.cross(map10,f2qtl,n=100,type="f2")
f2cross <- calc.genoprob(f2cross)
## Not run: # Permutations to obtain significance threshold
f2result <- mqmpermutation(f2cross, n.perm=1000, method="permutation")
## End(Not run)
# Plot results
mqmplot.permutations(f2result)

mqmplot.singletrait

Plot LOD curves of a multiple-QTL model

Description
Plot the LOD curve for a genome scan for a single trait, with a multiple-QTL model (the output of
mqmscan).
Usage
mqmplot.singletrait(result, extended = 0 ,...)
Arguments
result

mqmscan result.

extended

Extended plotting of the information content

...

Extra arguments passed to plot.scanone

Author(s)
Danny Arends 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density

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135

• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
#Simulated F2 Population
f2qtl <- c(3,15,1,0)
data(map10)

# QTL at chromosome 3
# Mouse genetic map

f2cross <- sim.cross(map10,f2qtl,n=100,type="f2")
# Simulate a F2 Cross
f2cross <- mqmaugment(f2cross)
f2result <- mqmscan(f2cross)
# Do a MQM scan of the genome
mqmplot.singletrait(f2result) # Use our fancy plotting routine

mqmprocesspermutation Convert mqmmulti objects into a scanoneperm object

Description
Function to convert mqmmulti objects into a scanoneperm object, this allows the use of R/qtl methods for permutation analysis that do not support the output of a multiple QTL scan using mqm’s
outputstructure.
Usage
mqmprocesspermutation(mqmpermutationresult = NULL)
Arguments
mqmpermutationresult
mqmmulti object obtained after performing permutations on a single trait.using
the function mqmpermutation
Value
Output of the algorithm is a scanoneperm object. See also: summary.scanoneperm
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
See Also
•
•
•
•
•
•
•
•
•

The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
MQM - MQM description and references
mqmscan - Main MQM single trait analysis
mqmscanall - Parallellized traits analysis
mqmaugment - Augmentation routine for estimating missing data
mqmautocofactors - Set cofactors using marker density
mqmsetcofactors - Set cofactors at fixed locations
mqmpermutation - Estimate significance levels
scanone - Single QTL scanning

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mqmscan

Examples
# QTL at chromosome 3
f2qtl <- c(3,15,1,0)
# Mouse genetic map
data(map10)
# Simulate a F2 Cross
f2cross <- sim.cross(map10,f2qtl,n=100,type="f2")
## Not run: # Bootstrap MQM mapping on the f2cross
f2result <- mqmpermutation(f2cross,scanfunction=mqmscan)
## End(Not run)
# Create a permutation object
f2perm <- mqmprocesspermutation(f2result)
# What LOD score is considered significant?
summary(f2perm)

mqmscan

Genome scan with a multiple QTL model (MQM)

Description
Genome scan with a multiple QTL model.
Usage
mqmscan(cross, cofactors=NULL, pheno.col = 1,
model=c("additive","dominance"), forceML=FALSE,
cofactor.significance=0.02, em.iter=1000,
window.size=25.0, step.size=5.0,
logtransform = FALSE, estimate.map = FALSE,
plot=FALSE, verbose=FALSE, outputmarkers=TRUE,
multicore=TRUE, batchsize=10, n.clusters=1, test.normality=FALSE,off.end=0
)
Arguments
cross

An object of class cross. See read.cross for details.

cofactors

List of cofactors to be analysed as cofactors in backward elimination procedure
when building the QTL model. See mqmsetcofactors on how-to manually set
cofactors for backward elimination. Or use mqmautocofactors for automatic
selection of cofactors. Only three kind of (integer) values are allowed in the
cofactor list. (0: no cofactor at this marker, 1: Use this marker as an additive
cofactor, 2: Use this marker as an sexfactor (Dominant cofactor))

pheno.col

Column number in the phenotype matrix which should be used as the phenotype.
This can be a vector of integers; One may also give a character strings matching
the phenotype names. Finally, one may give a numeric vector of phenotypeIDs.
This should consist of integers with 0 < value < no. phenotypes.

mqmscan
model

137
When scanning for QTLs should haplotype dominance be considered in an F2
intercross. Using the dominance model we scan for additive effects but also
allow an additional effect where AA+AB versus BB and AA versus AB+BB.
This setting is ignored for BC and RIL populations

forceML

Specify which statistical method to use to estimate variance components to use
when QTL modeling and mapping. Default usage is the Restricted maximum
likelihood approach (REML). With this option a user can disable REML and use
maximum likelihood.
cofactor.significance
Significance level at which a cofactor is considered significant. This is estimated
using an analysis of deviance, and compared to the level specified by the user.
The cofactors that dont reach this level of statistical significance are NOT used
in the mapping stage. Value between 0 and 1
em.iter

Maximum number of iterations for the EM algorithm to converge

window.size

Window size for mapping QTL locations, this parameter is used in the interval
mapping stage. When calculating LOD scores at a genomic position all cofactors within window.size are dropped to estimate the (unbiased) effect of the
location under interest.

step.size

Step size used in interval mapping. A lower step.size parameter increases the
number of output points, this creates a smoother QTL profile

off.end

Distance (in cM) past the terminal markers on each chromosome to which the
genotype simulations will be carried.

logtransform

Indicate if the algorithm should do a log transformation on the trait data in the
pheno.col

estimate.map

Should Re-estimation of the marker locations on the genetic map occur before
mapping QTLs. This method is deprecated rather use the est.map function in
R/qtl. This is because no map is returned into the crossobject. The old map
remains in the cross object.

plot

plot the results (default FALSE)

verbose

verbose output

outputmarkers

Needs to be explained

multicore

Use multicore (if available)

batchsize

Needs to be explained

n.clusters

Number of child processes to split the job into.

test.normality If TRUE, test whether the phenotype follows a normal distribution via mqmtestnormal.
Value
When scanning a single phenotype the function returns a scanone object.
The object contains a matrix of three columns for LOD scores, information content and LOD*information
content with pseudo markers sorted in increasing order. For more information on the scanone object
see: scanone
Note
The resulting scanone object itself can be visualized using the standard R/qtl plotting routines
(plot.scanone) or specialized function to show the mqm model (mqmplot.singletrait) and
QTL profile. If cofactors were specified the QTL model used in scanning is also returned as a

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mqmscanall
named attribute of the scanone object called mqmmodel. It can be extracted from the resulting
scanone object by using the mqmgetmodel function or the attr function.
Also note the estimate.map parameter does not return its re-estimated genetic map, altough it is
used internally. When scanning multiple genotypes a mqmmulti object is created. This object is just
a list composed of scanone objects. The results for a single trait can be obtained from the mqmmulti
object, in scanone format.

Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(map10)

# Genetic map modeled after mouse

# simulate a cross (autosomes 1-10)
qtl <- c(3,15,1,0)
# QTL model: chr, pos'n, add've & dom effects
cross <- sim.cross(map10[1:10],qtl,n=100,missing.prob=0.01)
# MQM
crossaug <- mqmaugment(cross) # Augmentation
cat(crossaug$mqm$Nind,'real individuals retained in dataset',
crossaug$mqm$Naug,'individuals augmented\n')
result <- mqmscan(crossaug)

# Scan

# show LOD interval of the QTL on chr 3
lodint(result,chr=3)

mqmscanall

Parallelized MQM on multiple phenotypes in a cross object

Description
Parallelized QTL analysis using MQM on multiple phenotypes in a cross object (uses SNOW)

mqmscanall

139

Usage
mqmscanall(cross, multicore=TRUE, n.clusters = 1,batchsize=10,cofactors=NULL, ...)
Arguments
cross

An object of class cross. See read.cross for details.

multicore

Use multiple cores (only if the package SNOW is available, otherwise this setting will be ignored)

n.clusters

Number of parallel processes to spawn, recommended is setting this lower than
the number of cores in the computer

batchsize

Batch size. The entire set is split in jobs to reduce memory load per core. Each
job contains batchsize number of traits per job.

cofactors

cofactors, only used when scanfunction is mqmscan. List of cofactors to be analysed in the QTL model. To set cofactors use mqmautocofactors or mqmsetcofactors.

...

Parameters passed through to the mqmscan function used in scanning for QTLs

Details
Uses mqmscan to scan for QTL’s for each phenotype in the cross object. It is recomended that the
package SNOW is installed before using this function on large numbers of phenotypes.
Value
Returns a MQMmulti object. This object is a list of scanone objects that can be plotted using
plot.scanone(result[[trait]]) or using mqmplot.multitrait(result)
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
References
• Rossini, A., Tierney, L., and Li, N. (2003), Simple parallel statistical computing. R. UW
Biostatistics working paper series University of Washington. 193
• Tierney, L., Rossini, A., Li, N., and Sevcikova, H. (2004), The snow Package: Simple Network
of Workstations. Version 0.2-1.
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning

140

mqmscanfdr

Examples
#Doing a multitrait analysis
data(multitrait)
multitrait <- calc.genoprob(multitrait)
cof <- mqmsetcofactors(multitrait,3)
multitrait <- fill.geno(multitrait)
result <- mqmscanall(multitrait,cofactors=cof,batchsize=5)
mqmplot.multitrait(result,"lines")

mqmscanfdr

Estimate FDR for multiple trait QTL analysis

Description
Estimate the false discovery rate (FDR) for multiple trait analysis
Usage
mqmscanfdr(cross, scanfunction=mqmscanall,
thresholds=c(1,2,3,4,5,7,10,15,20), n.perm=10,
verbose=FALSE, ...
)
Arguments
cross

An object of class cross. See read.cross for details.

scanfunction

QTL mapping function, Note: Must use scanall or mqmscanall. Otherwise this
will not produce usefull results. Reason: We need a function that maps all traits
ecause of the correlation structure which is not changed (between traits) during
permutation (Valis options: scanall or mqmscanall)

thresholds

False discovery rate (FDR) is calculated for peaks above these LOD thresholds
(DEFAULT=Range from 1 to 20, using 10 thresholds) Parameter is a list of LOD
scores at which FDR is calculated.

n.perm

Number of permutations (DEFAULT=10 for quick analysis, however for publications use 1000, or higher)

verbose

verbose output

...

Parameters passed to the mapping function

Details
This function wraps the analysis of scanone, cim and mqmscan to scan for QTL in shuffled/randomized
data. It is recommended to also install the snow library for parallelization of calculations. The snow
library allows calculations to run on multiple cores or even scale it up to an entire cluster, thus
speeding up calculation by the number of computers used.
Value
Returns a data.frame with 3 columns: FalsePositives, FalseNegatives and False Discovery Rates. In
the rows the userspecified thresholds are with scores for the 3 columns.

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141

Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
References
• Bruno M. Tesson, Ritsert C. Jansen (2009) Chapter 3.7. Determining the significance threshold eQTL Analysis in Mice and Rats 1, 20–25
• Churchill, G. A. and Doerge, R. W. (1994) Empirical threshold values for quantitative trait
mapping. Genetics 138, 963–971.
• Rossini, A., Tierney, L., and Li, N. (2003), Simple parallel statistical computing. R. UW
Biostatistics working paper series University of Washington. 193
• Tierney, L., Rossini, A., Li, N., and Sevcikova, H. (2004), The snow Package: Simple Network
of Workstations. Version 0.2-1.
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(multitrait)
# impute missing genotype data
multitrait <- fill.geno(multitrait)
## Not run: # Calculate the thresholds
result <- mqmscanfdr(multitrait, threshold=10.0, n.perm=1000)
## End(Not run)

mqmsetcofactors

Set cofactors at fixed intervals, to be used with MQM

Description
Set cofactors, at fixed marker intervals. Together with mqmscan cofactors are selected through
backward elimination.
Usage
mqmsetcofactors(cross, each = NULL, cofactors=NULL, sexfactors=NULL, verbose=FALSE)

142

mqmsetcofactors

Arguments
cross

An object of class cross. See read.cross for details.

each

Every ’each’ marker will be used as a cofactor, when each is used the cofactors
and sexfactors parameter is ignored

cofactors

List of cofactors to be analysed in the QTL model. To set cofactors use mqmautocofactors
or mqmsetcofactors; when each is set, this parameter is ignored

sexfactors

list of markers which should be treated as dominant cofactors (sexfactors), when
each is set, this parameter is ignored

verbose

If TRUE, print tracing information.

Value
An list of cofactors to be passed into mqmscan.
Author(s)
Ritsert C Jansen; Danny Arends; Pjotr Prins; Karl W Broman 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(hyper)

# Hyper dataset

hyperfilled <- fill.geno(hyper)
# Automatic cofactors every third marker
cofactors <- mqmsetcofactors(hyperfilled,3)
result <- mqmscan(hyperfilled,cofactors) # Backward model selection
mqmgetmodel(result)
#Manual cofactors at markers 3,6,9,12,40 and 60
cofactors <- mqmsetcofactors(hyperfilled,cofactors=c(3,6,9,12,40,60))
result <- mqmscan(hyperfilled,cofactors) # Backward model selection
mqmgetmodel(result)

mqmtestnormal

mqmtestnormal

143

Shapiro normality test used for MQM

Description
Wraps a shapiro’s normality test from the nortest package. This function is used in MQM to test
the normality of the trait under investigation
Usage
mqmtestnormal(cross, pheno.col = 1,significance=0.05, verbose=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype.
This can be a vector of integers.

significance

Significance level used in the normality test. Lower significance levels will accept larger deviations from normality.

verbose

If TRUE, print result as well as return it.

Details
For augmented data (as from mqmaugment), the cross is first reduced to distinct individuals. Furthermore the shapiro used to test normality works only for 3 <= nind(cross) <= 5000
Value
Boolean indicating normality of the trait in pheno.col. (FALSE when not normally distributed.)
Author(s)
Danny Arends 
See Also
• shapiro.test - Function wrapped by our mqmtestnormal
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis
• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning

144

multitrait

Examples
data(multitrait)
# test normality of 7th phenotype
mqmtestnormal(multitrait, pheno.col=7)
# take log
multitrait <- transformPheno(multitrait, pheno.col=7, transf=log)
# test again
mqmtestnormal(multitrait, pheno.col=7)

multitrait

Example Cross object from R/QTL with multiple traits

Description
Cross object from R/QTL, an object of class cross from R/QTL. See read.cross for details.
Usage
data(multitrait)
Format
Cross object from R/QTL
Details
Arabidopsis recombinant inbred lines by selfing. There are 162 lines, 24 phenotypes, and 117
markers on 5 chromosomes.
Source
Part of the Arabidopsis RIL selfing experiment with Landsberg erecta (Ler) and Cape Verde Islands
(Cvi) with 162 individuals scored (with errors at) 117 markers. Dataset obtained from GBIC Groningen BioInformatics Centre
References
• Keurentjes, J. J. and Fu, J. and de Vos, C. H. and Lommen, A. and Hall, R. D. and Bino, R. J.
and van der Plas, L. H. and Jansen, R. C. and Vreugdenhil, D. and Koornneef, M. (2006), The
genetics of plant metabolism. Nature Genetics. 38-7, 842–849.
• Alonso-Blanco, C. and Peeters, A. J. and Koornneef, M. and Lister, C. and Dean, C. and
van den Bosch, N. and Pot, J. and Kuiper, M. T. (1998), Development of an AFLP based
linkage map of Ler, Col and Cvi Arabidopsis thaliana ecotypes and construction of a Ler/Cvi
recombinant inbred line population
. Plant J. 14(2), 259–271.

nchr

145

Examples
data(multitrait) # Load dataset
multitrait <- fill.geno(multitrait)

# impute missing genotype data

result <- mqmscanall(multitrait, logtransform=TRUE) # Analyse all 24 traits

nchr

Determine the number of chromosomes

Description
Determine the number of chromosomes in a cross or map object.

Usage
nchr(object)
Arguments
object

An object of class cross (see read.cross for details) or map (see sim.map for
details).

Value
The number of chromosomes in the input.

Author(s)
Karl W Broman, 
See Also
read.cross, plot.cross, summary.cross, nind, totmar, nmar, nphe
Examples
data(fake.f2)
nchr(fake.f2)
map <- pull.map(fake.f2)
nchr(map)

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nmar

nind

Determine the number of individuals QTL experiment

Description
Determine the number of individuals in cross object.
Usage
nind(object)
Arguments
object

An object of class cross. See read.cross for details.

Value
The number of individuals in the input cross object.
Author(s)
Karl W Broman, 
See Also
read.cross, plot.cross, summary.cross, nmar, nchr, totmar, nphe
Examples
data(fake.f2)
nind(fake.f2)

nmar

Determine the numbers of markers on each chromosome

Description
Determine the number of markers on each chromosome in a cross or map object.
Usage
nmar(object)
Arguments
object

An object of class cross (see read.cross for details) or map (see sim.map for
details).

Value
A vector with the numbers of markers on each chromosome in the input.

nmissing

147

Author(s)
Karl W Broman, 
See Also
read.cross, plot.cross, summary.cross, nind, nchr, totmar, nphe
Examples
data(fake.f2)
nmar(fake.f2)
map <- pull.map(fake.f2)
nmar(map)

nmissing

Number of missing genotypes

Description
Count the number of missing genotypes for each individual or each marker in a cross.
Usage
nmissing(cross, what=c("ind","mar"))
Arguments
cross

An object of class cross. See read.cross for details.

what

Indicates whether to count missing genotypes for each individual or each marker.

Value
A vector containing the number of missing genotypes for each individual or for each marker.
Author(s)
Karl W Broman, 
See Also
ntyped, summary.cross, nind, totmar
Examples
data(listeria)
# plot number of missing genotypes for each individual
plot(nmissing(listeria))
# plot number of missing genotypes for each marker
plot(nmissing(listeria, what="mar"))

148

nqrank

nphe

Determine the number of phenotypes QTL experiment

Description
Determine the number of phenotypes in cross object.
Usage
nphe(object)
Arguments
object

An object of class cross. See read.cross for details.

Value
The number of phenotypes in the input cross object.
Author(s)
Karl W Broman, 
See Also
read.cross, plot.cross, summary.cross, nmar, nchr, totmar, nind
Examples
data(fake.f2)
nphe(fake.f2)

nqrank

Transform a vector of quantitative values to the corresponding normal
quantiles

Description
Transform a vector of quantitative values to the corresponding normal quantiles (preserving the
mean and SD).
Usage
nqrank(x, jitter)
Arguments
x

A numeric vector

jitter

If TRUE, randomly jitter the values to break ties.

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149

Value
A numeric vector; the input x is converted to ranks and then to normal quantiles.
Author(s)
Karl W Broman, 
See Also
rank, qnorm, transformPheno
Examples
data(hyper)
hyper <- transformPheno(hyper, pheno.col=1, transf=nqrank)

nqtl

Determine the number of QTL in a QTL object

Description
Determine the number of QTL in a QTL object.
Usage
nqtl(qtl)
Arguments
qtl

An object of class qtl. See makeqtl for details.

Value
The number of QTL in the input QTL object.
Author(s)
Karl W Broman, 
See Also
makeqtl, fitqtl, dropfromqtl, replaceqtl, addtoqtl, summary.qtl, reorderqtl

150

ntyped

Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c("1", "6", "13")
qp <- c(25.8, 33.6, 18.63)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
nqtl(qtl)

ntyped

Number of genotypes

Description
Count the number of genotypes for each individual or each marker in a cross.
Usage
ntyped(cross, what=c("ind","mar"))
Arguments
cross

An object of class cross. See read.cross for details.

what

Indicates whether to count genotypes for each individual or each marker.

Value
A vector containing the number of genotypes for each individual or for each marker.
Author(s)
Karl W Broman, 
See Also
nmissing, summary.cross, nind, totmar
Examples
data(listeria)
# plot number of genotypes for each individual
plot(ntyped(listeria))
# plot number of genotypes for each marker
plot(ntyped(listeria, what="mar"))

nullmarkers

151

nullmarkers

Identify markers without any genotype data

Description
Identify markers in a cross that have no genotype data.
Usage
nullmarkers(cross)
Arguments
cross

An object of class cross. See read.cross for details.

Value
Marker names (a vector of character strings) with no genotype data.
Author(s)
Karl W Broman, 
See Also
drop.nullmarkers
Examples
# one marker with no data
data(hyper)
nullmarkers(hyper)
# nothing in listeria
data(listeria)
nullmarkers(listeria)

orderMarkers

Find an initial order for markers within chromosomes

Description
Establish initial orders for markers within chromosomes by a greedy algorithm, adding one marker
at a time with locations of previous markers fixed, in the position giving the miniminum number of
obligate crossovers.
Usage
orderMarkers(cross, chr, window=7, use.ripple=TRUE, error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
maxit=4000, tol=1e-4, sex.sp=TRUE, verbose=FALSE)

152

orderMarkers

Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

window

If use.ripple=TRUE, this indicates the number of markers to include in the
sliding window of permuted markers. Larger numbers result in the comparison
of a greater number of marker orders, but will require a considerable increase in
computation time.

use.ripple

If TRUE, the initial order is refined by a call to the function ripple.

error.prob

Assumed genotyping error rate used in the final estimated map.

map.function

Indicates the map function to use in the final estimated map.

maxit

Maximum number of EM iterations to perform in the final estimated map.

tol

Tolerance for determining convergence in the final estimated map.

sex.sp

Indicates whether to estimate sex-specific maps in the final estimated map; this
is used only for the 4-way cross.

verbose

If TRUE, information about the progress of the calculations is displayed; if > 1,
even more information is given.

Details
Markers within a linkage group are considered in order of decreasing number of genotyped individuals. The first two markers are placed in an arbitrary order. Additional markers are considered one
at a time, and each possible placement of a marker is compared (with the order of the previously
placed markers taken as fixed) via the number of obligate crossovers (that is, the minimal number
of crossovers that would explain the observed data). The marker is placed in the position giving
the minimal number of obligate crossovers. If multiple positions give the same number of obligate
crossovers, a single location (among those positions) is chosen at random.
If use.ripple=TRUE, the final order is passed to ripple with method="countxo" to refine the
marker order. If use.ripple=TRUE and the number of markers on a chromosome is ≤ the argument
window, the initial greedy algorithm is skipped and all possible marker orders are compared via
ripple.
Value
The output is a cross object, as in the input, with orders of markers on selected chromosomes
revised.
Author(s)
Karl W Broman, 
See Also
formLinkageGroups, ripple, est.map, countXO

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153

Examples
data(listeria)
pull.map(listeria, chr=3)
revcross <- orderMarkers(listeria, chr=3, use.ripple=FALSE)
pull.map(revcross, chr=3)

phenames

Pull out the phenotypes names from a cross

Description
Pull out the phenotype names from a cross object as a vector.

Usage
phenames(cross)

Arguments
cross

An object of class cross. See read.cross for details.

Value
A vector of character strings (the phenotype names).

Author(s)
Karl W Broman, 

See Also
markernames, chrnames

Examples
data(listeria)
phenames(listeria)

154

pickMarkerSubset

pickMarkerSubset

Identify the largest subset of markers that are some distance apart

Description
Identify the largest subset of markers for which no two adjacent markers are separated by less than
some specified distance; if weights are provided, find the marker subset for which the sum of the
weights is maximized.
Usage
pickMarkerSubset(locations, min.distance, weights)
Arguments
locations

A vector of marker locations.

min.distance

Minimum distance between adjacent markers in the chosen subset.

weights

(Optional) vector of weights for the markers. If missing, we take weights == 1.

Details
Let di be the location of marker i, for i ∈ 1, . . . , M . We use the dynamic programming algorithm
of Broman and Weber
P (1999) to identify the subset of markers i1 , . . . , ik for which dij+1 − dij ≤
min.distance and wij is maximized.
If there are multiple optimal subsets, we pick one at random.
Value
A vector of marker names.
Author(s)
Karl W Broman, 
References
Broman, K. W. and Weber, J. L. (1999) Method for constructing confidently ordered linkage maps.
Genet. Epidemiol., 16, 337–343.
See Also
drop.markers, pull.markers
Examples
data(hyper)
# subset of markers on chr 4 spaced >= 5 cM
pickMarkerSubset(pull.map(hyper)[[4]], 5)
# no. missing genotypes at each chr 4 marker
n.missing <- nmissing(subset(hyper, chr=4), what="mar")

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155

# weight by -log(prop'n missing), but don't let 0 missing go to +Inf
wts <- -log( (n.missing+1) / (nind(hyper)+1) )
# subset of markers on chr 4 spaced >= 5 cM, with weights = -log(prop'n missing)
pickMarkerSubset(pull.map(hyper)[[4]], 5, wts)

plot.cross

Plot various features of a cross object

Description
Plots grid of the missing genotypes, genetic map, and histograms or barplots of phenotypes for the
data from an experimental cross.
Usage
## S3 method for class 'cross'
plot(x, auto.layout=TRUE, pheno.col,
alternate.chrid=TRUE, ...)
Arguments
x

An object of class cross. See read.cross for details.

auto.layout

If TRUE, par(mfrow) is set so that all plots fit within one figure.

pheno.col

Vector of numbers or character strings corresponding to phenotypes that should
be plotted. If unspecified, all phenotypes are plotted.

alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
...

Ignored at this point.

Details
Calls plotMissing, plotMap and plotPheno to plot the missing genotypes, genetic map, and histograms or barplots of all phenotypes.
If auto.format=TRUE, par(mfrow) is used with ceiling(sqrt(n.phe+2)) rows and the minimum number of columns so that all plots fit on the plotting device.
Numeric phenotypes are displayed as histograms or barplots by calling plotPheno.
Value
None.
Author(s)
Karl W Broman, ; Brian Yandell
See Also
plotMissing, plotMap, plotPheno

156

plot.qtl

Examples
data(fake.bc)
plot(fake.bc)

plot.qtl

Plot QTL locations

Description
Plot the locations of the QTL against a genetic map
Usage
## S3 method for class 'qtl'
plot(x, chr, horizontal=FALSE, shift=TRUE,
show.marker.names=FALSE, alternate.chrid=FALSE, justdots=FALSE,
col="red", ...)
Arguments
x

An object of class "qtl", as produced by makeqtl.

chr

Optional vector indicating the chromosomes to plot. This should be a vector of
character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

horizontal

Specifies whether the chromosomes should be plotted horizontally.

shift
If TRUE, shift the first marker on each chromosome to be at 0 cM.
show.marker.names
If TRUE, marker names are included.
alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
justdots

If FALSE, just plot dots at the QTL, rather than arrows and QTL names.

col

Color used to plot indications of QTL

...

Passed to plotMap.

Details
Creates a plot, via plotMap, and indicates the locations of the QTL in the input QTL object, x.
Value
None.
Author(s)
Karl W Broman, 

plot.rfmatrix

157

See Also
plotMap, makeqtl
Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c("1", "6", "13")
qp <- c(25.8, 33.6, 18.63)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
plot(qtl)
plot(qtl, justdots=TRUE, col="seagreen")

plot.rfmatrix

Plot recombination fractions or LOD scores for a single marker

Description
Plot a slice (corresponding to a single marker) through the pairwise recombination fractions or LOD
scores calculated by est.rf and extracted with pull.rf.
Usage
## S3 method for class 'rfmatrix'
plot(x, marker, ...)
Arguments
x

An object of class rfmatrix, as output by pull.rf.

marker

A single marker name, as a character string.

...

Optional arguments passed to plot.scanone.

Value
An object of class "scanone" (as output by scanone, and which may be summarized by summary.scanone
or plotted with plot.scanone), containing the estimated recombination fractions or LOD scores for
the input marker against all others.
Author(s)
Karl W Broman, 
See Also
pull.rf, est.rf, plotRF

158

plot.scanone

Examples
data(fake.f2)
fake.f2 <- est.rf(fake.f2)
marker <- markernames(fake.f2, chr=5)[6]
lod <- pull.rf(fake.f2, "lod")
plot(lod, marker, bandcol="gray70")

plot.scanone

Plot LOD curves

Description
Plot the LOD curve for a genome scan with a single-QTL model (the output of scanone).
Usage
## S3 method for class 'scanone'
plot(x, x2, x3, chr, lodcolumn=1, incl.markers=TRUE,
xlim, ylim, lty=1, col=c("black","blue","red"), lwd=2,
add=FALSE, gap=25, mtick = c("line", "triangle"),
show.marker.names=FALSE, alternate.chrid=FALSE,
bandcol=NULL, type="l", cex=1, pch=1, bg="transparent",
bgrect=NULL, ...)
Arguments
x

An object of class "scanone", as output by scanone.

x2

Optional second scanone object.

x3

Optional third scanone object.

chr

Optional vector indicating the chromosomes to plot. This should be a vector of
character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

lodcolumn

An integer, or vector of 3 integers, indicating which of the LOD score columns
should be plotted (generally this is 1).

incl.markers

Indicate whether to plot line segments at the marker locations.

xlim

Limits for x-axis (optional).

ylim

Limits for y-axis (optional).

lty

Line types; a vector of length 1 or 3.

col

Line colors; a vector of length 1 or 3.

lwd

Line widths; a vector of length 1 or 3.

add

If TRUE, add to a current plot.

gap

Gap separating chromosomes (in cM).

mtick

Tick mark type for markers (line segments or upward-pointing triangels).

plot.scanone

159

show.marker.names
If TRUE, show the marker names along the x axis.
alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
bandcol

Optional color for alternating bands to indicate chromosomes. If NULL (the
default), no bands are plotted. A good choice might be bandcol="gray70".

type

Type of plot (see plot): for example, type="l" for lines or type="p" for points
only, may be of length 1 or 3.

cex

Point size expansion, for example if type="p" is used. May be of length 1 or 3.

pch

Point type, for example if type="p" is used. See points. May be of length 1 or
3.

bg

Background color for points, for example if type="p" and pch=21 are used. See
points. May be of length 1 or 3.

bgrect

Optional background color for the rectangular plotting region.

...

Passed to the function plot when it is called.

Details
This function allows you to plot the results of up to three genome scans against one another. Such
objects must conform with each other.
One may alternatively use the argument add to add the plot of an additional genome scan to the
current figure, but some care is required: the same chromosomes should be selected, and the results
must concern crosses with the same genetic maps.
If a single scanone object containing multiple LOD score columns (for example, from different
phenotypes) is input, up to three LOD curves may be plotted, by providing a vector in the argument
lodcolumn. If multiple scanone objects are input (via x, x2 and x3), the LOD score columns to be
plotted are chosen from the corresponding element of the lodcolumn argument.
Value
None.
Author(s)
Karl W Broman, 
See Also
scanone, summary.scanone, par, colors, add.threshold, xaxisloc.scanone
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2,step=2.5)
out.mr <- scanone(fake.f2, method="mr")
out.em <- scanone(fake.f2, method="em")
plot(out.mr)
plot(out.mr, out.em, chr=c(1,13), lty=1, col=c("violetred","black"))
out.hk <- scanone(fake.f2, method="hk")

160

plot.scanoneboot
plot(out.hk, chr=c(1,13), add=TRUE, col="slateblue")
plot(out.hk, chr=13, show.marker.names=TRUE)
plot(out.hk, bandcol="gray70")
# plot points rather than lines
plot(out.hk, bandcol="gray70", type="p", cex=0.3, pch=21, bg="slateblue")

plot.scanoneboot

Plot results of bootstrap for QTL position

Description
Plot a histogram of the results of a nonparametric bootstrap to assess uncertainty in QTL position.
Usage
## S3 method for class 'scanoneboot'
plot(x, ...)
Arguments
x

An object of class "scanoneboot", as output by scanoneboot.

...

Passed to the function hist when it is called.

Details
The function plots a histogram of the bootstrap results obtained by scanoneboot. Genetic marker
locations are displayed by vertical lines at the bottom of the plot.
Value
None.
Author(s)
Karl W Broman, 
See Also
scanone, summary.scanoneboot
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=1)
## Not run: out.boot <- scanoneboot(fake.f2, chr=13, method="hk")
summary(out.boot)
plot(out.boot)

plot.scanoneperm

plot.scanoneperm

161

Plot permutation results for a single-QTL genome scan

Description
Plot a histogram of the permutation results from a single-QTL genome scan.
Usage
## S3 method for class 'scanoneperm'
plot(x, lodcolumn=1, ...)
Arguments
x

An object of class "scanoneperm", as output by scanone when n.perm is specified.

lodcolumn

This indicates the LOD score column to plot. This should be a single number
between 1 and the number of LOD columns in the object input.

...

Passed to the function hist when it is called.

Details
The function plots a histogram of the permutation results obtained by scanone when n.perm is
specified. If separate permutations were performed for the autosomes and the X chromosome (using
perm.Xsp=TRUE), separate histograms are given.
Value
None.
Author(s)
Karl W Broman, 
See Also
scanone, summary.scanoneperm
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc)
operm <- scanone(fake.bc, method="hk", n.perm=100)
plot(operm)

162

plot.scanPhyloQTL

plot.scanPhyloQTL

Plot LOD curves from single-QTL scan to map QTL to a phylogenetic
tree

Description
Plot the LOD curves for each partition for a genome scan with a single diallelic QTL (the output of
scanPhyloQTL).
Usage
## S3 method for class 'scanPhyloQTL'
plot(x, chr, incl.markers=TRUE,
col, xlim, ylim, lwd=2, gap=25, mtick=c("line", "triangle"),
show.marker.names=FALSE, alternate.chrid=FALSE, legend=TRUE, ...)
Arguments
x

An object of class "scanPhyloQTL", as output by scanPhyloQTL.

chr

Optional vector indicating the chromosomes to plot. This should be a vector of
character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

incl.markers

Indicate whether to plot line segments at the marker locations.

col

Optional vector of colors to use for each partition.

xlim

Limits for x-axis (optional).

ylim

Limits for y-axis (optional).

lwd

Line width.

gap

Gap separating chromosomes (in cM).

mtick
Tick mark type for markers (line segments or upward-pointing triangels).
show.marker.names
If TRUE, show the marker names along the x axis.
alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
legend

Indicates whether to include a legend in the plot.

...

Passed to the function plot.scanone when it is called.

Value
None.
Author(s)
Karl W Broman, 

plot.scantwo

163

References
Broman, K. W., Kim, S., An\’e, C. and Payseur, B. A. Mapping quantitative trait loci to a phylogenetic tree. In preparation.
See Also
scanPhyloQTL, max.scanPhyloQTL, summary.scanPhyloQTL, plot.scanone, inferredpartitions,
simPhyloQTL, par, colors
Examples
## Not run:
# example map; drop X chromosome
data(map10)
map10 <- map10[1:19]
# simulate data
x <- simPhyloQTL(4, partition="AB|CD", crosses=c("AB", "AC", "AD"),
map=map10, n.ind=150,
model=c(1, 50, 0.5, 0))
# run calc.genoprob on each cross
x <- lapply(x, calc.genoprob, step=2)
# scan genome, at each position trying all possible partitions
out <- scanPhyloQTL(x, method="hk")
# maximum peak
max(out, format="lod")
# approximate posterior probabilities at peak
max(out, format="postprob")
# all peaks above a threshold for LOD(best) - LOD(2nd best)
summary(out, threshold=1, format="lod")
# all peaks above a threshold for LOD(best), showing approx post'r prob
summary(out, format="postprob", threshold=3)
# plot of results
plot(out)
## End(Not run)

plot.scantwo

Plot LOD scores for a two-dimensional genome scan

Description
Plot the results of a two-dimensional, two-QTL genome scan.

164

plot.scantwo

Usage
## S3 method for class 'scantwo'
plot(x, chr, incl.markers=FALSE, zlim, lodcolumn=1,
lower = c("full", "add", "cond-int", "cond-add", "int"),
upper = c("int", "cond-add", "cond-int", "add", "full"),
nodiag=TRUE, contours=FALSE, main, zscale=TRUE, point.at.max=FALSE,
col.scheme = c("viridis", "redblue","cm","gray","heat","terrain","topo"),
gamma=0.6, allow.neg=FALSE, alternate.chrid=FALSE, ...)
Arguments
x

An object of class "scantwo", as output by scantwo.

chr

Optional vector indicating the chromosomes to plot. This should be a vector of
character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

incl.markers

If FALSE, plot LOD scores on an evenly spaced grid (not including the results
at the markers).

zlim

A vector of length 2 (optional), indicating the z limits for the lower-right and
upper-left triangles, respectively. If one number is given, the same limits are
used for both triangles. If zlim is missing, the maximum limits are used for
each.

lodcolumn

If the scantwo results contain LOD scores for multiple phenotypes, this argument indicates which to use in the plot.

lower

Indicates which LOD scores should be plotted in the lower triangle. See the
details below.

upper

Indicates which LOD scores should be plotted in the upper triangle. See the
details below.

nodiag

If TRUE, suppress the plot of the scanone output (which is normally along the
diagonal.)

contours

If TRUE, add a contour to the plot at 1.5-LOD below its maximum, using a call
to contour. If a numeric vector, contours are drawn at these values below the
maximum LOD.

main

An optional title for the plot.

zscale

If TRUE, a color scale is plotted at the right.

point.at.max

If TRUE, plot an X at the maximum LOD.

col.scheme

Name of color pallet. The default is "viridis"; see Option D at https://bids.
github.io/colormap

gamma

Parameter affecting range of colors when col.scheme="gray" or ="redblue".

allow.neg

If TRUE, allow the plot of negative LOD scores; in this case, the z-limits are
symmetric about 0. This option is chiefly to allow a plot of difference between
LOD scores from different methods, calculated via -.scantwo.

alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
...

Ignored at this point.

plot.scantwo

165

Details
Uses image to plot a grid of LOD scores. The particular LOD scores plotted in the upper-left
and lower-right triangles are selected via upper and lower, respectively. By default, the upper-left
triangle contains the epistasis LOD scores ("int"), and the lower-right triangle contains the LOD
scores for the full model ("full"). The diagonal contains either all zeros or the main effects LOD
scores (from scanone).
The scantwo function calculates, for each pair of putative QTLs, (q1 , q2 ), the likelihood under the
null model L0 , the likelihood under each of the single-QTL models, L(q1 ) and L(q2 ), the likelihood
under an additive QTL model, La (q1 , q2 ), and the likelihood under a full QTL model (including
QTL-QTL interaction), Lf (q1 , q2 ).
The five possible LOD scores that may be plotted are the following. The epistasis LOD scores
("int") are LODi = log10 Lf (q1 , q2 ) − log10 La (q1 , q2 ).
The full LOD scores ("full") are LODf = log10 Lf (q1 , q2 ) − log10 L0 .
The additive LOD scores ("add") are LODa = log10 La (q1 , q2 ) − log10 L0 .
In addition, we may calculate, for each pair of chromosomes, the difference between the full LOD
score and the maximum single-QTL LOD scores for that pair of chromosomes ("cond-int").
Finally, we may calculate, for each pair of chromosomes, the difference between the additive LOD
score and the maximum single-QTL LOD scores for that pair of chromosomes ("cond-add").
If a color scale is plotted (zscale=TRUE), the axis on the left indicates the scale for the upper-left
triangle, while the axis on the right indicates the scale for the lower-right triangle. Note that the axis
labels can get screwed up if you change the size of the figure window; you’ll need to redo the plot.
Value
None.
Output of addpair
Note that, for output from addpair in which the new loci are indicated explicitly in the formula,
the summary provided by plot.scantwo is somewhat special. In particular, the lower and upper
arguments are ignored.
In the case that the formula used in addpair was not symmetric in the two new QTL, the x-axis in
the plot corresponds to the first of the new QTL and the y-axis corresponds to the second of the new
QTL.
Author(s)
Hao Wu; Karl W Broman, ; Brian Yandell
See Also
scantwo, summary.scantwo, plot.scanone, -.scantwo
Examples
data(hyper)
hyper <- calc.genoprob(hyper, step=5)
# 2-d scan by EM and by Haley-Knott regression

166

plot.scantwoperm
out2.em <- scantwo(hyper, method="em")
out2.hk <- scantwo(hyper, method="hk")
# plot epistasis and full LOD scores
plot(out2.em)
# plot cond-int in upper triangle and full in lower triangle
#
for chromosomes 1, 4, 6, 15
plot(out2.em, upper="cond-int", chr=c(1,4,6,15))
# plot cond-add in upper triangle and add in lower triangle
#
for chromosomes 1, 4
plot(out2.em, upper="cond-add", lower="add", chr=c(1,4))
# plot the differences between the LOD scores from Haley-Knott
#
regression and the EM algorithm
plot(out2.hk - out2.em, allow.neg=TRUE)

plot.scantwoperm

Plot permutation results for a 2d, 2-QTL genome scan

Description
Plot a histogram of the permutation results from a two-dimensional, two-QTL genome scan.
Usage
## S3 method for class 'scantwoperm'
plot(x, lodcolumn=1, include_rug=TRUE, ...)
Arguments
x

An object of class "scantwoperm", as output by scantwo when n.perm is specified.

lodcolumn

This indicates the LOD score column to plot. This should be a single number
between 1 and the number of LOD columns in the object input.

include_rug

If TRUE, include a call to rug.

...

Passed to the function hist when it is called.

Details
The function plots a histogram of the permutation results obtained by scantwo when n.perm is
specified. Separate histograms are provided for the five LOD scores, full, fv1, int, add, and av1.
Value
None.
Author(s)
Karl W Broman, 

plotErrorlod

167

See Also
scantwo, summary.scantwoperm
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc)
operm2 <- scantwo(fake.bc, method="hk", n.perm=10)
plot(operm2)

plotErrorlod

Plot grid of error LOD values

Description
Plot a grid of the LOD scores indicating which genotypes are likely to be in error.
Usage
plotErrorlod(x, chr, ind, breaks=c(-Inf,2,3,4.5,Inf),
col=c("white","gray85","hotpink","purple3"),
alternate.chrid=FALSE, ...)
Arguments
x

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to be drawn in the plot. This should
be a vector of character strings referring to chromosomes by name; numeric
values are converted to strings. Refer to chromosomes with a preceding - to
have all chromosomes but those considered. A logical (TRUE/FALSE) vector
may also be used.

ind

Indicates the individuals for which the error LOD scores should be plotted
(passed to subset.cross).

breaks

A set of breakpoints for the colors; must give one more breakpoint than color.
Intervals are open on the left and closed on the right, except for the lowest interval.

col
A vector of colors to appear in the image.
alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
...

Ignored at this point.

Details
Uses image to plot a grid with different shades of pixels to indicate which genotypes are likely to
be in error.
Darker pixels have higher error LOD scores: LOD ≤ 2 in white; 2 < LOD ≤ 3 in gray; 3 <
LOD ≤ 4.5 in pink; LOD > 4.5 in purple.

168

plotGeno

Value
None.
Author(s)
Karl W Broman, 
References
Lincoln, S. E. and Lander, E. S. (1992) Systematic detection of errors in genetic linkage data.
Genomics 14, 604–610.
See Also
calc.errorlod, top.errorlod, image, subset.cross, plotGeno
Examples
data(hyper)
# Calculate error LOD scores
hyper <- calc.errorlod(hyper,error.prob=0.01)
# plot the error LOD scores; print those above a specified cutoff
plotErrorlod(hyper)
plotErrorlod(hyper,chr=1)

plotGeno

Plot observed genotypes, flagging likely errors

Description
Plot the genotypes on a particular chromosome for a set of individuals, flagging likely errors.
Usage
plotGeno(x, chr, ind, include.xo=TRUE, horizontal=TRUE,
cutoff=4, min.sep=2, cex=1.2, ...)
Arguments
x

An object of class cross. See read.cross for details.

chr

The chromosome to plot. Only one chromosome is allowed. (This should be a
character string referring to the chromosomes by name.)

ind

Vector of individuals to plot (passed to subset.cross). If missing, all individuals are plotted.

include.xo

If TRUE, plot X’s in intervals having a crossover. Not available for a 4-way
cross.

horizontal

If TRUE, chromosomes are plotted horizontally.

cutoff

Genotypes with error LOD scores above this value are flagged as possible errors.

plotGeno

169

min.sep

Markers separated by less than this value (as a percent of the chromosome
length) are pulled apart, so that they may be distinguished in the picture.

cex

Character expansion for the size of points in the plot. Larger numbers give larger
points; see par.

...

Ignored at this point.

Details
Plots the genotypes for a set of individuals. Likely errors are indicated by red squares. In a backcross, genotypes AA and AB are indicated by white and black circles, respectively. In an intercross,
genotypes AA, AB and BB are indicated by white, gray, and black circles, respectively, and the partially missing genotypes "not BB" (D in mapmaker) and "not AA" (C in mapmaker) are indicated
by green and orange circles, respectively.
For the X chromosome in a backcross or intercross, hemizygous males are plotted as if they were
homozygous (that is, with white and black circles).
For a 4-way cross, two lines are plotted for each individual. The left or upper line indicates the allele
A (white) or B (black); the right or lower line indicates the allele C (white) or D (black). For the
case that genotype is known to be only AC/BD or AD/BC, we use green and orange, respectively.

Value
None.

Author(s)
Karl W Broman, 

See Also
calc.errorlod, top.errorlod, subset.cross

Examples
data(hyper)
# Calculate error LOD scores
hyper <- calc.errorlod(hyper,error.prob=0.01)
# print those above a specified cutoff
top.errorlod(hyper,cutoff=4)
# plot genotype data, flagging genotypes with error LOD > cutoff
plotGeno(hyper, chr=1, ind=160:200, cutoff=7, min.sep=2)

170

plotInfo

plotInfo

Plot the proportion of missing genotype information

Description
Plot a measure of the proportion of missing information in the genotype data.
Usage
plotInfo(x, chr, method=c("entropy","variance","both"), step=1,
off.end=0, error.prob=0.001,
map.function=c("haldane","kosambi","c-f","morgan"),
alternate.chrid=FALSE, fourwaycross=c("all", "AB", "CD"),
include.genofreq=FALSE, ...)
Arguments
x

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to plot. This should be a vector of
character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

method

Indicates whether to plot the entropy version of the information, the variance
version, or both.

step

Maximum distance (in cM) between positions at which the missing information
is calculated, though for step=0, it is are calculated only at the marker locations.

off.end

Distance (in cM) past the terminal markers on each chromosome to which the
genotype probability calculations will be carried.

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi or Carter-Falconer map function
when converting genetic distances into recombination fractions.

alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
fourwaycross

For a phase-known four-way cross, measure missing genotype information overall ("all"), or just for the alleles from the first parent ("AB") or from the second
parent ("CD").

include.genofreq
If TRUE, estimated genotype frequencies (from the results of calc.genoprob
averaged across the individuals) are included as additional columns in the output.
...

Passed to plot.scanone.

plotLodProfile

171

Details
The entropy version of the missing information:P
for a single individual at a single genomic position,
we measure the missing information as H = g pg log pg / log n, where pg is the probability of
the genotype g, and n is the number of possible genotypes, defining 0 log 0 = 0. This takes values
between 0 and 1, assuming the value 1 when the genotypes (given the marker data) are equally
likely and 0 when the genotypes are completely determined. We calculate the missing information
at a particular position as the average of H across individuals. For an intercross, we don’t scale by
log n but by the entropy in the case of genotype probabilities (1/4, 1/2, 1/4).
The variance version of the missing information: we calculate the average, across individuals, of
the variance of the genotype distribution (conditional on the observed marker data) at a particular
locus, and scale by the maximum such variance.
Calculations are done in C (for the sake of speed in the presence of little thought about programming
efficiency) and the plot is created by a call to plot.scanone.
Note that summary.scanone may be used to display the maximum missing information on each
chromosome.
Value
An object with class scanone: a data.frame with columns the chromosome IDs and cM positions
followed by the entropy and/or variance version of the missing information.
Author(s)
Karl W Broman, 
See Also
plot.scanone, plotMissing, calc.genoprob, geno.table
Examples
data(hyper)
plotInfo(hyper,chr=c(1,4))
# save the results and view maximum missing info on each chr
info <- plotInfo(hyper)
summary(info)
plotInfo(hyper, bandcol="gray70")

plotLodProfile

Plot 1-d LOD profiles for a multiple QTL model

Description
Use the results of refineqtl to plot one-dimensional LOD profiles for each QTL.

172

plotLodProfile

Usage
plotLodProfile(qtl, chr, incl.markers=TRUE, gap=25, lwd=2, lty=1, col="black",
qtl.labels=TRUE, mtick=c("line", "triangle"),
show.marker.names=FALSE, alternate.chrid=FALSE,
add=FALSE, showallchr=FALSE, labelsep=5, ...)

Arguments
qtl

An object of class "qtl"; must have been produced by refineqtl using keeplodprofiles=TRUE.

chr

Optional vector indicating the chromosomes to plot. This should be a vector of
character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

incl.markers

Indicate whether to plot line segments at the marker locations.

gap

Gap separating chromosomes (in cM).

lwd

Line widths for each QTL trace (length 1 or the number of QTL).

lty

Line types for each QTL trace (length 1 or the number of QTL).

col

Line col for each QTL trace (length 1 or the number of QTL).

qtl.labels

If TRUE, place a label on each QTL trace.

mtick
Tick mark type for markers (line segments or upward-pointing triangels).
show.marker.names
If TRUE, show the marker names along the x axis.
alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
add

If TRUE, add curves to a current plot.

showallchr

If FALSE (the default), only show the chr with a QTL

labelsep

If qtl.labels=TRUE, separation between peak LOD and QTL label, as percent
of the height of the plot.

...

Passed to the function plot when it is called.

Details
The function plots LOD profiles in the context of a multiple QTL model, using a scheme best
described in Zeng et al. (2000). The position of each QTL is varied, keeping all other loci fixed.
If a QTL is isolated on a chromosome, the entire chromosome is scanned; if there are additional
linked QTL, the position of a QTL is scanned over the largest interval possible without allowing
the order of QTLs along a chromosome to change. At each position for the QTL being scanned, we
calculate a LOD score comparing the full model, with the QTL of interest at that particular position
(and all others at their fixed positions) to the model with the QTL of interest (and any interactions
that include that QTL) omitted.
Care should be take regarding the arguments lwd, lty, and col; if vectors are given, they should be
in the order of the QTL within the object, which may be different than the order in which they are
plotted. (The LOD profiles are sorted by chromosome and position.)

plotMap

173

Value
None.
Author(s)
Karl W Broman, 
References
Zeng Z.-B., Liu, J., Stam, L. F., Kao, C.-H., Mercer, J. M. and Laurie, C. C. (2000) Genetic architecture of a morphological shape difference between two Drosophila species. Genetics 154,
299–310.
See Also
refineqtl, makeqtl, scanqtl
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=2)
qtl <- makeqtl(fake.bc, chr=c(2,5), pos=c(32.5, 17.5), what="prob")
out <- scanone(fake.bc, method="hk")
# refine QTL positions and keep LOD profiles
rqtl <- refineqtl(fake.bc, qtl=qtl, method="hk", keeplodprofile=TRUE)
# plot the LOD profiles
plotLodProfile(rqtl)
# add the initial scan results, for comparison
plot(out, add=TRUE, chr=c(2,5), col="red")

plotMap

Plot genetic map

Description
Plot genetic map of marker locations for all chromosomes.
Usage
## S3 method for class 'map'
plot(x, map2, chr, horizontal=FALSE, shift=TRUE,
show.marker.names=FALSE, alternate.chrid=FALSE, ...)
plotMap(x, map2, chr, horizontal=FALSE, shift=TRUE,
show.marker.names=FALSE, alternate.chrid=FALSE, ...)

174

plotMap

Arguments
x

A list whose components are vectors of marker locations. A cross object may
be given instead, in which case the genetic map it contains is used.

map2

An optional second genetic map with the same number (and names) of chromosomes. As with the first argument, a cross object may be given instead. If this
argument is given, a comparison of the two genetic maps is plotted.

chr

Optional vector indicating the chromosomes to plot. This should be a vector of
character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

horizontal

Specifies whether the chromosomes should be plotted horizontally.

shift
If TRUE, shift the first marker on each chromosome to be at 0 cM.
show.marker.names
If TRUE, marker names are included.
alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
...

Passed to plot.

Details
Plots the genetic map for each chromosome, or a comparison of the genetic maps if two maps are
given.
For a comparison of two maps, the first map is on the left (or, if horizontal=TRUE, on the top).
Lines are drawn to connect markers. Markers that exist in just one map and not the other are
indicated by short line segments, on one side or the other, that are not connected across.
For a sex-specific map, female and male maps are plotted against one another. For two sex-specific
maps, the two female maps are plotted against one another and the two male maps are plotted
against one another.
Value
None.
Author(s)
Karl W Broman, 
See Also
est.map, plot.cross
Examples
data(fake.bc)
plotMap(fake.bc)
plotMap(fake.bc,horizontal=TRUE)
newmap <- est.map(fake.bc)

plotMissing

175

plot(newmap)
plotMap(fake.bc, newmap)
plotMap(fake.bc, show.marker.names=TRUE)

plotMissing

Plot grid of missing genotypes

Description
Plot a grid showing which genotypes are missing.
Usage
plotMissing(x, chr, reorder=FALSE, main="Missing genotypes",
alternate.chrid=FALSE, ...)
Arguments
x

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to plot. This should be a vector of
character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

reorder

Specify whether to reorder individuals according to their phenotypes.
FALSE
TRUE
n

Don’t reorder
Reorder according to the sum of the phenotypes
Reorder according to phenotype n

main
Title to place on plot.
alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
...

Ignored at this point.

Details
Uses image to plot a grid with black pixels where the genotypes are missing. For intercross and
4-way cross data, gray pixels are plotted for the partially missing genotypes (for example, "not
AA").
Value
None.
Author(s)
Karl W Broman, 

176

plotModel

See Also
plot.cross, geno.image, image
Examples
data(fake.f2)
plotMissing(fake.f2)

plotModel

Plot a QTL model

Description
Plot a graphical representation of a QTL model, with nodes representing QTL and line segments
representing pairwise interactions.
Usage
plotModel(qtl, formula, circrad.rel=0.25, circrad.abs,
cex.name=1, chronly=FALSE, order, ...)
Arguments
qtl

A QTL object (as created by makeqtl) or vector of character strings indicating
the names for the QTL. This is also allowed to be a list that contains a component
named "chr" (and, optionally, components names "pos" and "formula").

formula

Optional formula defining the QTL model. If missing, we look for an attribute
"formula" to the input QTL object or a item named "formula" within the QTL
object.

circrad.rel

Radius of the circles that indicate the QTL, relative to the distance between the
circles.

circrad.abs

Optional radius of the circles that indicate the QTL; note that the plotting region
will have x- and y-axis limits spanning 3 units.

cex.name

Character expansion for the QTL names.

chronly

If TRUE and a formal QTL object is given, only the chromosome IDs are used
to identify the QTL.

order

Optional vector indicating a permutation of the QTL to define where they are to
appear in the plot. QTL are placed around a circle, starting at the top and going
clockwise.

...

Passed to the function plot.

Value
None.
Author(s)
Karl W Broman, 

plotPheno

177

See Also
stepwiseqtl, makeqtl
Examples
# plot a QTL model, using a vector of character strings to define the QTL
plotModel(c("1","4","6","15"), formula=y~Q1+Q2+Q3*Q4)
# plot an additive QTL model
data(hyper)
hyper <- calc.genoprob(hyper)
qtl <- makeqtl(hyper, chr=c(1,4,6,15), pos=c(68.3,30,60,18), what="prob")
plotModel(qtl)
# include an interaction
plotModel(qtl, formula=y~Q1+Q2+Q3*Q4)
# alternatively, include the formula as an attribute to the QTL object
attr(qtl, "formula") <- y~Q1+Q2+Q3*Q4
plotModel(qtl)
# if formula given, the attribute within the object is ignored
plotModel(qtl, y~Q1+Q2+Q3+Q4)
# NULL formula indicates additive QTL model
plotModel(qtl, NULL)
# reorder the QTL in the figure
plotModel(qtl, order=c(1,3,4,2))
# show just the chromosome numbers
plotModel(qtl, chronly=TRUE)

plotPheno

Plot a phenotype distribution

Description
Plots a histogram or barplot of the data for a phenotype from an experimental cross.
Usage
plotPheno(x, pheno.col=1, ...)
Arguments
x

An object of class cross. See read.cross for details.

pheno.col

The phenotype column to plot: a numeric index, or the phenotype name as a
character string. Alternatively, one may give a numeric vector of phenotypes,
in which case it must have the length equal to the number of individuals in the
cross, and there must be either non-integers or values < 1 or > no. phenotypes;
this last case may be useful for studying transformations.

...

Passed to hist or barplot.

178

plotPXG

Details
√
Numeric phenotypes are displayed as histograms with approximately 2 n bins. Phenotypes that
are factors or that have very few unique values are displayed as barplots.
Value
None.
Author(s)
Karl W Broman, 
See Also
plot.cross, plotMap, plotMissing, hist, barplot
Examples
data(fake.bc)
plotPheno(fake.bc, pheno.col=1)
plotPheno(fake.bc, pheno.col=3)
plotPheno(fake.bc, pheno.col="age")

plotPXG

Plot phenotypes versus marker genotypes

Description
Plot the phenotype values versus the genotypes at a marker or markers.
Usage
plotPXG(x, marker, pheno.col=1, jitter=1, infer=TRUE,
pch, ylab, main, col, ...)
Arguments
x

An object of class cross. See read.cross for details.

marker

Marker name (a character string; can be a vector).

pheno.col

Column number in the phenotype matrix which should be used as the phenotype.
One may also give a character string matching a phenotype name. Finally, one
may give a numeric vector of phenotypes, in which case it must have the length
equal to the number of individuals in the cross, and there must be either nonintegers or values < 1 or > no. phenotypes; this last case may be useful for
studying transformations.

jitter

A positive number indicating how much to spread out the points horizontally.
(Larger numbers correspond to greater spread.)

infer

If TRUE, missing genotypes are filled in with a single random imputation and
plotted in red; if FALSE, only individuals typed at the specified marker are
plotted.

plotPXG

179

pch

Plot symbol.

ylab

Label for y-axis.

main

Main title for the plot. If missing, the names of the markers are used.

col

A vector of colors to use for the confidence intervals (optional).

...

Passed to plot.

Details
Plots the phenotype data against the genotypes at the specified marker. If infer=TRUE, the genotypes of individuals that were not typed is inferred based the genotypes at linked markers via a single
imputation from sim.geno; these points are plotted in red. For each genotype, the phenotypic mean
is plotted, with error bars at ± 1 SE.
Value
A data.frame with initial columns the marker genotypes, then the phenotype data, then a column
indicating whether any of the marker genotypes were inferred (1=at least one genotype inferred,
0=none were inferred).
Author(s)
Karl W Broman, ; Brian Yandell
See Also
find.marker, effectplot, find.flanking, effectscan
Examples
data(listeria)
mname <- find.marker(listeria, 5, 28) # marker D5M357
plotPXG(listeria, mname)
mname2 <- find.marker(listeria, 13, 26) # marker D13Mit147
plotPXG(listeria, c(mname, mname2))
plotPXG(listeria, c(mname2, mname))
# output of the function contains the raw data
output <- plotPXG(listeria, mname)
head(output)
# another example
data(fake.f2)
mname <- find.marker(fake.f2, 1, 37) # marker D1M437
plotPXG(fake.f2, mname)
mname2 <- find.marker(fake.f2, "X", 14) # marker DXM66
plotPXG(fake.f2, mname2)
plotPXG(fake.f2, c(mname,mname2))
plotPXG(fake.f2, c(mname2,mname))

180

plotRF

plotRF

Plot recombination fractions

Description
Plot a grid showing the recombination fractions for all pairs of markers, and/or the LOD scores for
tests of linkage between pairs of markers.
Usage
plotRF(x, chr, what=c("both","lod","rf"), alternate.chrid=FALSE,
zmax=12, mark.diagonal=FALSE,
col.scheme=c("viridis", "redblue"), ...)
Arguments
x

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to plot. This should be a vector of
character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

what
Indicate whether to plot LOD scores, recombination fractions or both.
alternate.chrid
If TRUE and more than one chromosome is plotted, alternate the placement of
chromosome axis labels, so that they may be more easily distinguished.
zmax

Maximum LOD score plotted; values above this are all thresholded at this value.

mark.diagonal

If TRUE, include black line segments around the pixels along the diagonal, to
better separate the upper left triangle from the lower right triangle.

col.scheme

The color palette. The default is "viridis"; see Option D at https://bids.
github.io/colormap

...

Generally ignored, but you can include main to change or omit the title of the
figure.

Details
Uses image to plot a grid showing the recombination fractions and/or LOD scores for all pairs of
markers. (The LOD scores are for a test of r = 1/2.) If both are plotted, the recombination fractions
are in the upper left triangle while the LOD scores are in the lower right triangle.
With col.scheme="viridis" (the default), purple corresponds to a large LOD score or a small
recombination fraction, while yellow is the reverse. With col.scheme="redblue", red corresponds
to a large LOD or a small recombination fraction, while blue is the reverse. Note that missing values
appear in light gray.
Recombination fractions are transformed by −4(log2 r + 1) to make them on the same sort of scale
as LOD scores. Values of LOD or the transformed recombination fraction that are above 12 are set
to 12.

pull.argmaxgeno

181

Value
None.
Author(s)
Karl W Broman, 
See Also
est.rf, pull.rf, plot.rfmatrix, image, badorder, ripple
Examples
data(badorder)
badorder <- est.rf(badorder)
plotRF(badorder)
# plot just chr 1
plotRF(badorder, chr=1)
# plot just the recombination fractions
plotRF(badorder, what="rf")
# plot just the LOD scores, and just for chr 2 and 3
plotRF(badorder, chr=2:3, what="lod")

pull.argmaxgeno

Pull out the results of the Viterbi algorithm from a cross

Description
Pull out the results of argmax.geno from a cross as a matrix.
Usage
pull.argmaxgeno(cross, chr, include.pos.info=FALSE, rotate=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.
include.pos.info
If TRUE, include columns with marker name, chromosmoe ID, and cM position.
(If include.pos.info=TRUE, we take rotate=TRUE.)

rotate

If TRUE, return matrix with individuals as columns and positions as rows. If
FALSE, rows correspond to individuals.

182

pull.draws

Value
A matrix containing numeric indicators of the inferred genotypes. Multiple chromosomes are pasted
together.
Author(s)
Karl W Broman, 
See Also
pull.geno, pull.genoprob, pull.draws, argmax.geno
Examples
data(listeria)
listeria <- argmax.geno(listeria, step=1, stepwidth="max")
amg <- pull.argmaxgeno(listeria, chr=c(5,13), include.pos.info=TRUE, rotate=TRUE)
amg[1:5,1:10]

pull.draws

Pull out the genotype imputations from a cross

Description
Pull out the results of sim.geno from a cross as an array.
Usage
pull.draws(cross, chr)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

Value
An array containing numeric indicators of the imputed genotypes. Multiple chromosomes are pasted
together. The dimensions are individuals by positions by imputations
Author(s)
Karl W Broman, 
See Also
pull.geno, pull.genoprob, pull.argmaxgeno, sim.geno

pull.geno

183

Examples
data(listeria)
listeria <- sim.geno(listeria, step=5, stepwidth="max", n.draws=8)
dr <- pull.draws(listeria, chr=c(5,13))
dr[1:20,1:10,1]

pull.geno

Pull out the genotype data from a cross

Description
Pull out the genotype data from a cross object, as a single big matrix.
Usage
pull.geno(cross, chr)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

Value
A matrix of size n.ind x tot.mar. The raw genotype data in the input cross object, with the chromosomes pasted together.
Author(s)
Karl W Broman, 
See Also
pull.pheno, pull.map pull.draws, pull.genoprob, pull.argmaxgeno
Examples
data(listeria)
dat <- pull.geno(listeria)
# image of the genotype data
image(1:ncol(dat),1:nrow(dat),t(dat),ylab="Individuals",xlab="Markers",
col=c("red","yellow","blue","green","violet"))
abline(v=cumsum(c(0,nmar(listeria)))+0.5)
abline(h=nrow(dat)+0.5)

184

pull.genoprob

pull.genoprob

Pull out the genotype probabilities from a cross

Description
Pull out the results of calc.genoprob from a cross as a matrix.
Usage
pull.genoprob(cross, chr, omit.first.prob=FALSE,
include.pos.info=FALSE, rotate=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

omit.first.prob
If TRUE, omit the probabilities for the first genotype at each position (since they
sum to 1).
include.pos.info
If TRUE, include columns with marker name, genotype, chromosome ID, and
cM position. (If include.pos.info=TRUE, we take rotate=TRUE.)
rotate

If TRUE, return matrix with individuals as columns and positions/genotypes as
rows. If FALSE, rows correspond to individuals.

Value
A matrix containing genotype probabilities. Multiple chromosomes and the multiple genotypes at
each position are pasted together.
Author(s)
Karl W Broman, 
See Also
pull.geno, pull.argmaxgeno, pull.draws, calc.genoprob
Examples
data(listeria)
listeria <- calc.genoprob(listeria, step=1, stepwidth="max")
pr <- pull.genoprob(listeria, chr=c(5,13), omit.first.prob=TRUE, include.pos.info=TRUE, rotate=TRUE)
pr[1:5,1:10]

pull.map

pull.map

185

Pull out the genetic map from a cross

Description
Pull out the map portion of a cross object.
Usage
pull.map(cross, chr, as.table=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

as.table

If TRUE, return the genetic map as a table with chromosome assignments and
marker names. If FALSE, return the map as a "map" object.

Value
The genetic map: a list with each component containing the marker positions (in cM) for a chromosome. Each component has class A or X according to whether it is an autosome or the X chromosome. The components are either vectors of marker positions or, for a sex-specific map, 2-row
matrices containing the female and male marker locations. The map itself is given class map.
Author(s)
Karl W Broman, 
See Also
replace.map, plotMap, map2table
Examples
data(fake.f2)
map <- pull.map(fake.f2)
plot(map)

186

pull.pheno

pull.markers

Drop all but a selected set of markers

Description
Drop all but a selected set of markers from the data matrices and genetic maps.
Usage
pull.markers(cross, markers)
Arguments
cross
markers

An object of class cross. See read.cross for details.
A character vector of marker names.

Value
The input object, with any markers not specified in the vector markers removed from the genotype
data matrices, genetic maps, and, if applicable, any derived data (such as produced by calc.genoprob).
(It might be a good idea to re-derive such things after using this function.)
Author(s)
Karl W Broman, 
See Also
drop.nullmarkers, drop.markers, geno.table, clean.cross
Examples
data(listeria)
listeria2 <- pull.markers(listeria, c("D10M44","D1M3","D1M75"))

pull.pheno

Pull out phenotype data from a cross

Description
Pull out selected phenotype data from a cross object, as a data frame or vector.
Usage
pull.pheno(cross, pheno.col)
Arguments
cross
pheno.col

An object of class cross. See read.cross for details.
A vector specifying which phenotypes to keep or discard. This may be a logical
vector, a numeric vector, or a vector of character strings (for the phenotype
names). If missing, the entire set of phenotypes is output.

pull.rf

187

Value
A data.frame with columns specifying phenotypes and rows specifying individuals. If there is just
one phenotype, a vector (rather than a data.frame) is returned.
Author(s)
Karl W Broman, 
See Also
pull.geno, pull.map
Examples
data(listeria)
pull.pheno(listeria, "sex")

pull.rf

Pull out recombination fractions or LOD scores from a cross object

Description
Pull out either the pairwise recombination fractions or the LOD scores, as calculated by est.rf,
from a cross object.
Usage
pull.rf(cross, what=c("rf", "lod"), chr)
Arguments
cross

An object of class cross. See read.cross for details.

what

Indicates whether to pull out a matrix of estimated recombination fractions or a
matrix of LOD scores.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

Value
An object of class "rfmatrix", which is a matrix of either estimated recombination fractions between all marker pairs or of LOD scores (for the test of rf=1/2) for all marker pairs.
The genetic map is included as an attribute.
Author(s)
Karl W Broman, 

188

read.cross

See Also
est.rf, plot.rfmatrix, plotRF
Examples
data(fake.f2)
fake.f2 <- est.rf(fake.f2)
rf <- pull.rf(fake.f2)
lod <- pull.rf(fake.f2, "lod")
plot(rf[1,], lod[1,], xlab="rec frac", ylab="LOD score")
marker <- markernames(fake.f2, chr=5)[6]
par(mfrow=c(2,1))
plot(rf, marker, bandcol="gray70")
plot(lod, marker, bandcol="gray70")

qtlversion

Installed version of R/qtl

Description
Print the version number of the currently installed version of R/qtl.
Usage
qtlversion()
Value
A character string with the version number of the currently installed version of R/qtl.
Author(s)
Karl W Broman, 
Examples
qtlversion()

read.cross

Read data for a QTL experiment

Description
Data for a QTL experiment is read from a set of files and converted into an object of class cross.
The comma-delimited format (csv) is recommended. All formats require chromosome assignments
for the genetic markers, and assume that markers are in their correct order.

read.cross

189

Usage
read.cross(format=c("csv", "csvr", "csvs", "csvsr", "mm", "qtx",
"qtlcart", "gary", "karl", "mapqtl", "tidy"),
dir="", file, genfile, mapfile, phefile, chridfile,
mnamesfile, pnamesfile, na.strings=c("-","NA"),
genotypes=c("A","H","B","D","C"), alleles=c("A","B"),
estimate.map=FALSE, convertXdata=TRUE, error.prob=0.0001,
map.function=c("haldane", "kosambi", "c-f", "morgan"),
BC.gen=0, F.gen=0, crosstype, ...)
Arguments
format

Specifies the format of the data.

dir

Directory in which the data files will be found. In Windows, use forward slashes
("/") or double backslashes ("\\") to specify directory trees.

file

The main input file for formats csv, csvr and mm.

genfile

File with genotype data (formats csvs, csvsr, karl, gary and mapqtl only).

mapfile

File with marker position information (all except the csv formats).

phefile

File with phenotype data (formats csvs, csvsr, karl, gary and mapqtl only).

chridfile

File with chromosome ID for each marker (gary format only).

mnamesfile

File with marker names (gary format only).

pnamesfile

File with phenotype names (gary format only).

na.strings

A vector of strings which are to be interpreted as missing values (csv and gary
formats only). For the csv formats, these are interpreted globally for the entire
file, so missing value codes in phenotypes must not be valid genotypes, and vice
versa. For the gary format, these are used only for the phenotype data.

genotypes

A vector of character strings specifying the genotype codes (csv formats only).
Generally this is a vector of length 5, with the elements corresponding to AA,
AB, BB, not BB (i.e., AA or AB), and not AA (i.e., AB or BB). Note: Pay careful attention to the third and fourth of these; the order of these can be confusing.
If you are trying to read 4-way cross data, your file must have genotypes coded
as described below, and you need to set genotypes=NULL so that no re-coding
gets done.

alleles

A vector of two one-letter character strings (or four, for the four-way cross), to
be used as labels for the two alleles.

estimate.map

For all formats but qtlcart, mapqtl, and karl: if TRUE and marker positions
are not included in the input files, the genetic map is estimated using the function
est.map.

convertXdata

If TRUE, any X chromosome genotype data is converted to the internal standard, using columns sex and pgm in the phenotype data if they available or by
inference if they are not. If FALSE, the X chromsome data is read as is.

error.prob

In the case that the marker map must be estimated: Assumed genotyping error rate used in the calculation of the penetrance Pr(observed genotype | true
genotype).

map.function

In the case that the marker map must be estimated: Indicates whether to use the
Haldane, Kosambi, Carter-Falconer, or Morgan map function when converting
genetic distances into recombination fractions. (Ignored if m > 0.)

190

read.cross
BC.gen
F.gen
crosstype
...

Used only for cross type "bcsft".
Used only for cross type "bcsft".
Optional character string to force a particular cross type.
Additional arguments, passed to the function read.table in the case of csv
and csvr formats. In particular, one may use the argument sep to specify the
field separator (the default is a comma), dec to specify the character used for the
decimal point (the default is a period), and comment.char to specify a character
to indicate comment lines.

Details
The available formats are comma-delimited (csv), rotated comma-delimited (csvr), comma-delimited
with separate files for genotype and phenotype data (csvs), rotated comma-delimited with separate
files for genotype and phenotype data (csvsr), Mapmaker (mm), Map Manager QTX (qtx), Gary
Churchill’s format (gary), Karl Broman’s format (karl) and MapQTL/JoinMap (mapqtl). The required files and their specification for each format appears below. The comma-delimited formats
are recommended. Note that most of these formats work only for backcross and intercross data.
The sampledata directory in the package distribution contains sample data files in multiple formats.
Also see https://rqtl.org/sampledata.
The ... argument enables additional arguments to be passed to the function read.table in the case
of csv and csvr formats. In particular, one may use the argument sep to specify the field separator
(the default is a comma), dec to specify the character used for the decimal point (the default is a
period), and comment.char to specify a character to indicate comment lines.
Value
An object of class cross, which is a list with two components:
geno

pheno

This is a list with elements corresponding to chromosomes. names(geno) contains the names of the chromsomes. Each chromosome is itself a list, and is
given class A or X according to whether it is autosomal or the X chromosome.
There are two components for each chromosome: data, a matrix whose rows are
individuals and whose columns are markers, and map, either a vector of marker
positions (in cM) or a matrix of dim (2 x n.mar) where the rows correspond to
marker positions in female and male genetic distance, respectively.
The genotype data gets converted into numeric codes, as follows.
The genotype data for a backcross is coded as NA = missing, 1 = AA, 2 = AB.
For an F2 intercross, the coding is NA = missing, 1 = AA, 2 = AB, 3 = BB, 4 =
not BB (i.e. AA or AB; D in Mapmaker/qtl), 5 = not AA (i.e. AB or BB; C in
Mapmaker/qtl).
For a 4-way cross, the mother and father are assumed to have genotypes AB and
CD, respectively. The genotype data for the progeny is assumed to be phaseknown, with the following coding scheme: NA = missing, 1 = AC, 2 = BC, 3 =
AD, 4 = BD, 5 = A = AC or AD, 6 = B = BC or BD, 7 = C = AC or BC, 8 = D =
AD or BD, 9 = AC or BD, 10 = AD or BC, 11 = not AC, 12 = not BC, 13 = not
AD, 14 = not BD.
data.frame of size (n.ind x n.phe) containing the phenotypes. If a phenotype with the name id or ID is included, these identifiers will be used in
top.errorlod, plotErrorlod, and plotGeno as identifiers for the individual.

While the data format is complicated, there are a number of functions, such as subset.cross, to
assist in pulling out portions of the data.

read.cross

191

X chromosome
The genotypes for the X chromosome require special care!
The X chromosome should be given chromosome identifier X or x. If it is labeled by a number or
by Xchr, it will be interpreted as an autosome.
The phenotype data should contain a column named "sex" which indicates the sex of each individual, either coded as 0=female and 1=male, or as a factor with levels female/male or f/m. Case will
be ignored both in the name and in the factor levels. If no such phenotype column is included, it
will be assumed that all individuals are of the same sex.
In the case of an intercross, the phenotype data may also contain a column named "pgm" (for
"paternal grandmother") indicating the direction of the cross. It should be coded as 0/1 with 0
indicating the cross (AxB)x(AxB) or (BxA)x(AxB) and 1 indicating the cross (AxB)x(BxA) or
(BxA)x(BxA). If no such phenotype column is included, it will be assumed that all individuals
come from the same direction of cross.
The internal storage of X chromosome data is quite different from that of autosomal data. Males
are coded 1=AA and 2=BB; females with pgm==0 are coded 1=AA and 2=AB; and females with
pgm==1 are coded 1=BB and 2=AB. If the argument convertXdata is TRUE, conversion to this
format is made automatically; if FALSE, no conversion is done, summary.cross will likely return
a warning, and most analyses will not work properly.
Use of convertXdata=FALSE (in which case the X chromosome genotypes will not be converted
to our internal standard) can be useful for diagnosing problems in the data, but will require some
serious mucking about in the internal data structure.
CSV format
The input file is a comma-delimited text file. A different field separator may be specified via the
argument sep, which will be passed to the function read.table). For example, in Europe, it is
common to use a comma in place of the decimal point in numbers and so a semi-colon in place of
a comma as the field separator; such data may be read by using sep=";" and dec=",".
The first line should contain the phenotype names followed by the marker names. At least one
phenotype must be included; for example, include a numerical index for each individual.
The second line should contain blanks in the phenotype columns, followed by chromosome identifiers for each marker in all other columns. If a chromosome has the identifier X or x, it is assumed
to be the X chromosome; otherwise, it is assumed to be an autosome.
An optional third line should contain blanks in the phenotype columns, followed by marker positions, in cM.
Marker order is taken from the cM positions, if provided; otherwise, it is taken from the column
order.
Subsequent lines should give the data, with one line for each individual, and with phenotypes followed by genotypes. If possible, phenotypes are made numeric; otherwise they are converted to
factors.
The genotype codes must be the same across all markers. For example, you can’t have one marker
coded AA/AB/BB and another coded A/H/B. This includes genotypes for the X chromosome, for
which hemizygous individuals should be coded as if they were homoyzogous.
The cross is determined to be a backcross if only the first two elements of the genotypes string are
found; otherwise, it is assumed to be an intercross.

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CSVr format
This is just like the csv format, but rotated (or really transposed), so that rows are columns and
columns are rows.
CSVs format
This is like the csv format, but with separate files for the genotype and phenotype data.
The first column in the genotype data must specify individuals’ identifiers, and there must be a
column in the phenotype data with precisely the same information (and with the same name). These
IDs will be included in the data as a phenotype. If the name id or ID is used, these identifiers will
be used in top.errorlod, plotErrorlod, and plotGeno as identifiers for the individual.
The first row in each file contains the column names. For the phenotype file, these are the names of
the phenotypes. For the genotype file, the first cell will be the name of the identifier column (id or
ID) and the subsequent fields will be the marker names.
In the genotype data file, the second row gives the chromosome IDs. The cell in the second row,
first column, must be blank. A third row giving cM positions of markers may be included, in which
case the cell in the third row, first column, must be blank.
There need be no blank rows in the phenotype data file.
CSVsr format
This is just like the csvs format, but with each file rotated (or really transposed), so that rows are
columns and columns are rows.
Mapmaker format
This format requires two files. The so-called rawfile, specified by the argument file, contains the
genotype and phenotype data. Rows beginning with the symbol # are ignored. The first line should
be either data type f2 intercross or data type f2 backcross. The second line should begin
with three numbers indicating the numbers of individuals, markers and phenotypes in the file. This
line may include the word symbols followed by symbol assignments (see the documentation for
mapmaker, and cross your fingers). The rest of the lines give genotype data followed by phenotype
data, with marker and phenotype names always beginning with the * symbol.
A second file contains the genetic map information, specified with the argument mapfile. The
map file may be in one of two formats. The function will determine which format of map file is
presented.
The simplest format for the map file is not standard for the Mapmaker software, but is easy to
create. The file contains two or three columns separated by white space and with no header row.
The first column gives the chromosome assignments. The second column gives the marker names,
with markers listed in the order along the chromosomes. An optional third column lists the map
positions of the markers.
Another possible format for the map file is the .maps format, which is produced by Mapmaker. The
code for reading this format was written by Brian Yandell.
Marker order is taken from the map file, either by the order they are presented or by the cM positions, if specified.
Map Manager QTX format
This format requires a single file (that produced by the Map Manager QTX program).

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QTL Cartographer format
This format requires two files: the .cro and .map files for QTL Cartographer (produced by the QTL
Cartographer sub-program, Rmap and Rcross).
Note that the QTL Cartographer cross types are converted as follows: RF1 to riself, RF2 to risib,
RF0 (doubled haploids) to bc, B1 or B2 to bc, RF2 or SF2 to f2.
Tidy format
This format requires three simple CSV files, separating the genotype, phenotype, and marker map
information so that each file may be of a simple form.
Gary format
This format requires the six files. All files have default names, and so the file names need not be
specified if the default names are used.
genfile (default = "geno.dat") contains the genotype data. The file contains one line per individual, with genotypes for the set of markers separated by white space. Missing values are coded as 9,
and genotypes are coded as 0/1/2 for AA/AB/BB.
mapfile (default = "markerpos.txt") contains two columns with no header row: the marker
names in the first column and their cM position in the second column. If marker positions are
not available, use mapfile=NULL, and a dummy map will be inserted.
phefile (default = "pheno.dat") contains the phenotype data, with one row for each mouse and
one column for each phenotype. There should be no header row, and missing values are coded as
"-".
chridfile (default = "chrid.dat") contains the chromosome identifier for each marker.
mnamesfile (default = "mnames.txt") contains the marker names.
pnamesfile (default = "pnames.txt") contains the names of the phenotypes. If phenotype names
file is not available, use pnamesfile=NULL; arbitrary phenotype names will then be assigned.
Karl format
This format requires three files; all files have default names, and so need not be specified if the
default name is used.
genfile (default = "gen.txt") contains the genotype data. The file contains one line per individual, with genotypes separated by white space. Missing values are coded 0; genotypes are coded as
1/2/3/4/5 for AA/AB/BB/not BB/not AA.
mapfile (default = "map.txt") contains the map information, in the following complicated format:
n.chr
n.mar(1) rf(1,1) rf(1,2) ... rf(1,n.mar(1)-1)
mar.name(1,1)
mar.name(1,2)
...
mar.name(1,n.mar(1))
n.mar(2)
...
etc.
phefile (default = "phe.txt") contains a matrix of phenotypes, with one individual per line. The
first line in the file should give the phenotype names.

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MapQTL format
This format requires three files, described in the manual of the MapQTL program (same as JoinMap).
genfile corresponds to the loc file containing the genotype data. Each marker and its genotypes
should be on a single line.
mapfile corresponds to the map file containing the linkage group assignment, marker names and
their map positions.
phefile corresponds to the qua file containing the phenotypes.
For the moment, only 4-way crosses are supported (CP population type in MapQTL).
Author(s)
Karl W Broman, ; Brian S. Yandell; Aaron Wolen
References
Broman, K. W. and Sen, Ś. (2009) A guide to QTL mapping with R/qtl. Springer. https://rqtl.
org/book
See Also
subset.cross, summary.cross, plot.cross, c.cross, clean.cross, write.cross, sim.cross,
read.table. The sampledata directory in the package distribution contains sample data files in
multiple formats. Also see https://rqtl.org/sampledata.
Examples
## Not run:
# CSV format
dat1 <- read.cross("csv", dir="Mydata", file="mydata.csv")
# CSVS format
dat2 <- read.cross("csvs", dir="Mydata", genfile="mydata_gen.csv",
phefile="mydata_phe.csv")
# you can read files directly from the internet
datweb <- read.cross("csv", "https://rqtl.org/sampledata",
"listeria.csv")
# Mapmaker format
dat3 <- read.cross("mm", dir="Mydata", file="mydata.raw",
mapfile="mydata.map")
# Map Manager QTX format
dat4 <- read.cross("qtx", dir="Mydata", file="mydata.qtx")
# QTL Cartographer format
dat5 <- read.cross("qtlcart", dir="Mydata", file="qtlcart.cro",
mapfile="qtlcart.map")
# Gary format
dat6 <- read.cross("gary", dir="Mydata", genfile="geno.dat",
mapfile="markerpos.txt", phefile="pheno.dat",
chridfile="chrid.dat", mnamesfile="mnames.txt",

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195
pnamesfile="pnames.txt")

# Karl format
dat7 <- read.cross("karl", dir="Mydata", genfile="gen.txt",
phefile="phe.txt", mapfile="map.txt")
## End(Not run)

readMWril

Read data for 4- or 8-way RIL

Description
Data for a set of 4- or 8-way recombinant inbred lines (RIL) is read from a pair of comma-delimited
files and converted into an object of class cross. We require chromosome assignments for the
genetic markers, and assume that markers are in their correct order.
Usage
readMWril(dir="", rilfile, founderfile,
type=c("ri4self", "ri4sib", "ri8self", "ri8selfIRIP1", "ri8sib", "bgmagic16"),
na.strings=c("-","NA"), rotate=FALSE, ...)
Arguments
dir
rilfile
founderfile
type
na.strings

rotate
...

Directory in which the data files will be found. In Windows, use forward slashes
("/") or double backslashes ("\\") to specify directory trees.
Comma-delimited file for the RIL, in the "csv" format described in the help file
for read.cross.
File with founder strains’ genotypes, in the same orientation as the rilfile, but
with just marker names and the founders’ marker genotypes.
The type of RIL.
A vector of strings which are to be interpreted as missing values. For the csv
formats, these are interpreted globally for the entire file, so missing value codes
in phenotypes must not be valid genotypes, and vice versa. For the gary format,
these are used only for the phenotype data.
If TRUE, the rilfile and founderfile are rotated (really transposed), with
rows corresponding to markers and columns corresponding to individuals.
Additional arguments, passed to the function read.table in the case of csv and
csvr formats. In particular, one may use the argument sep to specify the field
separator (the default is a comma) and dec to specify the character used for the
decimal point (the default is a period).

Details
The rilfile should include a phenotype cross containing character strings of the form ABCDEFGH,
indicating the cross used to generate each RIL. The genotypes should be coded as integers (e.g., 1
and 2).
The founder strains in the founderfile should be the strains A, B, C, . . . , as indicated in the cross
phenotype.
The default arrangement of the files is to have markers as columns and individuals/founders as rows.
If rotate=TRUE, do the opposite: markers as rows and individuals/founders as columns.

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reduce2grid

Value
An object of class cross; see the help file for read.cross for details.
An additional component crosses is included; this is a matrix indicating the crosses used to generate the RIL.
Author(s)
Karl W Broman, 
See Also
read.cross, sim.cross
Examples
## Not run:
ril <- read.cross("../Data", "ril_data.csv", "founder_geno.csv", "ri4self",
rotate=TRUE)
## End(Not run)

reduce2grid

Reduce to a grid of pseudomarkers.

Description
For high-density marker data, rather than run scanone at both the markers and at a set of pseudomarkers, we reduce to just a set of evenly-spaced pseudomarkers
Usage
reduce2grid(cross)
Arguments
cross

An object of class cross. See read.cross for details.

Details
Genotype probabilities (from calc.genoprob) and/or imputations (from sim.geno) are subset to a
grid of pseudomarkers.
This is so that, in the case of high-density markers, we can do the genome scan calculations at a
smaller set of points (on an evenly-spaced grid, but not at the markers) to save computation time.
You need to first have run calc.genoprob and/or sim.geno, and you must use stepwidth="fixed".
When plotting results with plot.scanone, use incl.markers=FALSE, as the output of scanone
won’t include information about the marker locations and so will plot tick marks only at the first
marker on each chromosome.
Value
The input cross object with included genotype probabilities or imputations subset to an evenlyspaced grid.

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197

Author(s)
Karl W Broman, 
See Also
calc.genoprob, sim.geno, scanone, plot.scanone
Examples
data(hyper)
hyper <- calc.genoprob(hyper, step=2)
hypersub <- reduce2grid(hyper)
## Not run: out <- scanone(hypersub)
plot(out, incl.markers=FALSE)
## End(Not run)

refineqtl

Refine the positions of QTL

Description
Iteratively scan the positions for QTL in the context of a multiple QTL model, to try to identify the
positions with maximum likelihood, for a fixed QTL model.
Usage
refineqtl(cross, pheno.col=1, qtl, chr, pos, qtl.name, covar=NULL, formula,
method=c("imp","hk"), model=c("normal", "binary"), verbose=TRUE, maxit=10,
incl.markers=TRUE, keeplodprofile=TRUE, tol=1e-4,
maxit.fitqtl=1000, forceXcovar=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

pheno.col

Column number in the phenotype matrix to be used as the phenotype. One may
also give a character string matching the phenotype name. Finally, one may give
a numeric vector of phenotypes, in which case it must have the length equal to
the number of individuals in the cross, and there must be either non-integers
or values < 1 or > no. phenotypes; this last case may be useful for studying
transformations.

qtl

A QTL object, as produced by makeqtl, containing the positions of the QTL.
Provide either qtl or the pair chr and pos.

chr

Vector indicating the chromosome for each QTL; if qtl is provided, this should
not be.

pos

Vector indicating the positions for each QTL; if qtl is provided, this should not
be.

qtl.name

Optional user-specified name for each QTL. If qtl is provided, this should not
be.

covar

A matrix or data.frame of covariates. These must be strictly numeric.

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refineqtl
formula

An object of class formula indicating the model to be fitted. (It can also be the
character string representation of a formula.) QTLs are indicated as Q1, Q2, etc.
Covariates are indicated by their names in covar.

method

Indicates whether to use multiple imputation or Haley-Knott regression.

model

The phenotype model: the usual model or a model for binary traits

verbose

If TRUE, give feedback about progress. If verbose is an integer > 1, further
messages from scanqtl are also displayed.

maxit

Maximum number of iterations.

incl.markers

If FALSE, do calculations only at points on an evenly spaced grid.

keeplodprofile If TRUE, keep the LOD profiles from the last iteration as attributes to the output.
tol

Tolerance for convergence for the binary trait model.

maxit.fitqtl

Maximum number of iterations for fitting the binary trait model.

forceXcovar

If TRUE, force inclusion of X-chr-related covariates (like sex and cross direction).

Details
QTL positions are optimized, within the context of a fixed QTL model, by a scheme described
in Zeng et al. (1999). Each QTL is considered one at a time (in a random order), and a scan is
performed, allowing the QTL to vary across its chromosome, keeping the positions of all other
QTL fixed. If there is another QTL on the chromosome, the position of the floating QTL is scanned
from the end of the chromosome to the position of the flanking QTL. If the floating QTL is between
two QTL on a chromosome, its position is scanned between those two QTL positions. Each QTL
is moved to the position giving the highest likelihood, and the entire process is repeated until no
further improvement in likelihood can be obtained.
One may provide either a qtl object (as produced by makeqtl), or vectors chr and pos (and,
optionally, qtl.name) indicating the positions of the QTL.
If a qtl object is provided, QTL that do not appear in the model formula are ignored, but they
remain part of the QTL object that is output.
Value
An object of class qtl, with QTL placed in their new positions.
If keeplodprofile=TRUE, LOD profiles from the last pass through the refinement algorithm are
retained as an attribute, "lodprofile", to the object. These may be plotted with plotLodProfile.
Author(s)
Karl W Broman, 
References
Zeng, Z.-B., Kao, C.-H., and Basten, C. J. (1999) Estimating the genetic architecture of quantitative
traits. Genet. Res. 74, 279–289.
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.

reorderqtl

199

See Also
fitqtl, makeqtl, scanqtl, addtoqtl, dropfromqtl, replaceqtl, plotLodProfile
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=2)
qtl <- makeqtl(fake.bc, chr=c(2,5), pos=c(32.5, 17.5), what="prob")
rqtl <- refineqtl(fake.bc, qtl=qtl, method="hk")

reorderqtl

Reorder the QTL in a qtl object

Description
This function changes the order of the QTL in a QTL object.
Usage
reorderqtl(qtl, neworder)
Arguments
qtl

A qtl object, as created by makeqtl.

neworder

A vector containing the positive integers up to the number of QTL in qtl, indicating the new order for the QTL. If missing, the QTL are ordered by chromosome and then by their position within a chromosome.

Details
Everything in the input qtl is reordered except the altname component, which contains names of
the form Q1, Q2, etc.
Value
The input qtl object, with the loci reordered.
Author(s)
Karl W Broman, 
See Also
makeqtl, fitqtl, dropfromqtl, addtoqtl, replaceqtl

200

replace.map

Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c(1, 6, 13)
qp <- c(25.8, 33.6, 18.63)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- calc.genoprob(fake.f2)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
qtl <- reorderqtl(qtl, c(2,3,1))
qtl
qtl <- reorderqtl(qtl)
qtl

replace.map

Replace the genetic map of a cross

Description
Replace the map portion of a cross object.
Usage
replace.map(cross, map)
## S3 method for class 'cross'
replacemap(object, map)
Arguments
cross

An object of class cross. See read.cross for details.

object

Same as cross.

map

A list containing the new genetic map. This must be the same length and with
the same marker names as that contained in cross.

Value
The input cross object with the genetic map replaced by the input map. Maps for results from
calc.genoprob, sim.geno and argmax.geno are also replaced, using interpolation if necessary.
Author(s)
Karl W Broman, 
See Also
pull.map, est.map

replacemap.scanone

201

Examples
data(fake.f2)
newmap <- est.map(fake.f2)
plotMap(fake.f2, newmap)
fake.f2 <- replace.map(fake.f2, newmap)

replacemap.scanone

Replace the genetic map in QTL mapping results with an alternate
map

Description
Replace the positions of LOD scores in output from scanone with values based on an alternative
map (such as a physical map), with pseudomarker locations determined by linear interpolation.
Usage
## S3 method for class 'scanone'
replacemap(object, map)
Arguments
object

An object of class "scanone", as output by the function scanone.

map

A list containing the alternative genetic map. All chromosomes in object
should have corresponding chromosomes in map, and markers must be in the
same order in the two maps. There must be at least two markers on each chromosome in map that appear in object.

Details
The positions of pseudomarkers are determined by linear interpolation between markers. In the case
of pseudomarkers beyond the ends of the terminal markers on chromosomes, we use the overall
lengths of the chromosome in object and map to determine the new spacing.
Value
The input object with the positions of LOD scores revised to match those in the input map.
Author(s)
Karl W Broman, 
See Also
replacemap.cross, est.map, replacemap.scantwo

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replacemap.scantwo

Examples
data(fake.f2)
origmap <- pull.map(fake.f2)
newmap <- est.map(fake.f2)
fake.f2 <- replacemap(fake.f2, newmap)
fake.f2 <- calc.genoprob(fake.f2, step=2.5)
out <- scanone(fake.f2, method="hk")
out.rev <- replacemap(out, origmap)

replacemap.scantwo

Replace the genetic map in QTL mapping results with an alternate
map

Description
Replace the positions of LOD scores in output from scantwo with values based on an alternative
map (such as a physical map), with pseudomarker locations determined by linear interpolation.
Usage
## S3 method for class 'scantwo'
replacemap(object, map)
Arguments
object

An object of class "scantwo", as output by the function scantwo.

map

A list containing the alternative genetic map. All chromosomes in object
should have corresponding chromosomes in map, and markers must be in the
same order in the two maps. There must be at least two markers on each chromosome in map that appear in object.

Details
The positions of pseudomarkers are determined by linear interpolation between markers. In the case
of pseudomarkers beyond the ends of the terminal markers on chromosomes, we use the overall
lengths of the chromosome in object and map to determine the new spacing.
Value
The input object with the positions of LOD scores revised to match those in the input map.
Author(s)
Karl W Broman, 
See Also
replacemap.cross, est.map, replacemap.scanone

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203

Examples
data(hyper)
origmap <- pull.map(hyper)
newmap <- est.map(hyper)
hyper <- replacemap(hyper, newmap)
hyper <- calc.genoprob(hyper, step=0)
out <- scantwo(hyper, method="hk")
out.rev <- replacemap(out, origmap)

replaceqtl

Replace a QTL in a qtl object with a different position

Description
This function replaces a QTL or QTLs in a qtl object with a different position.
Usage
replaceqtl(cross, qtl, index, chr, pos, qtl.name, drop.lod.profile=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

qtl

A qtl object, as created by makeqtl.

index

Numeric index indicating the QTL to be replaced.

chr

Vector (of same length as index) indicating the chromosomes for the new QTL.

pos

Vector (of same length as index) indicating the positions for the new QTL. If
there is no marker or pseudomarker at a position, the nearest position is used.

qtl.name

Optional vector (of same length as index) of user-specified names for each new
QTL, used in the drop-one-term ANOVA table in fitqtl. If unspecified, the
names will be of the form "Chr1@10" for a QTL on Chromsome 1 at 10 cM.
drop.lod.profile
If TRUE, remove any LOD profiles from the object.

Value
The input qtl object, but with some QTL replaced by new ones. See makeqtl for details on the
format.
Author(s)
Karl W Broman, 
See Also
makeqtl, fitqtl, dropfromqtl, addtoqtl, reorderqtl

204

rescalemap

Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c(1, 6, 13)
qp <- c(25.8, 33.6, 18.63)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
qtl <- replaceqtl(fake.f2, qtl, 2, 6, 48.1)

rescalemap

Rescale genetic maps

Description
Rescale a genetic map by multiplying all positions by a constant
Usage
rescalemap(object, scale=1e-6)
Arguments
object

An object of class cross (see read.cross for details) or map (see sim.map for
details).

scale

Scale factor by which all positions will be multiplied.

Details
This function is included particularly for the case that map positions in a cross object were provided
in basepairs and one wishes to quickly convert them to Mbp or some other approximation of cM
distances. (In the mouse, 1 cM is approximation 2 Mbp, so one might use scale=5e-7 in this
function.)
Value
If the input is a map object, a map object is returned; if the input is a cross object, a cross object is
returned. In either case, the positions of markers are simply multiplied by scale.
Author(s)
Karl W Broman, 
See Also
replace.map, est.map

ripple

205

Examples
data(hyper)
rescaled <- rescalemap(hyper, scale=2)
plotMap(hyper, rescaled)

ripple

Compare marker orders

Description
Investigate different marker orders for a given chromosome, comparing all possible permutations
of a sliding window of markers.
Usage
ripple(cross, chr, window=4, method=c("countxo","likelihood"),
error.prob=0.0001, map.function=c("haldane","kosambi","c-f","morgan"),
maxit=4000, tol=1e-6, sex.sp=TRUE, verbose=TRUE, n.cluster=1)
Arguments
cross

An object of class cross. See read.cross for details.

chr

The chromosome to investigate. Only one chromosome is allowed. (This should
be a character string referring to the chromosomes by name.)

window

Number of markers to include in the sliding window of permuted markers.
Larger numbers result in the comparison of a greater number of marker orders,
but will require a considerable increase in computation time.

method

Indicates whether to compare orders by counting the number of obligate crossovers,
or by a likelihood analysis.

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi, Carter-Falconer, or Morgan map
function when converting genetic distances into recombination fractions.

maxit

Maximum number of EM iterations to perform.

tol

Tolerance for determining convergence.

sex.sp

Indicates whether to estimate sex-specific maps; this is used only for the 4-way
cross.

verbose

If TRUE, information about the number of orders (and, if method="likelihood",
about progress) are printed.

n.cluster

If the package snow is available and n.perm > 0, permutations are run in parallel
using this number of nodes. This is really only useful with method="likelihood".

Details
For method="likelihood", calculations are done by first constructing a matrix of marker orders
and then making repeated calls to the R function est.map. Of course, it would be faster to do
everything within C, but this was a lot easier to code.
For method="countxo", calculations are done within C.

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scanone

Value
A matrix, given class "ripple"; the first set of columns are marker indices describing the order.
In the case of method="countxo", the last column is the number of obligate crossovers for each
particular order. In the case of method="likelihood", the last two columns are LOD scores (log
base 10 likelihood ratios) comparing each order to the initial order and the estimated chromosome
length for the given order. Positive LOD scores indicate that the alternate order has more support
than the original.
Author(s)
Karl W Broman, 
See Also
summary.ripple, switch.order, est.map, est.rf
Examples
data(badorder)
rip1 <- ripple(badorder, chr=1, window=3)
summary(rip1)
## Not run:
rip2 <- ripple(badorder, chr=1, window=2, method="likelihood")
summary(rip2)
## End(Not run)
badorder <- switch.order(badorder, 1, rip1[2,])

scanone

Genome scan with a single QTL model

Description
Genome scan with a single QTL model, with possible allowance for covariates, using any of several
possible models for the phenotype and any of several possible numerical methods.
Usage
scanone(cross, chr, pheno.col=1, model=c("normal","binary","2part","np"),
method=c("em","imp","hk","ehk","mr","mr-imp","mr-argmax"),
addcovar=NULL, intcovar=NULL, weights=NULL,
use=c("all.obs", "complete.obs"), upper=FALSE,
ties.random=FALSE, start=NULL, maxit=4000,
tol=1e-4, n.perm, perm.Xsp=FALSE, perm.strata=NULL, verbose,
batchsize=250, n.cluster=1, ind.noqtl)

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Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes for which LOD scores should be
calculated. This should be a vector of character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes
with a preceding - to have all chromosomes but those considered. A logical
(TRUE/FALSE) vector may also be used.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype. This can be a vector of integers; for methods "hk" and "imp" this can be
considerably faster than doing them one at a time. One may also give a character strings matching the phenotype names. Finally, one may give a numeric
vector of phenotypes, in which case it must have the length equal to the number
of individuals in the cross, and there must be either non-integers or values < 1
or > no. phenotypes; this last case may be useful for studying transformations.

model

The phenotype model: the usual normal model, a model for binary traits, a twopart model or non-parametric analysis

method

Indicates whether to use the EM algorithm, imputation, Haley-Knott regression,
the extended Haley-Knott method, or marker regression. Not all methods are
available for all models. Marker regression is performed either by dropping individuals with missing genotypes ("mr"), or by first filling in missing data using
a single imputation ("mr-imp") or by the Viterbi algorithm ("mr-argmax").

addcovar

Additive covariates; allowed only for the normal and binary models.

intcovar

Interactive covariates (interact with QTL genotype); allowed only for the normal
and binary models.

weights

Optional weights of individuals. Should be either NULL or a vector of length
n.ind containing positive weights. Used only in the case model="normal".

use

In the case that multiple phenotypes are selected to be scanned, this argument indicates whether to use all individuals, including those missing some phenotypes,
or just those individuals that have data on all selected phenotypes.

upper

Used only for the two-part model; if true, the "undefined" phenotype is the maximum observed phenotype; otherwise, it is the smallest observed phenotype.

ties.random

Used only for the non-parametric "model"; if TRUE, ties in the phenotypes are
ranked at random. If FALSE, average ranks are used and a corrected LOD score
is calculated.

start

Used only for the EM algorithm with the normal model and no covariates. If
NULL, use the usual starting values; if length 1, use random initial weights for
EM; otherwise, this should be a vector of length n+1 (where n is the number of
possible genotypes for the cross), giving the initial values for EM.

maxit

Maximum number of iterations for methods "em" and "ehk".

tol

Tolerance value for determining convergence for methods "em" and "ehk".

n.perm

If specified, a permutation test is performed rather than an analysis of the observed data. This argument defines the number of permutation replicates.

perm.Xsp

If n.perm > 0, so that a permutation test will be performed, this indicates whether
separate permutations should be performed for the autosomes and the X chromosome, in order to get an X-chromosome-specific LOD threshold. In this case,
additional permutations are performed for the X chromosome.

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perm.strata

If n.perm > 0, this may be used to perform a stratified permutation test. This
should be a vector with the same number of individuals as in the cross data.
Unique values indicate the individual strata, and permutations will be performed
within the strata.

verbose

In the case n.perm is specified, display information about the progress of the
permutation tests.

batchsize

The number of phenotypes (or permutations) to be run as a batch; used only for
methods "hk" and "imp".

n.cluster

If the package snow is available and n.perm > 0, permutations are run in parallel
using this number of nodes.

ind.noqtl

Indicates individuals who should not be allowed a QTL effect (used rarely, if at
all); this is a logical vector of same length as there are individuals in the cross.

Details
Use of the EM algorithm, Haley-Knott regression, and the extended Haley-Knott method require
that multipoint genotype probabilities are first calculated using calc.genoprob. The imputation
method uses the results of sim.geno.
Individuals with missing phenotypes are dropped.
In the case that n.perm>0, so that a permutation test is performed, the R function scanone is called
repeatedly. If perm.Xsp=TRUE, separate permutations are performed for the autosomes and the X
chromosome, so that an X-chromosome-specific threshold may be calculated. In this case, n.perm
specifies the number of permutations used for the autosomes; for the X chromosome, n.perm
× LA /LX permutations will be run, where LA and LX are the total genetic lengths of the autosomes and X chromosome, respectively. More permutations are needed for the X chromosome in
order to obtain thresholds of similar accuracy.
For further details on the models, the methods and the use of covariates, see below.
Value
If n.perm is missing, the function returns a data.frame whose first two columns contain the chromosome IDs and cM positions. Subsequent columns contain the LOD scores for each phenotype. In
the case of the two-part model, there are three LOD score columns for each phenotype: LOD(p, µ),
LOD(p) and LOD(µ). The result is given class "scanone" and has attributes "model", "method",
and "type" (the latter is the type of cross analyzed).
If n.perm is specified, the function returns the results of a permutation test and the output has class
"scanoneperm". If perm.Xsp=FALSE, the function returns a matrix with n.perm rows, each row
containing the genome-wide maximum LOD score for each of the phenotypes. In the case of the
two-part model, there are three columns for each phenotype, corresponding to the three different
LOD scores. If perm.Xsp=TRUE, the result contains separate permutation results for the autosomes
and the X chromosome respectively, and an attribute indicates the lengths of the chromosomes and
an indicator of which chromosome is X.
Models
The normal model is the standard model for QTL mapping (see Lander and Botstein 1989). The
residual phenotypic variation is assumed to follow a normal distribution, and analysis is analogous
to analysis of variance.
The binary model is for the case of a binary phenotype, which must have values 0 and 1. The
proportions of 1’s in the different genotype groups are compared. Currently only methods em, hk,
and mr are available for this model. See Xu and Atchley (1996) and Broman (2003).

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209

The two-part model is appropriate for the case of a spike in the phenotype distribution (for example, metastatic density when many individuals show no metastasis, or survival time following an
infection when individuals may recover from the infection and fail to die). The two-part model was
described by Boyartchuk et al. (2001) and Broman (2003). Individuals with QTL genotype g have
probability pg of having an undefined phenotype (the spike), while if their phenotype is defined,
it comes from a normal distribution with mean µg and common standard deviation σ. Three LOD
scores are calculated: LOD(p, µ) is for the test of the hypothesis that pg = p and µg = µ. LOD(p)
is for the test that pg = p while the µg may vary. LOD(µ) is for the test that µg = µ while the pg
may vary.
With the non-parametric "model", an extension of the Kruskal-Wallis test is used; this is similar to the method described by Kruglyak and Lander (1995). In the case of incomplete genotype
information (such as at locations between genetic markers), the Kruskal-Wallis statistic is modified
so that the rank for each individual is weighted by the genotype probabilities, analogous to HaleyKnott regression. For this method, if the argument ties.random is TRUE, ties in the phenotypes
are assigned random ranks; if it is FALSE, average ranks are used and a corrected LOD score is
calculate. Currently the method argument is ignored for this model.
Methods
em: maximum likelihood is performed via the EM algorithm (Dempster et al. 1977), first used in
this context by Lander and Botstein (1989).
imp: multiple imputation is used, as described by Sen and Churchill (2001).
hk: Haley-Knott regression is used (regression of the phenotypes on the multipoint QTL genotype
probabilities), as described by Haley and Knott (1992).
ehk: the extended Haley-Knott method is used (like H-K, but taking account of the variances), as
described in Feenstra et al. (2006).
mr: Marker regression is used. Analysis is performed only at the genetic markers, and individuals
with missing genotypes are discarded. See Soller et al. (1976).
Covariates
Covariates are allowed only for the normal and binary models. The normal model is y = βq +
Aγ + Zδq +  where q is the unknown QTL genotype, A is a matrix of additive covariates, and Z
is a matrix of covariates that interact with the QTL genotype. The columns of Z are forced to be
contained in the matrix A. The binary model is the logistic regression analog.
The LOD score is calculated comparing the likelihood of the above model to that of the null model
y = µ + Aγ + .
Covariates must be numeric matrices. Individuals with any missing covariates are discarded.
X chromosome
The X chromosome must be treated specially in QTL mapping. See Broman et al. (2006).
If both males and females are included, male hemizygotes are allowed to be different from female
homozygotes. Thus, in a backcross, we will fit separate means for the genotype classes AA, AB,
AY, and BY. In such cases, sex differences in the phenotype could cause spurious linkage to the
X chromosome, and so the null hypothesis must be changed to allow for a sex difference in the
phenotype.
Numerous special cases must be considered, as detailed in the following table.
BC

Sexes

Null

Alternative

df

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F2

Direction
Both

Forward

Backward

both sexes
all female
all male

sex
grand mean
grand mean

AA/AB/AY/BY
AA/AB
AY/BY

2
1
1

Sexes
both sexes
all female
all male
both sexes
all female
all male
both sexes
all female
all male

Null
femaleF/femaleR/male
pgm
grand mean
sex
grand mean
grand mean
sex
grand mean
grand mean

Alternative
AA/ABf/ABr/BB/AY/BY
AA/ABf/ABr/BB
AY/BY
AA/AB/AY/BY
AA/AB
AY/BY
AB/BB/AY/BY
AB/BB
AY/BY

df
3
2
1
2
1
1
2
1
1

In the case that the number of degrees of freedom for the linkage test for the X chromosome is different from that for autosomes, a separate X-chromosome LOD threshold is recommended. Autosomeand X-chromosome-specific LOD thresholds may be estimated by permutation tests with scanone
by setting n.perm>0 and using perm.Xsp=TRUE.
Author(s)
Karl W Broman, ; Hao Wu
References
Boyartchuk, V. L., Broman, K. W., Mosher, R. E., D’Orazio S. E. F., Starnbach, M. N. and Dietrich,
W. F. (2001) Multigenic control of Listeria monocytogenes susceptibility in mice. Nature Genetics
27, 259–260.
Broman, K. W. (2003) Mapping quantitative trait loci in the case of a spike in the phenotype distribution. Genetics 163, 1169–1175.
Broman, K. W., Sen, Ś, Owens, S. E., Manichaikul, A., Southard-Smith, E. M. and Churchill G. A.
(2006) The X chromosome in quantitative trait locus mapping. Genetics, 174, 2151–2158.
Churchill, G. A. and Doerge, R. W. (1994) Empirical threshold values for quantitative trait mapping.
Genetics 138, 963–971.
Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977) Maximum likelihood from incomplete data
via the EM algorithm. J. Roy. Statist. Soc. B, 39, 1–38.
Feenstra, B., Skovgaard, I. M. and Broman, K. W. (2006) Mapping quantitative trait loci by an
extension of the Haley-Knott regression method using estimating equations. Genetics, 173, 2111–
2119.
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
Kruglyak, L. and Lander, E. S. (1995) A nonparametric approach for mapping quantitative trait loci.
Genetics 139, 1421–1428.
Lander, E. S. and Botstein, D. (1989) Mapping Mendelian factors underlying quantitative traits
using RFLP linkage maps. Genetics 121, 185–199.
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.

scanone

211

Soller, M., Brody, T. and Genizi, A. (1976) On the power of experimental designs for the detection
of linkage between marker loci and quantitative loci in crosses between inbred lines. Theor. Appl.
Genet. 47, 35–39.
Xu, S., and Atchley, W.R. (1996) Mapping quantitative trait loci for complex binary diseases using
line crosses. Genetics 143, 1417–1424.
See Also
plot.scanone, summary.scanone, scantwo, calc.genoprob, sim.geno, max.scanone, summary.scanoneperm,
-.scanone, +.scanone
Examples
###################
# Normal Model
###################
data(hyper)
# Genotype probabilities for EM and H-K
## Not run: hyper <- calc.genoprob(hyper, step=2.5)
out.em <- scanone(hyper, method="em")
out.hk <- scanone(hyper, method="hk")
# Summarize results: peaks above 3
summary(out.em, thr=3)
summary(out.hk, thr=3)
# An alternate method of summarizing:
#
patch them together and then summarize
out <- c(out.em, out.hk)
summary(out, thr=3, format="allpeaks")
# Plot the results
plot(out.hk, out.em)
plot(out.hk, out.em, chr=c(1,4), lty=1, col=c("blue","black"))
# Imputation; first need to run sim.geno
# Do just chromosomes 1 and 4, to save time
## Not run: hyper.c1n4 <- sim.geno(subset(hyper, chr=c(1,4)),
step=2.5, n.draws=8)
## End(Not run)
out.imp <- scanone(hyper.c1n4, method="imp")
summary(out.imp, thr=3)
# Plot all three results
plot(out.imp, out.hk, out.em, chr=c(1,4), lty=1,
col=c("red","blue","black"))
# extended Haley-Knott
out.ehk <- scanone(hyper, method="ehk")
plot(out.hk, out.em, out.ehk, chr=c(1,4))
# Permutation tests
## Not run: permo <- scanone(hyper, method="hk", n.perm=1000)

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# Threshold from the permutation test
summary(permo, alpha=c(0.05, 0.10))
# Results above the 0.05 threshold
summary(out.hk, perms=permo, alpha=0.05)
####################
# scan with square-root of phenotype
# (Note that pheno.col can be a vector of phenotype values)
####################
out.sqrt <- scanone(hyper, pheno.col=sqrt(pull.pheno(hyper, 1)))
plot(out.em - out.sqrt, ylim=c(-0.1,0.1),
ylab="Difference in LOD")
abline(h=0, lty=2, col="gray")
####################
# Stratified permutations
####################
extremes <- (nmissing(hyper)/totmar(hyper) < 0.5)
## Not run: operm.strat <- scanone(hyper, method="hk", n.perm=1000,
perm.strata=extremes)
## End(Not run)
summary(operm.strat)

####################
# X-specific permutations
####################
data(fake.f2)
## Not run: fake.f2 <- calc.genoprob(fake.f2, step=2.5)
# genome scan
out <- scanone(fake.f2, method="hk")
# X-chr-specific permutations
## Not run: operm <- scanone(fake.f2, method="hk", n.perm=1000, perm.Xsp=TRUE)
# thresholds
summary(operm)
# scanone summary with p-values
summary(out, perms=operm, alpha=0.05, pvalues=TRUE)

###################

scanone
# Non-parametric
###################
out.np <- scanone(hyper, model="np")
summary(out.np, thr=3)
# Plot with previous results
plot(out.np, chr=c(1,4), lty=1, col="green")
plot(out.imp, out.hk, out.em, chr=c(1,4), lty=1,
col=c("red","blue","black"), add=TRUE)
###################
# Two-part Model
###################
data(listeria)
## Not run: listeria <- calc.genoprob(listeria,step=2.5)
out.2p <- scanone(listeria, model="2part", upper=TRUE)
summary(out.2p, thr=c(5,3,3), format="allpeaks")
# Plot all three LOD scores together
plot(out.2p, out.2p, out.2p, lodcolumn=c(2,3,1), lty=1, chr=c(1,5,13),
col=c("red","blue","black"))
# Permutation test
## Not run: permo <- scanone(listeria, model="2part", upper=TRUE,
n.perm=1000)
## End(Not run)
# Thresholds
summary(permo)
###################
# Binary model
###################
binphe <- as.numeric(pull.pheno(listeria,1)==264)
out.bin <- scanone(listeria, pheno.col=binphe, model="binary")
summary(out.bin, thr=3)
# Plot LOD for binary model with LOD(p) from 2-part model
plot(out.bin, out.2p, lodcolumn=c(1,2), lty=1, col=c("black", "red"),
chr=c(1,5,13))
# Permutation test
## Not run: permo <- scanone(listeria, pheno.col=binphe, model="binary",
n.perm=1000)
## End(Not run)
# Thresholds
summary(permo)
###################
# Covariates
###################
data(fake.bc)

213

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## Not run: fake.bc <- calc.genoprob(fake.bc, step=2.5)
# genome scans without covariates
out.nocovar <- scanone(fake.bc)
# genome scans with covariates
ac <- pull.pheno(fake.bc, c("sex","age"))
ic <- pull.pheno(fake.bc, "sex")
out.covar <- scanone(fake.bc, pheno.col=1,
addcovar=ac, intcovar=ic)
summary(out.nocovar, thr=3)
summary(out.covar, thr=3)
plot(out.covar, out.nocovar, chr=c(2,5,10))

scanoneboot

Bootstrap to get interval estimate of QTL location

Description
Nonparametric bootstrap to get an estimated confidence interval for the location of a QTL, in the
context of a single-QTL model.
Usage
scanoneboot(cross, chr, pheno.col=1, model=c("normal","binary","2part","np"),
method=c("em","imp","hk","ehk","mr","mr-imp","mr-argmax"),
addcovar=NULL, intcovar=NULL, weights=NULL,
use=c("all.obs", "complete.obs"), upper=FALSE,
ties.random=FALSE, start=NULL, maxit=4000,
tol=1e-4, n.boot=1000, verbose=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

The chromosome to investigate. Only one chromosome is allowed. (This should
be a character string referring to the chromosomes by name.)

pheno.col

Column number in the phenotype matrix which should be used as the phenotype.
One may also give a character string matching a phenotype name. Finally, one
may give a numeric vector of phenotypes, in which case it must have the length
equal to the number of individuals in the cross, and there must be either nonintegers or values < 1 or > no. phenotypes; this last case may be useful for
studying transformations.

model

The phenotypic model: the usual normal model, a model for binary traits, a
two-part model or non-parametric analysis

method

Indicates whether to use the EM algorithm, imputation, Haley-Knott regression,
the extended Haley-Knott method, or marker regression. Not all methods are
available for all models. Marker regression is performed either by dropping individuals with missing genotypes ("mr"), or by first filling in missing data using
a single imputation ("mr-imp") or by the Viterbi algorithm ("mr-argmax").

scanoneboot
addcovar
intcovar
weights
use

upper
ties.random

start

maxit
tol
n.boot
verbose

215
Additive covariates; allowed only for the normal and binary models.
Interactive covariates (interact with QTL genotype); allowed only for the normal
and binary models.
Optional weights of individuals. Should be either NULL or a vector of length
n.ind containing positive weights. Used only in the case model="normal".
In the case that multiple phenotypes are selected to be scanned, this argument indicates whether to use all individuals, including those missing some phenotypes,
or just those individuals that have data on all selected phenotypes.
Used only for the two-part model; if true, the "undefined" phenotype is the maximum observed phenotype; otherwise, it is the smallest observed phenotype.
Used only for the non-parametric "model"; if TRUE, ties in the phenotypes are
ranked at random. If FALSE, average ranks are used and a corrected LOD score
is calculated.
Used only for the EM algorithm with the normal model and no covariates. If
NULL, use the usual starting values; if length 1, use random initial weights for
EM; otherwise, this should be a vector of length n+1 (where n is the number of
possible genotypes for the cross), giving the initial values for EM.
Maximum number of iterations for methods "em" and "ehk".
Tolerance value for determining convergence for methods "em" and "ehk".
Number of bootstrap replicates.
If TRUE, display information about the progress of the bootstrap.

Details
We recommend against the use of the bootstrap to derive a confidence interval for the location of a
QTL; see Manichaikul et al. (2006). Use lodint or bayesint instead.
The bulk of the arguments are the same as for the scanone function. A single chromosome should
be indicated with the chr argument; otherwise, we focus on the first chromosome in the input cross
object.
A single-dimensional scan on the relevant chromosome is performed. We further perform a nonparametric bootstrap (sampling individuals with replacement from the available data, to create a
new data set with the same size as the input cross; some individuals with be duplicated and some
omitted). The same scan is performed with the resampled data; for each bootstrap replicate, we
store only the location with maximum LOD score.
Use summary.scanoneboot to obtain the desired confidence interval.
Value
A vector of length n.boot, giving the estimated QTL locations in the bootstrap replicates. The
results for the original data are included as an attribute, "results".
Author(s)
Karl W Broman, 
References
Manichaikul, A., Dupuis, J., Sen, Ś and Broman, K. W. (2006) Poor performance of bootstrap
confidence intervals for the location of a quantitative trait locus. Genetics 174, 481–489.
Visscher, P. M., Thompson, R. and Haley, C. S. (1996) Confidence intervals in QTL mapping by
bootstrap. Genetics 143, 1013–1020.

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See Also
scanone, summary.scanoneboot, plot.scanoneboot, lodint, bayesint
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=1, err=0.001)
## Not run: bootoutput <- scanoneboot(fake.f2, chr=13, method="hk")
plot(bootoutput)
summary(bootoutput)

scanonevar

Genome scan for QTL affecting mean and/or variance

Description
Genome scan with a single QTL model for loci that can affect the variance as well as the mean.
Usage
scanonevar(cross, pheno.col=1, mean_covar=NULL, var_covar=NULL,
maxit=25, tol=1e-6, quiet=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype. This must be a single value (integer index or phenotype name) or a numeric vector of phenotype values, in which case it must have the length equal
to the number of individuals in the cross, and there must be either non-integers
or values < 1 or > no. phenotypes; this last case may be useful for studying
transformations.

mean_covar

Numeric matrix with covariates affecting the mean.

var_covar

Numeric matrix with covariates affecting the variances.

maxit

Maximum number of iterations in the algorithm to fit the model at a given position.

tol

Tolerance for convergence.

quiet

If FALSE, print some information about the course of the calculations.

Value
A data frame (with class "scanone", in the form output by scanone), with four columns: chromosome, position, the -log P-value for the mean effect, and the -log P-value for the effect on the
variance. The result is given class "scanone"
Author(s)
Lars Ronnegard and Karl Broman

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217

References
Ronnegard, L. and Valdar W. (2011) Detecting major genetic loci controlling phenotypic variability
in experimental crosses. Genetics 188:435-447
Ronnegard, L. and Valdar W. (2012) Recent developments in statistical methods for detecting genetic loci affecting phenotypic variability. BMC Genetics 13:63
See Also
scanone, summary.scanone, calc.genoprob, summary.scanoneperm
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=2.5)
out <- scanonevar(fake.bc)
color <- c("slateblue", "violetred")
plot(out, lod=1:2, col=color, bandcol="gray80")
legend("topright", lwd=2, c("mean", "variance"), col=color)
# use format="allpeaks" to get summary for each of mean and variance
# also consider format="tabByCol" or format="tabByChr"
summary(out, format="allpeaks")
# with sex and age as covariates
covar <- fake.bc$pheno[,c("sex", "age")]
out.cov <- scanonevar(fake.bc, mean_covar=covar, var_covar=covar)

scanonevar.meanperm

Permutation test for mean effect in scanonevar

Description
Executes permutations of the genotypes in the mean-effect part of scanonevar
Usage
scanonevar.meanperm(cross, pheno.col=1, mean_covar=NULL, var_covar=NULL,
maxit=25, tol=1e-6, n.mean.perm = 2, seed = 27517, quiet=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype. This must be a single value (integer index or phenotype name) or a numeric vector of phenotype values, in which case it must have the length equal
to the number of individuals in the cross, and there must be either non-integers
or values < 1 or > no. phenotypes; this last case may be useful for studying
transformations.

mean_covar

Numeric matrix with covariates affecting the mean.

var_covar

Numeric matrix with covariates affecting the variances.

218

scanonevar.varperm
maxit

Maximum number of iterations in the algorithm to fit the model at a given position.

tol

Tolerance for convergence.

n.mean.perm

Numeric vector of length one indicates the number of permutations to execute.

seed

Numeric vector of length one indicates the random seed to start the permutations.

quiet

If FALSE, print some information about the course of the calculations.

Value
A vector of length n.mean.perm of the maximum negative log10 p-value that resulted from each
permutation.

scanonevar.varperm

Permutation test for variance effect in scanonevar

Description
Executes permutations of the genotypes in the variance-effect part of scanonevar
Usage
scanonevar.varperm(cross, pheno.col=1, mean_covar=NULL, var_covar=NULL,
maxit=25, tol=1e-6, n.var.perm = 2, seed = 27517, quiet=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype. This must be a single value (integer index or phenotype name) or a numeric vector of phenotype values, in which case it must have the length equal
to the number of individuals in the cross, and there must be either non-integers
or values < 1 or > no. phenotypes; this last case may be useful for studying
transformations.

mean_covar

Numeric matrix with covariates affecting the mean.

var_covar

Numeric matrix with covariates affecting the variances.

maxit

Maximum number of iterations in the algorithm to fit the model at a given position.

tol

Tolerance for convergence.

n.var.perm

Numeric vector of length one indicates the number of permutations to execute.

seed

Numeric vector of length one indicates the random seed to start the permutations.

quiet

If FALSE, print some information about the course of the calculations.

Value
A vector of length n.var.perm of the maximum negative log10 p-value that resulted from each
permutation.

scanPhyloQTL

scanPhyloQTL

219

Single-QTL genome scan to map QTL to a phylogenetic tree

Description
Jointly consider multiple intercrosses with a single diallelic QTL model, considering all possible
partitions of the strains into the two QTL allele groups.
Usage
scanPhyloQTL(crosses, partitions, chr, pheno.col=1,
model=c("normal", "binary"), method=c("em", "imp", "hk"),
addcovar, maxit=4000, tol=0.0001, useAllCrosses=TRUE,
verbose=FALSE)
Arguments
crosses

A list with each component being an intercross, as an object of class cross (see
read.cross for details). The names (of the form "AB") indicate the strains in
the cross.

partitions

A vector of character strings of the form "AB|CD" or "A|BCD" indicating the
set of paritions of the strains into two allele groups. If missing, all partitions
should be considered.

chr

Optional vector indicating the chromosomes for which LOD scores should be
calculated. This should be a vector of character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes
with a preceding - to have all chromosomes but those considered. A logical
(TRUE/FALSE) vector may also be used.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype. This can be a vector of integers; for methods "hk" and "imp" this can be
considerably faster than doing them one at a time. One may also give a character strings matching the phenotype names. Finally, one may give a numeric
vector of phenotypes, in which case it must have the length equal to the number
of individuals in the cross, and there must be either non-integers or values < 1
or > no. phenotypes; this last case may be useful for studying transformations.

model

The phenotype model: the usual normal model or a model for binary traits

method

Indicates whether to use the EM algorithm, imputation, or Haley-Knott regression.

addcovar

Optional set of additive covariates to include in the analysis, as a list with the
same length as crosses. They must be numeric vectors or matrices, as for
scanone.

maxit

Maximum number of iterations for method "em".

tol

Tolerance value for determining convergence for method "em".

useAllCrosses

If TRUE, use all crosses in the analysis of all partitions, with crosses not segregating the QTL included in the estimation of the residual variance.

verbose

If TRUE, print information about progress.

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Details
The aim is to jointly consider multiple intercrosses to not just map QTL but to also, under the
assumption of a single diallelic QTL, identify the set of strains with each QTL allele.
For each partition (of the strains into two groups) that is under consideration, we pull out the set
of crosses that are segregating the QTL, re-code the alleles, and combine the crosses into one large
cross. Crosses not segregating the QTL are also used, though with no QTL effects.
Additive covariate indicators for the crosses are included in the analysis, to allow for the possibility
that there are overall shifts in the phenotypes between crosses.
Value
A data frame, as for the output of scanone, though with LOD score columns for each partition that
is considered. The result is given class "scanPhyloQTL".
Author(s)
Karl W Broman, 
References
Broman, K. W., Kim, S., An\’e, C. and Payseur, B. A. Mapping quantitative trait loci to a phylogenetic tree. In preparation.
See Also
plot.scanPhyloQTL, summary.scanPhyloQTL, max.scanPhyloQTL, inferredpartitions, simPhyloQTL
Examples
# example map; drop X chromosome
data(map10)
map10 <- map10[1:19]
# simulate data
x <- simPhyloQTL(4, partition="AB|CD", crosses=c("AB", "AC", "AD"),
map=map10, n.ind=150,
model=c(1, 50, 0.5, 0))
# run calc.genoprob on each cross
## Not run: x <- lapply(x, calc.genoprob, step=2)
# scan genome, at each position trying all possible partitions
out <- scanPhyloQTL(x, method="hk")
# maximum peak
max(out, format="lod")
# approximate posterior probabilities at peak
max(out, format="postprob")
# all peaks above a threshold for LOD(best) - LOD(2nd best)
summary(out, threshold=1, format="lod")

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# all peaks above a threshold for LOD(best), showing approx post'r prob
summary(out, format="postprob", threshold=3)
# plot results
plot(out)

scanqtl

General QTL scan

Description
Performs a multiple QTL scan for specified chromosomes and positions or intervals, with the possible inclusion of QTL-QTL interactions and/or covariates.
Usage
scanqtl(cross, pheno.col=1, chr, pos, covar=NULL, formula,
method=c("imp","hk"), model=c("normal", "binary"),
incl.markers=FALSE, verbose=TRUE, tol=1e-4, maxit=1000,
forceXcovar=FALSE)
Arguments
cross
pheno.col

chr
pos

covar
formula

method
model
incl.markers

verbose
tol
maxit
forceXcovar

An object of class cross. See read.cross for details.
Column number in the phenotype matrix to be used as the phenotype. One may
also give a character string matching a phenotype name. Finally, one may give
a numeric vector of phenotypes, in which case it must have the length equal to
the number of individuals in the cross, and there must be either non-integers
or values < 1 or > no. phenotypes; this last case may be useful for studying
transformations.
Vector indicating the chromosome for each QTL. (These should be character
strings referring to the chromosomes by name.)
List indicating the positions or intervals on the chromosome to be scanned. Each
element should be either a single number (for a specific position) or a pair of
numbers (for an interval).
A matrix or data.frame of covariates. These must be strictly numeric.
An object of class formula indicating the model to be fitted. (It can also be the
character string representation of a formula.) QTLs are indicated as Q1, Q2, etc.
Covariates are indicated by their names in covar.
Indicates whether to use multiple imputation or Haley-Knott regression.
The phenotype model: the usual model or a model for binary traits
If FALSE, do calculations only at points on an evenly spaced grid. If calc.genoprob
or sim.geno were run with stepwidth="variable" or stepwidth="max", we
force incl.markers=TRUE.
If TRUE, give feedback about progress.
Tolerance for convergence for the binary trait model.
Maximum number of iterations for fitting the binary trait model.
If TRUE, force inclusion of X-chr-related covariates (like sex and cross direction).

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Details
The formula is used to specified the model to be fit. In the formula, use Q1, Q2, etc., or q1, q2, etc.,
to represent the QTLs, and the column names in the covariate data frame to represent the covariates.
We enforce a hierarchical structure on the model formula: if a QTL or covariate is in involved in an
interaction, its main effect are also be included.
Only the interaction terms need to be specifed in the formula. The main effects of all input QTLs
(as specified by chr and pos) and covariates (as specifed by covar) will be included by default.
For example, if the formula is y~Q1*Q2*Sex, and there are three elements in input chr and pos
and Sex is one of the column names for input covariates, the formula used in genome scan will be
y ~ Q1 + Q2 + Q3 + Sex + Q1:Q2 + Q1:Sex + Q2:Sex + Q1:Q2:Sex.
The input pos is a list or vector to specify the position/range of the input chromosomes to be
scanned. If it is a vector, it gives the precise positions of the QTL on the chromosomes. If it is a list,
it will contain either the precise positions or a range on the chromosomes. For example, consider
the case that the input chr = c(1, 6,
13). If pos = c(9.8, 34.0, 18.6), it means to
fit a model with QTL on chromosome 1 at 9.8cM, chromosome 6 at 34cM and chromosome 13 at
18.6cM. If pos = list(c(5,15), c(30,36), 18), it means to scan chromosome 1 from 5cM to
15cM, chromosome 6 from 30cM to 36cM, fix the QTL on chromosome 13 at 18cM.
Value
An object of class scanqtl. It is a multi-dimensional array of LOD scores, with the number of
dimension equal to the number of QTLs specifed.
Author(s)
Hao Wu
References
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.
See Also
fitqtl, makeqtl, refineqtl
Examples
data(fake.f2)
# take out several QTLs
qc <- c(1, 8, 13)
fake.f2 <- subset(fake.f2, chr=qc)
# imputate genotypes
fake.f2 <- calc.genoprob(fake.f2, step=5, err=0.001)
# 2-dimensional genome scan with additive 3-QTL model
pos <- list(c(15,35), c(45,65), 28)
result <- scanqtl(fake.f2, pheno.col=1, chr=qc, pos=pos,

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223
formula=y~Q1+Q2+Q3, method="hk")

# image of the results
# chr locations
chr1 <- as.numeric(matrix(unlist(strsplit(colnames(result),"@")),
ncol=2,byrow=TRUE)[,2])
chr8 <- as.numeric(matrix(unlist(strsplit(rownames(result),"@")),
ncol=2,byrow=TRUE)[,2])
# image plot
image(chr1, chr8, t(result), las=1, col=rev(rainbow(256,start=0,end=2/3)))
# do the same, allowing the QTLs on chr 1 and 13 to interact
result2 <- scanqtl(fake.f2, pheno.col=1, chr=qc, pos=pos,
formula=y~Q1+Q2+Q3+Q1:Q3, method="hk")
# image plot
image(chr1, chr8, t(result2), las=1, col=rev(rainbow(256,start=0,end=2/3)))

scantwo

Two-dimensional genome scan with a two-QTL model

Description
Perform a two-dimensional genome scan with a two-QTL model, with possible allowance for covariates.
Usage
scantwo(cross, chr, pheno.col=1, model=c("normal","binary"),
method=c("em","imp","hk","mr","mr-imp","mr-argmax"),
addcovar=NULL, intcovar=NULL, weights=NULL,
use=c("all.obs", "complete.obs"),
incl.markers=FALSE, clean.output=FALSE,
clean.nmar=1, clean.distance=0,
maxit=4000, tol=1e-4,
verbose=TRUE, n.perm, perm.Xsp=FALSE, perm.strata=NULL,
assumeCondIndep=FALSE, batchsize=250, n.cluster=1)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes for which LOD scores should be
calculated. This should be a vector of character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes
with a preceding - to have all chromosomes but those considered. A logical
(TRUE/FALSE) vector may also be used.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype. This can be a vector of integers; for methods "hk" and "imp" this can be
considerably faster than doing them one at a time. One may also give character
strings matching the phenotype names. Finally, one may give a numeric vector
of phenotypes, in which case it must have the length equal to the number of
individuals in the cross, and there must be either non-integers or values < 1 or >
no. phenotypes; this last case may be useful for studying transformations.

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scantwo
model

The phenotype model: the usual normal model or a model for binary traits.

method

Indicates whether to use the the EM algorithm, imputation, Haley-Knott regression, or marker regression. Marker regression is performed either by dropping
individuals with missing genotypes ("mr"), or by first filling in missing data using a single imputation ("mr-imp") or by the Viterbi algorithm ("mr-argmax").

addcovar

Additive covariates.

intcovar

Interactive covariates (interact with QTL genotype).

weights

Optional weights of individuals. Should be either NULL or a vector of length
n.ind containing positive weights. Used only in the case model="normal".

use

In the case that multiple phenotypes are selected to be scanned, this argument indicates whether to use all individuals, including those missing some phenotypes,
or just those individuals that have data on all selected phenotypes.

incl.markers

If FALSE, do calculations only at points on an evenly spaced grid. If calc.genoprob
or sim.geno were run with stepwidth="variable" or stepwidth="max", we
force incl.markers=TRUE.

clean.output

If TRUE, clean the output with clean.scantwo, replacing LOD scores for pairs
of positions that are not well separated with 0. In permutations, this will be
done for each permutation replicate. This can be important for the case of
method="em", as there can be difficulty with algorithm convergence in these
regions.

clean.nmar

If clean.output=TRUE, this is the number of markers that must separate two
positions.

clean.distance If clean.output=TRUE, this is the cM distance that must separate two positions.
maxit

Maximum number of iterations; used only with method "em".

tol

Tolerance value for determining convergence; used only with method "em".

verbose

If TRUE, display information about the progress of calculations. For method
"em", if verbose is an integer above 1, further details on the progress of the
algorithm will be displayed.

n.perm

If specified, a permutation test is performed rather than an analysis of the observed data. This argument defines the number of permutation replicates.

perm.Xsp

If n.perm > 0, so that a permutation test will be performed, this indicates whether
separate permutations should be performed for the autosomes and the X chromosome, in order to get an X-chromosome-specific LOD threshold. In this case,
additional permutations are performed for the X chromosome.

perm.strata

If n.perm > 0, this may be used to perform a stratified permutation test. This
should be a vector with the same number of individuals as in the cross data.
Unique values indicate the individual strata, and permutations will be performed
within the strata.

assumeCondIndep
If TRUE, assume conditional independence of QTL genotypes given marker
genotypes. This is an approximation, but it may speed things up.
batchsize

The number of phenotypes (or permutations) to be run as a batch; used only for
methods "hk" and "imp".

n.cluster

If the package snow is available and n.perm > 0, permutations are run in parallel
using this number of nodes.

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225

Details
Standard interval mapping (method="em") and Haley-Knott regression (method="hk") require that
multipoint genotype probabilities are first calculated using calc.genoprob. The imputation method
uses the results of sim.geno.
The method "em" is standard interval mapping by the EM algorithm (Dempster et al. 1977; Lander
and Botstein 1989). Marker regression (method="mr") is simply linear regression of phenotypes
on marker genotypes (individuals with missing genotypes are discarded). Haley-Knott regression
(method="hk") uses the regression of phenotypes on multipoint genotype probabilities. The imputation method (method="imp") uses the pseudomarker algorithm described by Sen and Churchill
(2001).
Individuals with missing phenotypes are dropped.
In the presence of covariates, the full model is
y = µ + βq1 + βq2 + βq1 ×q2 + Aγ + Zδq1 + Zδq2 + Zδq1 ×q2 + 
where q1 and q2 are the unknown QTL genotypes at two locations, A is a matrix of covariates, and
Z is a matrix of covariates that interact with QTL genotypes. The columns of Z are forced to be
contained in the matrix A.
The above full model is compared to the additive QTL model,
y = µ + βq1 + βq2 + Aγ + Zδq1 + Zδq2 + 
and also to the null model, with no QTL,
y = µ + Aγ + 
In the case that n.perm is specified, the R function scantwo is called repeatedly.
For model="binary", a logistic regression model is used.
Value
If n.perm is missing, the function returns a list with class "scantwo" and containing three components. The first component is a matrix of dimension [tot.pos x tot.pos]; the upper triangle contains
the LOD scores for the additive model, and the lower triangle contains the LOD scores for the full
model. The diagonal contains the results of scanone. The second component of the output is a
data.frame indicating the locations at which the two-QTL LOD scores were calculated. The first
column is the chromosome identifier, the second column is the position in cM, the third column is
a 1/0 indicator for ease in later pulling out only the equally spaced positions, and the fourth column
indicates whether the position is on the X chromosome or not. The final component is a version of
the results of scanone including sex and/or cross direction as additive covariates, which is needed
for a proper calculation of conditional LOD scores.
If n.perm is specified, the function returns a list with six different LOD scores from each of the
permutation replicates. First, the maximum LOD score for the full model (two QTLs plus an interaction). Second, for each pair of chromosomes, we take the difference between the full LOD
and the maximum single-QTL LOD for those two chromosomes, and then maximize this across
chromosome pairs. Third, for each pair of chromosomes we take the difference between the maximum full LOD and the maximum additive LOD, and then maximize this across chromosome pairs.
Fourth, the maximum LOD score for the additive QTL model. Fifth, for each pair of chromosomes,
we take the difference between the additive LOD and the maximum single-QTL LOD for those two
chromosomes, and then maximize this across chromosome pairs. Finally, the maximum single-QTL
LOD score (that is, from a single-QTL scan). The latter is not used in summary.scantwo, but does
get calculated at each permutation, so we include it for the sake of completeness.

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scantwo
If n.perm is specified and perm.Xsp=TRUE, the result is a list with the permutation results for the
regions A:A, A:X, and X:X, each of which is a list with the six different LOD scores. Independent
permutations are performed in each region, n.perm is the number of permutations for the A:A
region; additional permutations are are used for the A:X and X:X parts, as estimates of quantiles
farther out into the tails are needed.

X chromosome
The X chromosome must be treated specially in QTL mapping.
As in scanone, if both males and females are included, male hemizygotes are allowed to be different
from female homozygotes, and the null hypothesis must be changed in order to ensure that sex- or
pgm-differences in the phenotype do not results in spurious linkage to the X chromosome. (See the
help file for scanone.)
If n.perm is specified and perm.Xsp=TRUE, X-chromosome-specific permutations are performed, to
obtain separate thresholds for the regions A:A, A:X, and X:X.
Author(s)
Karl W Broman, ; Hao Wu
References
Churchill, G. A. and Doerge, R. W. (1994) Empirical threshold values for quantitative trait mapping.
Genetics 138, 963–971.
Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977) Maximum likelihood from incomplete data
via the EM algorithm. J. Roy. Statist. Soc. B, 39, 1–38.
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
Lander, E. S. and Botstein, D. (1989) Mapping Mendelian factors underlying quantitative traits
using RFLP linkage maps. Genetics 121, 185–199.
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.
Soller, M., Brody, T. and Genizi, A. (1976) On the power of experimental designs for the detection
of linkage between marker loci and quantitative loci in crosses between inbred lines. Theor. Appl.
Genet. 47, 35–39.
See Also
plot.scantwo, summary.scantwo, scanone, max.scantwo, summary.scantwoperm, c.scantwoperm
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=5)
out.2dim <- scantwo(fake.f2, method="hk")
plot(out.2dim)
# permutations
## Not run: permo.2dim <- scantwo(fake.f2, method="hk", n.perm=1000)
summary(permo.2dim, alpha=0.05)

scantwopermhk

227

# summary with p-values
summary(out.2dim, perms=permo.2dim, pvalues=TRUE,
alphas=c(0.05, 0.10, 0.10, 0.05, 0.10))
# covariates
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=10)
ac <- pull.pheno(fake.bc, c("sex","age"))
ic <- pull.pheno(fake.bc, "sex")
out <- scantwo(fake.bc, method="hk", pheno.col=1,
addcovar=ac, intcovar=ic)
plot(out)

scantwopermhk

Permutation test for 2d genome scan by Haley-Knott regression

Description
Perform a permutation test with a two-dimensional genome scan with a two-QTL model, with
possible allowance for additive covariates, by Haley-Knott regression.
Usage
scantwopermhk(cross, chr, pheno.col=1,
addcovar=NULL, weights=NULL, n.perm=1,
batchsize=1000,
perm.strata=NULL, perm.Xsp=NULL,
verbose=FALSE, assumeCondIndep=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes for which LOD scores should be
calculated. This should be a vector of character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes
with a preceding - to have all chromosomes but those considered. A logical
(TRUE/FALSE) vector may also be used.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype.
This should be a single value (numeric index or character string for a phenotype
name), but it may also be a vector of numeric values with length equal to the
number of individuals in the cross, in which case it is taken to be a vector of
individuals’ phenotypes.

addcovar

Additive covariates.

weights

Optional weights of individuals. Should be either NULL or a vector of length
n.ind containing positive weights. Used only in the case model="normal".

n.perm

Number of permutation replicates.

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scantwopermhk
batchsize

If n.perm > batchsize, permutations will be run in batches of no more than
batchsize permutations.

perm.strata

Used to perform a stratified permutation test. This should be a vector with the
same number of individuals as in the cross data. Unique values indicate the
individual strata, and permutations will be performed within the strata.

perm.Xsp

If TRUE, run separate permutations for A:A, A:X, and X:X. In this case, n.perm
refers to the number of permutations for the A:A part; more permutations are
used for the A:X and X:X parts, as estimates of quantiles farther out into the
tails are needed.

verbose
If TRUE, display information about the progress of calculations.
assumeCondIndep
If TRUE, assume conditional independence of QTL genotypes given marker
genotypes. This is an approximation, but it may speed things up.
Details
This is a scaled-back version of the permutation test provided by scantwo: only for a normal model
with Haley-Knott regression, and not allowing interactive covariates.
This is an attempt to speed things up and attentuate the memory usage problems in scantwo.
In the case of perm.Xsp=TRUE (X-chr-specific thresholds), we use a stratified permutation test,
stratified by sex and cross-direction.
Value
A list with six different LOD scores from each of the permutation replicates. First, the maximum
LOD score for the full model (two QTLs plus an interaction). Second, for each pair of chromosomes, we take the difference between the full LOD and the maximum single-QTL LOD for those
two chromosomes, and then maximize this across chromosome pairs. Third, for each pair of chromosomes we take the difference between the maximum full LOD and the maximum additive LOD,
and then maximize this across chromosome pairs. Fourth, the maximum LOD score for the additive
QTL model. Fifth, for each pair of chromosomes, we take the difference between the additive LOD
and the maximum single-QTL LOD for those two chromosomes, and then maximize this across
chromosome pairs. Finally, the maximum single-QTL LOD score (that is, from a single-QTL scan).
The latter is not used in summary.scantwoperm, but does get calculated at each permutation, so we
include it for the sake of completeness.
If perm.Xsp=TRUE, this is a list of lists, for the A:A, A:X, and X:X sections, each being a list as
described above.
Author(s)
Karl W Broman, ; Hao Wu
References
Churchill, G. A. and Doerge, R. W. (1994) Empirical threshold values for quantitative trait mapping.
Genetics 138, 963–971.
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
See Also
scantwo, plot.scantwoperm, summary.scantwoperm, c.scantwoperm

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229

Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=5)
operm <- scantwopermhk(fake.f2, n.perm=2)
summary(operm, alpha=0.05)

shiftmap

Shift starting points in genetic maps

Description
Shift starting points in a genetic map to a set of defined positions
Usage
shiftmap(object, offset=0)
Arguments
object

An object of class cross (see read.cross for details) or map (see sim.map for
details).

offset

Defines the starting position for each chromosome. This should be a single value
(to be used for all chromosomes) or a vector with length equal to the number of
chromosomes, defining individual starting positions for each chromosome. For
a sex-specific map (as in a 4-way cross), we use the same offset for both the
male and female maps.

Value
If the input is a map object, a map object is returned; if the input is a cross object, a cross object is
returned. In either case, the positions of markers are shifted so that the starting positions are as in
offset.
Author(s)
Karl W Broman, 
See Also
replace.map, est.map
Examples
data(hyper)
shiftedhyper <- shiftmap(hyper, offset=0)
par(mfrow=c(1,2))
plotMap(hyper, shift=FALSE, alternate.chrid=TRUE)
plotMap(shiftedhyper, shift=FALSE, alternate.chrid=TRUE)

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sim.cross

sim.cross

Simulate a QTL experiment

Description
Simulates data for a QTL experiment using a model in which QTLs act additively.
Usage
sim.cross(map, model=NULL, n.ind=100,
type=c("f2", "bc", "4way", "risib", "riself",
"ri4sib", "ri4self", "ri8sib", "ri8self", "bcsft"),
error.prob=0, missing.prob=0, partial.missing.prob=0,
keep.qtlgeno=TRUE, keep.errorind=TRUE, m=0, p=0,
map.function=c("haldane","kosambi","c-f","morgan"),
founderGeno, random.cross=TRUE, ...)
Arguments
map

A list whose components are vectors containing the marker locations on each of
the chromosomes.

model

A matrix where each row corresponds to a different QTL, and gives the chromosome number, cM position and effects of the QTL.

n.ind

Number of individuals to simulate.

type

Indicates whether to simulate an intercross (f2), a backcross (bc), a phaseknown 4-way cross (4way), or recombinant inbred lines (by selfing or by sibmating, and with the usual 2 founder strains or with 4 or 8 founder strains).

error.prob

The genotyping error rate.

missing.prob
The rate of missing genotypes.
partial.missing.prob
When simulating an intercross or 4-way cross, this gives the rate at which markers will be incompletely informative (i.e., dominant or recessive).
keep.qtlgeno

If TRUE, genotypes for the simulated QTLs will be included in the output.

keep.errorind

If TRUE, and if error.prob > 0, the identity of genotyping errors will be
included in the output.

m

Interference parameter; a non-negative integer. 0 corresponds to no interference.

p

Probability that a chiasma comes from the no-interference mechanism

map.function

Indicates whether to use the Haldane, Kosambi, Carter-Falconer, or Morgan map
function when converting genetic distances into recombination fractions.

founderGeno

For 4- or 8-way RIL, the genotype data of the founder strains, as a list whose
components are numeric matrices (no. markers x no. founders), one for each
chromosome.

random.cross

For 4- or 8-way RIL, indicates whether the order of the founder strains should
be randomized, independently for each RIL, or whether all RIL be derived
from a common cross. In the latter case, for a 4-way RIL, the cross would
be (AxB)x(CxD).

...

For type = "bcsft", additional arguments passed to sim.cross.bcsft.

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Details
Meiosis is assumed to follow the Stahl model for crossover interference (see the references, below),
of which the no interference model and the chi-square model are special cases. Chiasmata on the
four-strand bundle are a superposition of chiasmata from two different mechanisms. With probability p, they arise by a mechanism exhibiting no interference; the remainder come from a chi-square
model with inteference parameter m. Note that m=0 corresponds to no interference, and with p=0,
one gets a pure chi-square model.
If a chromosomes has class X, it is assumed to be the X chromosome, and is assumed to be segregating in the cross. Thus, in an intercross, it is segregating like a backcross chromosome. In a 4-way
cross, a second phenotype, sex, will be generated.
QTLs are assumed to act additively, and the residual phenotypic variation is assumed to be normally
distributed with variance 1.
For a backcross, the effect of a QTL is a single number corresponding to the difference between the
homozygote and the heterozygote.
For an intercross, the effect of a QTL is a pair of numbers, (a, d), where a is the additive effect (half
the difference between the homozygotes) and d is the dominance deviation (the difference between
the heterozygote and the midpoint between the homozygotes).
For a four-way cross, the effect of a QTL is a set of three numbers, (a, b, c), where, in the case of
one QTL, the mean phenotype, conditional on the QTL genotyping being AC, BC, AD or BD, is a,
b, c or 0, respectively.
Value
An object of class cross. See read.cross for details.
If keep.qtlgeno is TRUE, the cross object will contain a component qtlgeno which is a matrix
containing the QTL genotypes (with complete data and no errors), coded as in the genotype data.
If keep.errorind is TRUE and errors were simulated, each component of geno will each contain
a matrix errors, with 1’s indicating simulated genotyping errors.
Recombinant inbred lines
In the simulation of recombinant inbred lines (RIL), we simulate a single individual from each line,
and no phenotypes are simulated (so the argument model is ignored).
The types riself and risib are the usual two-way RIL.
The types ri4self, ri4sib, ri8self, and ri8sib are RIL by selfing or sib-mating derived from
four or eight founding parental strains.
For the 4- and 8-way RIL, one must include the genotypes of the founding individuals; these may
be simulated with simFounderSnps. Also, the output cross will contain a component cross, which
is a matrix with rows corresponding to RIL and columns corresponding to the founders, indicating
order of the founder strains in the crosses used to generate the RIL.
The coding of genotypes in 4- and 8-way RIL is rather complicated. It is a binary encoding of which
founder strains’ genotypes match the RIL’s genotype at a marker, and not that this is specific to the
order of the founders in the crosses used to generate the RIL. For example, if an RIL generated
from 4 founders has the 1 allele at a SNP, and the four founders have SNP alleles 0, 1, 0, 1, then
the RIL allele matches that of founders B and D. If the RIL was derived by the cross (AxB)x(CxD),
then the RIL genotype would be encoded 22−1 + 23−1 = 6. If the cross was derived by the cross
(DxA)x(CxB), then the RIL genotype would be encoded 21−1 + 24−1 = 9. These get reorganized
after calls to calc.genoprob, sim.geno, or argmax.geno, and this approach simplifies the hidden
Markov model (HMM) code.

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For the 4- and 8-way RIL, genotyping errors are simulated only if the founder genotypes are 0/1
SNPs.

Author(s)
Karl W Broman, 
References
Copenhaver, G. P., Housworth, E. A. and Stahl, F. W. (2002) Crossover interference in arabidopsis.
Genetics 160, 1631–1639.
Foss, E., Lande, R., Stahl, F. W. and Steinberg, C. M. (1993) Chiasma interference as a function of
genetic distance. Genetics 133, 681–691.
Zhao, H., Speed, T. P. and McPeek, M. S. (1995) Statistical analysis of crossover interference using
the chi-square model. Genetics 139, 1045–1056.
Broman, K. W. (2005) The genomes of recombinant inbred lines Genetics 169, 1133–1146.
Teuscher, F. and Broman, K. W. (2007) Haplotype probabilities for multiple-strain recombinant
inbred lines. Genetics 175, 1267–1274.
See Also
sim.map, read.cross, fake.f2, fake.bc fake.4way, simFounderSnps
Examples
# simulate a genetic map
map <- sim.map()
### simulate 250 intercross individuals with 2 QTLs
fake <- sim.cross(map, type="f2", n.ind=250,
model = rbind(c(1,45,1,1),c(5,20,0.5,-0.5)))
### simulate 100 backcross individuals with 3 QTL
# a 10-cM map model after the mouse
data(map10)
fakebc <- sim.cross(map10, type="bc", n.ind=100,
model=rbind(c(1,45,1), c(5,20,1), c(5,50,1)))
### simulate 8-way RIL by sibling mating
# get lengths from the above 10-cM map
L <- ceiling(sapply(map10, max))
# simulate a 1 cM map
themap <- sim.map(L, n.mar=L+1, eq.spacing=TRUE)
# simulate founder genotypes
pg <- simFounderSnps(themap, "8")
# simulate the 8-way RIL by sib mating (256 lines)
ril <- sim.cross(themap, n.ind=256, type="ri8sib", founderGeno=pg)

sim.geno

sim.geno

233

Simulate genotypes given observed marker data

Description
Uses the hidden Markov model technology to simulate from the joint distribution Pr(g | O) where
g is the underlying genotype vector and O is the observed multipoint marker data, with possible
allowance for genotyping errors.
Usage
sim.geno(cross, n.draws=16, step=0, off.end=0, error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
stepwidth=c("fixed", "variable", "max"))
Arguments
cross

An object of class cross. See read.cross for details.

n.draws

Number of simulation replicates to perform.

step

Maximum distance (in cM) between positions at which the simulated genotypes
will be drawn, though for step=0, genotypes are drawn only at the marker locations.

off.end

Distance (in cM) past the terminal markers on each chromosome to which the
genotype simulations will be carried.

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi, Carter-Falconer, or Morgan map
function when converting genetic distances into recombination fractions.

stepwidth

Indicates whether the intermediate points should with fixed or variable step
sizes. We recommend using "fixed"; "variable" is included for the qtlbim
package (http://www.ssg.uab.edu/qtlbim). The "max" option inserts the
minimal number of intermediate points so that the maximum distance between
points is step.

Details
After performing the forward-backward equations, we draw from P r(g1 = v|O) and then P r(gk+1 =
v|O, gk = u).
In the case of the 4-way cross, with a sex-specific map, we assume a constant ratio of female:male
recombination rates within the inter-marker intervals.
Value
The input cross object is returned with a component, draws, added to each component of cross$geno.
This is an array of size [n.ind x n.pos x n.draws] where n.pos is the number of positions at which
the simulations were performed and n.draws is the number of replicates. Attributes "error.prob",
"step", and "off.end" are set to the values of the corresponding arguments, for later reference.

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Author(s)
Karl W Broman, 
See Also
calc.genoprob, argmax.geno
Examples
data(fake.f2)
fake.f2 <- sim.geno(fake.f2, step=2, n.draws=8)

sim.map

Simulate a genetic map

Description
Simulate the positions of markers on a genetic map.
Usage
sim.map(len=rep(100,20), n.mar=10, anchor.tel=TRUE,
include.x=TRUE, sex.sp=FALSE, eq.spacing=FALSE)
Arguments
len

A vector specifying the chromosome lengths (in cM)

n.mar

A vector specifying the number of markers per chromosome.

anchor.tel

If true, markers at the two telomeres will always be included, so if n.mar = 1 or
2, we’ll give just the two telomeric markers.

include.x

Indicates whether the last chromosome should be considered the X chromosome.

sex.sp

Indicates whether to create sex-specific maps, in which case the output will be
a vector of 2-row matrices, with rows corresponding to the maps for the two
sexes.

eq.spacing

If TRUE, markers will be equally spaced.

Details
Aside from the telomeric markers, marker positions are simulated as iid Uniform(0, L). If len or
n.mar has just one element, it is expanded to the length of the other argument. If they both have
just one element, only one chromosome is simulated.
If eq.spacing is TRUE, markers are equally spaced between 0 and L. If anchor.tel is FALSE,
telomeric markers are not included.
Value
A list of vectors, each specifying the locations of the markers. Each component of the list is given
class A or X, according to whether it is autosomal or the X chromosome.

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Author(s)
Karl W Broman, 
See Also
sim.cross, plotMap, replace.map, pull.map
Examples
# simulate 4 autosomes, each with 10 markers
map <- sim.map(c(100,90,80,40), 10, include.x=FALSE)
plotMap(map)
# equally spaced markers
map2 <- sim.map(c(100,90,80,40), 10, include.x=FALSE, eq.spacing=TRUE)
plot(map2)

simFounderSnps

Simulate founder SNPs for a multiple-strain RIL

Description
Simulate genotype data for the founding strains for a panel of multiple-strain RIL.
Usage
simFounderSnps(map, n.str=c("4","8"), pat.freq)
Arguments
map

A list whose components are vectors containing the marker locations on each of
the chromosomes.

n.str

Number of founding strains (4 or 8).

pat.freq

Frequency of SNP genotype patterns in the founder (a vector of length n.str/2
+ 1): (monoallelic, SNP unique to one founder, SNP present in 2 founders, [and,
for the case of 8 founders, SNP in 3/8 founders, SNP in 4/8 founders].)

Details
The SNPs are simulated to be in linkage equilibrium.
Value
A vector of the same length as there are chromosomes in map, with each component being a matrix
of 0’s and 1’s, of dim n.str x n.mar.
Author(s)
Karl W Broman, 

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simPhyloQTL

See Also
sim.map, sim.cross
Examples
data(map10)
x <- simFounderSnps(map10, "8", c(0, 0.5, 0.2, 0.2, 0.1))

simPhyloQTL

Simulate a set of intercrosses for a single diallelic QTL

Description
Simulate a set of intercrosses with a single diallelic QTL.
Usage
simPhyloQTL(n.taxa=3, partition, crosses, map, n.ind=100, model,
error.prob=0, missing.prob=0, partial.missing.prob=0,
keep.qtlgeno=FALSE, keep.errorind=TRUE, m=0, p=0,
map.function=c("haldane","kosambi","c-f","morgan"))
Arguments
n.taxa

Number of taxa (i.e., strains).

partition

A vector of character strings of the form "AB|CD" or "A|BCD" indicating, for
each QTL, which taxa have which allele. If missing, simulate under the null
hypothesis of no QTL.

crosses

A vector of character strings indicating the crosses to do (for the form "AB",
"AC", etc.). These will be sorted and then only unique ones used. If missing, all
crosses will be simulated.

map

A list whose components are vectors containing the marker locations on each of
the chromosomes.

n.ind

The number of individuals in each cross. If length 1, all crosses will have
the same number of individuals; otherwise the length should be the same as
crosses.

model

A matrix where each row corresponds to a different QTL, and gives the chromosome number, cM position and effects of the QTL (assumed to be the same
in each cross in which the QTL is segregating).

error.prob

The genotyping error rate.

missing.prob
The rate of missing genotypes.
partial.missing.prob
When simulating an intercross or 4-way cross, this gives the rate at which markers will be incompletely informative (i.e., dominant or recessive).
keep.qtlgeno

If TRUE, genotypes for the simulated QTLs will be included in the output.

keep.errorind

If TRUE, and if error.prob > 0, the identity of genotyping errors will be
included in the output.

m

Interference parameter; a non-negative integer. 0 corresponds to no interference.

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237

p

Probability that a chiasma comes from the no-interference mechanism

map.function

Indicates whether to use the Haldane, Kosambi, Carter-Falconer, or Morgan map
function when converting genetic distances into recombination fractions.

Details
Meiosis is assumed to follow the Stahl model for crossover interference (see the references, below),
of which the no interference model and the chi-square model are special cases. Chiasmata on the
four-strand bundle are a superposition of chiasmata from two different mechanisms. With probability p, they arise by a mechanism exhibiting no interference; the remainder come from a chi-square
model with inteference parameter m. Note that m=0 corresponds to no interference, and with p=0,
one gets a pure chi-square model.
QTLs are assumed to act additively, and the residual phenotypic variation is assumed to be normally
distributed with variance 1.
The effect of a QTL is a pair of numbers, (a, d), where a is the additive effect (half the difference between the homozygotes) and d is the dominance deviation (the difference between the heterozygote
and the midpoint between the homozygotes).
Value
A list with each component being an object of class cross. See read.cross for details. The names
(e.g. "AB", "AC", "BC") indicate the crosses.
If keep.qtlgeno is TRUE, each cross object will contain a component qtlgeno which is a matrix
containing the QTL genotypes (with complete data and no errors), coded as in the genotype data.
If keep.errorind is TRUE and errors were simulated, each component of geno in each cross will
each contain a matrix errors, with 1’s indicating simulated genotyping errors.
Author(s)
Karl W Broman, 
References
Broman, K. W., Kim, S., An\’e, C. and Payseur, B. A. Mapping quantitative trait loci to a phylogenetic tree. In preparation.
See Also
scanPhyloQTL, inferredpartitions, summary.scanPhyloQTL, max.scanPhyloQTL, plot.scanPhyloQTL,
sim.cross, read.cross
Examples
## Not run:
# example map; drop X chromosome
data(map10)
map10 <- map10[1:19]
# simulate data
x <- simPhyloQTL(4, partition="AB|CD", crosses=c("AB", "AC", "AD"),
map=map10, n.ind=150,
model=c(1, 50, 0.5, 0))

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simulatemissingdata
# run calc.genoprob on each cross
x <- lapply(x, calc.genoprob, step=2)
# scan genome, at each position trying all possible partitions
out <- scanPhyloQTL(x, method="hk")
# maximum peak
max(out, format="lod")
# approximate posterior probabilities at peak
max(out, format="postprob")
# all peaks above a threshold for LOD(best) - LOD(2nd best)
summary(out, threshold=1, format="lod")
# all peaks above a threshold for LOD(best), showing approx post'r prob
summary(out, format="postprob", threshold=3)
# plot of results
plot(out)
## End(Not run)

simulatemissingdata

Simulates missing genotype data

Description
Simulate missing genotype data by removing some genotype data from the cross object
Usage
simulatemissingdata(cross, percentage = 5)
Arguments
cross

An object of class cross. See read.cross for details.

percentage

How much of the genotype data do we need to randomly drop?

Value
An object of class cross with percentage
Author(s)
Danny Arends 
See Also
• The MQM tutorial: https://rqtl.org/tutorials/MQM-tour.pdf
• MQM - MQM description and references
• mqmscan - Main MQM single trait analysis

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239

• mqmscanall - Parallellized traits analysis
• mqmaugment - Augmentation routine for estimating missing data
• mqmautocofactors - Set cofactors using marker density
• mqmsetcofactors - Set cofactors at fixed locations
• mqmpermutation - Estimate significance levels
• scanone - Single QTL scanning
Examples
data(multitrait)
multitrait <- fill.geno(multitrait)
multimissing5 <- simulatemissingdata(multitrait,perc=5)
perc <- (sum(nmissing(multimissing5))/sum(ntyped(multimissing5)))

stepwiseqtl

Stepwise selection for multiple QTL

Description
Performs forward/backward selection to identify a multiple QTL model, with model choice made
via a penalized LOD score, with separate penalties on main effects and interactions.
Usage
stepwiseqtl(cross, chr, pheno.col=1, qtl, formula, max.qtl=10, covar=NULL,
method=c("imp", "hk"), model=c("normal", "binary"),
incl.markers=TRUE, refine.locations=TRUE,
additive.only=FALSE, scan.pairs=FALSE, penalties,
keeplodprofile=TRUE, keeptrace=FALSE, verbose=TRUE,
tol=1e-4, maxit=1000, require.fullrank=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider in search for QTL. This
should be a vector of character strings referring to chromosomes by name; numeric values are converted to strings. Refer to chromosomes with a preceding to have all chromosomes but those considered. A logical (TRUE/FALSE) vector
may also be used.

pheno.col

Column number in the phenotype matrix which should be used as the phenotype.
One may also give character strings matching the phenotype names. Finally, one
may give a numeric vector of phenotypes, in which case it must have the length
equal to the number of individuals in the cross, and there must be either nonintegers or values < 1 or > no. phenotypes; this last case may be useful for
studying transformations.

qtl

Optional QTL object (of class "qtl", as created by makeqtl) to use as a starting
point.

formula

Optional formula to define the QTL model to be used as a starting point.

max.qtl

Maximum number of QTL to which forward selection should proceed.

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covar

Data frame of additive covariates.

method

Indicates whether to use multiple imputation or Haley-Knott regression.

model

The phenotype model: the usual model or a model for binary traits

incl.markers
If FALSE, do calculations only at points on an evenly spaced grid.
refine.locations
If TRUE, use refineqtl to refine the QTL locations after each step of forward
and backward selection.
additive.only

If TRUE, allow only additive QTL models; if FALSE, consider also pairwise
interactions among QTL.

scan.pairs

If TRUE, perform a two-dimensional, two-QTL scan at each step of forward
selection.

penalties

Vector of three (or six) values indicating the penalty on the number of QTL
terms. If three values, these are the penalties on main effects and heavy and
light penalties on interactions. If six values, these include X-chr-specific penalties, and the values are: main effect for autosomes, main effect for X chr, heavy
penalty on A:A interactions, light penalty on A:A interactions, penalty on A:X
interactions, and penalty on X:X interactions. See the Details below. If missing, default values are used that are based on simulations of backcrosses and
intercrosses with genomes modeled after that of the mouse.

keeplodprofile If TRUE, keep the LOD profiles from the last iteration as attributes to the output.
keeptrace

If TRUE, keep information on the sequence of models visited through the course
of forward and backward selection as an attribute to the output.

verbose

If TRUE, give feedback about progress. If verbose is an integer > 1, even more
information is printed.

tol

Tolerance for convergence for the binary trait model.

maxit
Maximum number of iterations for fitting the binary trait model.
require.fullrank
If TRUE, give LOD=0 when covariate matrix in the linear regression is not of
full rank.
Details
We seek to identify the model with maximal penalized LOD score. The penalized LOD score,
defined in Manichaikul et al. (2009), is the LOD score for the model (the log10 likelihood ratio
comparing the model to the null model with no QTL) with penalties on the number of QTL and
QTL:QTL interactions.
We consider QTL models allowing pairwise interactions among QTL but with an enforced hierarchy
in which inclusion of a pairwise interaction requires the inclusion of both of the corresponding
main effects. Additive covariates may be included, but currently we do not explore QTL:covariate
interactions. Also, the penalized LOD score criterion is currently defined only for autosomal loci,
and results with the X chromosome should be considered with caution.
The penalized LOD score is of the form pLOD(γ) = LOD(γ) − Tm pm − Th ph − Tl pl where
γ denotes a model, pm is the number of QTL in the model ("main effects"), ph is the number of
pairwise interactions that will be given a heavy interaction penalty, pl is the number of pairwise
interactions that will be given a light interaction penalty, Tm is the penalty on main effects, Th is
the heavy interaction penalty, and Tl is the light interaction penalty. The penalties argument is
the vector (Tm , Th , Tl ). If Tl is missing (penalties has a vector of length 2), we assume Tl = Th ,
and so all pairwise interactions are assigned the same penalty.

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241

The "heavy" and "light" interaction penalties can be a bit confusing. Consider the clusters of QTL
that are connected via one or more pairwise interactions. To each such cluster, we assign at most
one "light" interaction penalty, and give all other pairwise interactions the heavy interaction penalty.
In other words, if pi is the total number of pairwise interactions for a QTL model, we let pl be the
number of clusters of connected QTL with at least one pairwise interaction, and then let ph −pi −pl .
Let us give an explicit example. Consider a model with 6 QTL, and with interactions between QTL 2
and 3, QTL 4 and 5 and QTL 4 and 6 (so we have the model formula y ~ Q1 + Q2 + Q3 + Q4 + Q5 + Q6 + Q2:Q3 + Q4:Q5
There are three clusters of connected QTL: (1), (2,3) and (4,5,6). We would assign 6 main effect
penalties (Tm ), 2 light interaction penalties (Tl ), and 1 heavy interaction penalty (Th ).
Manichaikul et al. (2009) described a system for deriving the three penalties on the basis of permutation results from a two-dimensional, two-QTL genome scan (as calculated with scantwo). These
may be calculated with the function calc.penalties.
A forward/backward search method is used, with the aim to optimize the penalized LOD score
criterion. That is, we seek to identify the model with maximal the penalized LOD score. The search
algorithm was based closely on an algorithm described by Zeng et al. (1999).
We use forward selection to a model of moderate size (say 10 QTL), followed by backward elimination all the way to the null model. The chosen model is that which optimizes the penalized
LOD score criterion, among all models visited. The detailed algorithm is as follows. Note that if
additive.only=TRUE, no pairwise interactions are considered.
1. Start at the null model, and perform a single-QTL genome scan, and choose the position giving
the largest LOD score. If scan.pairs=TRUE, start with a two-dimensional, two-QTL genome
scan instead. If an initial QTL model were defined through the arguments qtl and formula,
start with this model and jump immediately to step 2.
2. With a fixed QTL model in hand:
(a) Scan for an additional additive QTL.
(b) For each QTL in the current model, scan for an additional interacting QTL.
(c) If there are ≥ 2 QTL in the current model, consider adding one of the possible pairwise
interactions.
(d) If scan.pairs=TRUE perform a two-dimensional, two-QTL scan, seeking to add a pair of
novel QTL, either additive or interacting.
(e) Step to the model that gives the largest value for the model comparison criterion, among
those considered at the current step.
3. Refine the locations of the QTL in the current model (if refine.locations=TRUE).
4. Repeat steps 2 and 3 up to a model with some pre-determined number of loci.
5. Perform backward elimination, all the way back to the null model. At each step, consider
dropping one of the current main effects or interactions; move to the model that maximizes the
model comparison criterion, among those considered at this step. Follow this with a refinement
of the locations of the QTL.
6. Finally, choose the model having the largest model comparison criterion, among all models
visited.
In this forward/backward algorithm, it is likely best to build up to an overly large model and then
prune it back. Note that there is no "stopping rule"; the chosen model is that which optimizes
the model comparison criterion, among all models visited. The search can be time consuming,
particularly if a two-dimensional scan is performed at each forward step. Such two-dimensional
scans may be useful for identifying QTL linked in repulsion (having effects of opposite sign) or
interacting QTL with limited marginal effects, but our limited experience suggests that they are not
necessary; important linked or interacting QTL pairs can be picked up in the forward selection to a
large model, and will be retained in the backward elimination phase.

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Value
The output is a representation of the best model, as measured by the penalized LOD score (see
Details), among all models visited. This is QTL object (of class "qtl", as produced by makeqtl),
with attributes "formula", indicating the model formula, and "pLOD" indicating the penalized LOD
score.
If keeplodprofile=TRUE, LOD profiles from the last pass through the refinement algorithm are
retained as an attribute, "lodprofile", to the object. These may be plotted with plotLodProfile.
If keeptrace=TRUE, the output will contain an attribute "trace" containing information on the
best model at each step of forward and backward elimination. This is a list of objects of class
"compactqtl", which is similar to a QTL object (as produced by makeqtl) but containing just a
vector of chromosome IDs and positions for the QTL. Each will also have attributes "formula"
(containing the model formula) and "pLOD" (containing the penalized LOD score.
Methods
imp: multiple imputation is used, as described by Sen and Churchill (2001).
hk: Haley-Knott regression is used (regression of the phenotypes on the multipoint QTL genotype
probabilities), as described by Haley and Knott (1992).
Author(s)
Karl W Broman, 
References
Manichaikul, A., Moon, J. Y., Sen, Ś, Yandell, B. S. and Broman, K. W. (2009) A model selection
approach for the identification of quantitative trait loci in experimental crosses, allowing epistasis.
Genetics, 181, 1077–1086.
Broman, K. W. and Speed, T. P. (2002) A model selection approach for the identification of quantitative trait loci in experimental crosses (with discussion). J Roy Stat Soc B 64, 641–656, 731–775.
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci
in line crosses using flanking markers. Heredity 69, 315–324.
Sen, Ś. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics
159, 371–387.
Zeng, Z.-B., Kao, C.-H. and Basten, C. J. (1999) Estimating the genetic architecture of quantitative
traits. Genetical Research, 74, 279–289.
See Also
calc.penalties, plotModel, makeqtl, fitqtl, refineqtl, addqtl, addpair
Examples
data(fake.bc)
## Not run: fake.bc <- calc.genoprob(fake.bc, step=2.5)
outsw <- stepwiseqtl(fake.bc, max.qtl=3, method="hk", keeptrace=TRUE)
# best model
outsw

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243

plotModel(outsw)
# path through model space
thetrace <- attr(outsw, "trace")
# plot of these
par(mfrow=c(3,3))
for(i in seq(along=thetrace))
plotModel(thetrace[[i]], main=paste("pLOD =",round(attr(thetrace[[i]],"pLOD"), 2)))

strip.partials

Strip partially informative genotypes

Description
Replace all partially informative genotypes (e.g., dominant markers in an intercross) with missing
values.
Usage
strip.partials(cross, verbose=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

verbose

If TRUE, print the number of genotypes removed.

Value
The same class cross object as in the input, but with partially informative genotypes made missing.
Author(s)
Karl W Broman, 
See Also
plotMissing, plotInfo
Examples
data(listeria)
sum(nmissing(listeria))
listeria <- strip.partials(listeria)
sum(nmissing(listeria))

244

subset.cross

subset.cross

Subsetting data for QTL experiment

Description
Pull out a specified set of chromosomes and/or individuals from a cross object.
Usage
## S3 method for class 'cross'
subset(x, chr, ind, ...)
## S3 method for class 'cross'
x[chr, ind]
Arguments
x
chr
ind
...

An object of class cross. See read.cross for details.
Optional vector specifying which chromosomes to keep or discard. This may be
a logical, numeric, or character string vector. See Details, below.
Optional vector specifying which individuals to keep discard. This may be a
logical, numeric or chacter string vector. See Details, below.
Ignored at this point.

Details
The chr argument may be a logical vector with length equal to the number of chromosomes in the
input cross x. Alternatively, it should be a vector of character strings referring to chromosomes by
name. Numeric values are converted to strings. Refer to chromosomes with a preceding - to have
all chromosomes but those considered.
If the ind argument is a logical vector (TRUE/FALSE), it should have length equal to the number of
individuals in the input cross x. The individuals with corresponding TRUE values are retained.
If the ind argument is numeric, it should have values either between 1 and the number of individuals
in the input cross x (in which case these individuals will be retained), or it should have values
between -1 and -n, where n is the number of individuals in the input cross x, in which case all
except these individuals will be retained.
If the input cross object x contains individual identifiers (a phenotype column labeled "id" or "ID"),
and if the ind argument contains character strings, then these will be matched against the individual
identifiers. If all values in ind are preceded by a -), we omit those individuals whose IDs match
those in ind. Otherwise, we retain those individuals whose IDs match those in ind.
Value
The input cross object, but with only the specified subset of the data.
Author(s)
Karl W Broman, 
See Also
pull.map, drop.markers, subset.map

subset.map

245

Examples
data(fake.f2)
fake.f2.A <- subset(fake.f2, chr=c("5","13"))
fake.f2.B <- subset(fake.f2, ind = -c(1,5,10))
fake.f2.C <- subset(fake.f2, chr=1:5, ind=1:50)
data(listeria)
y <- pull.pheno(listeria, 1)
listeriaB <- subset(listeria, ind = (!is.na(y) & y < 264))
# individual identifiers
listeria$pheno$ID <- paste("mouse", 1:nind(listeria), sep="")
listeriaC <- subset(listeria, ind=c("mouse1","mouse11","mouse21"))
listeriaD <- subset(listeria, ind=c("-mouse1","-mouse11","-mouse21"))
# you can also use brackets (like
temp <- listeria[c("5","13"),] #
temp <- listeria[ , 1:10]
#
temp <- listeria[5, 1:10]
#

subset.map

matrix with rows=chromosomes and columns=individuals)
chr 5 and 13
first ten individuals
chr 5 for first ten individuals

Subsetting chromosomes for a genetic map

Description
Pull out a specified set of chromosomes from a map object.
Usage
## S3 method for class 'map'
subset(x, ...)
## S3 method for class 'map'
x[...]
Arguments
x

A list whose components are vectors of marker locations.

...

Vector of chromosome indices.

Value
The input map object, but with only the specified subset of chromosomes.
Author(s)
Karl W Broman, 
See Also
subset.cross

246

subset.scanone

Examples
data(map10)
map10 <- subset(map10, chr=1:5)
# you can also use brackets
map10 <- map10[2:3]

subset.scanone

Subsetting the results of a genome scan

Description
Pull out a specified set of chromosomes and/or LOD columns from scanone output.
Usage
## S3 method for class 'scanone'
subset(x, chr, lodcolumn, ...)
Arguments
x

An object of class scanone, output from scanone.

chr

Optional vector specifying which chromosomes to keep. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

lodcolumn

A vector specifying which LOD columns to keep (or, if negative), omit. These
should be between 1 and the number of LOD columns in the input x.

...

Ignored at this point.

Value
The input scanone object, but with only the specified subset of the data.
Author(s)
Karl W Broman, 
See Also
summary.scanone, scanone
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=2.5)
out <- scanone(fake.bc, method="hk", pheno.col=1:2)
summary(subset(out, chr=18:19), format="allpeaks")

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247

subset.scanoneperm

Subsetting permutation test results

Description
Pull out results for a specified set LOD columns from permutation results from scanone.
Usage
## S3 method for class 'scanoneperm'
subset(x, repl, lodcolumn, ...)
## S3 method for class 'scanoneperm'
x[repl, lodcolumn]
Arguments
x

Permutation results from scanone, run with n.perm>0.

repl

A vector specifying which permutation replicates to keep or (if negative) omit.

lodcolumn

A vector specifying which LOD columns to keep or (if negative) omit. These
should be between 1 and the number of LOD columns in the input x.

...

Ignored at this point.

Value
The input scanone permutation results, but with only the specified subset of the data.
Author(s)
Karl W Broman, 
See Also
summary.scanoneperm, scanone, c.scanoneperm, cbind.scanoneperm, rbind.scanoneperm
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=5)
operm <- scanone(fake.bc, method="hk", pheno.col=1:2, n.perm=25)
operm2 <- subset(operm, lodcolumn=2)
# alternatively
operm2alt <- operm[,2]

248

subset.scantwo

subset.scantwo

Subsetting the results of a 2-d genome scan

Description
Pull out a specified set of chromosomes and/or LOD columns from scantwo output.
Usage
## S3 method for class 'scantwo'
subset(x, chr, lodcolumn, ...)
Arguments
x

An object of class scantwo, output from scantwo.

chr

Optional vector specifying which chromosomes to keep. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

lodcolumn

A vector specifying which LOD columns to keep (or, if negative), omit. These
should be between 1 and the number of LOD columns in the input x.

...

Ignored at this point.

Value
The input scantwo object, but with only the specified subset of the data.
Author(s)
Karl W Broman, 
See Also
summary.scantwo, scantwo
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc)
out <- scantwo(fake.bc, method="hk", pheno.col=1:2)
summary(subset(out, chr=18:19))

subset.scantwoperm

249

subset.scantwoperm

Subsetting two-dimensional permutation test results

Description
Pull out results for a specified set LOD columns from permutation results from scantwo.
Usage
## S3 method for class 'scantwoperm'
subset(x, repl, lodcolumn, ...)
## S3 method for class 'scantwoperm'
x[repl, lodcolumn]
Arguments
x

Permutation results from scantwo, run with n.perm>0.

repl

A vector specifying which permutation replicates to keep or (if negative) omit.
Ignored in case of X-chr specific permutations

lodcolumn

A vector specifying which LOD columns to keep or (if negative) omit. These
should be between 1 and the number of LOD columns in the input x.

...

Ignored at this point.

Value
The input scantwo permutation results, but with only the specified subset of the data.
Author(s)
Karl W Broman, 
See Also
summary.scantwoperm, scantwo, c.scantwoperm, rbind.scantwoperm
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=0)
operm <- scantwo(fake.bc, method="hk", pheno.col=1:2, n.perm=5)
operm2 <- subset(operm, lodcolumn=2)
# alternatively
operm2alt <- operm[,2]

250

summary.fitqtl

summary.cross

Print summary of QTL experiment

Description
Print summary information about a cross object.
Usage
## S3 method for class 'cross'
summary(object, ...)
Arguments
object

An object of class cross. See read.cross for details.

...

Ignored at this point.

Value
An object of class summary.cross containing a variety of summary information about the cross
(this is generally printed automatically).
Author(s)
Karl W Broman, 
See Also
read.cross, plot.cross, nind, nmar, nchr, totmar, nphe
Examples
data(fake.f2)
summary(fake.f2)

summary.fitqtl

Summary of fit of qtl model

Description
Print summary information about the results of fitqtl.
Usage
## S3 method for class 'fitqtl'
summary(object, pvalues=TRUE, simple=FALSE, ...)

summary.qtl

251

Arguments
object
pvalues
simple
...

Output from fitqtl.
If FALSE, don’t include p-values in the summary.
If TRUE, don’t include p-values or sums of squares in the summary.
Ignored at this point.

Value
An object of class summary.fitqtl, which is not all that different than the input, but when printed
gives summary information about the results.
Author(s)
Hao Wu; Karl W Broman, 
See Also
fitqtl, makeqtl, scanqtl
Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c(1, 8, 13)
qp <- c(26, 56, 28)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
# fit model with 3 interacting QTLs interacting
# (performing a drop-one-term analysis)
lod <- fitqtl(fake.f2, pheno.col=1, qtl, formula=y~Q1*Q2*Q3,
method="hk")
summary(lod)

summary.qtl

Print summary of a QTL object

Description
Print summary information about a qtl object.
Usage
## S3 method for class 'qtl'
summary(object, ...)
Arguments
object
...

An object of class qtl, created by makeqtl.
Ignored at this point.

252

summary.ripple

Value
An object of class summary.qtl, which is just a data.frame containing the chromosomes, positions,
and number of possible genotypes for each QTL.
Author(s)
Karl W Broman, 
See Also
makeqtl
Examples
data(fake.f2)
# take out several QTLs and make QTL object
qc <- c(1, 6, 13)
qp <- c(25.8, 33.6, 18.63)
fake.f2 <- subset(fake.f2, chr=qc)
fake.f2 <- calc.genoprob(fake.f2, step=2, err=0.001)
qtl <- makeqtl(fake.f2, qc, qp, what="prob")
summary(qtl)

summary.ripple

Print summary of ripple results

Description
Print marker orders, from the output of the function ripple, for which the log10 likelihood relative
to the initial order is above a specified cutoff.
Usage
## S3 method for class 'ripple'
summary(object, lod.cutoff = -1, ...)
Arguments
object

An object of class ripple, the output of the function ripple.

lod.cutoff

Only marker orders with LOD score (relative to the initial order) above this
cutoff will be displayed. For output of ripple in the case of minimization of
the number of obligate crossovers, we double this argument and treat it as a
cutoff for the number of obligate crossovers.

...

Ignored at this point.

summary.scanone

253

Value
An object of class summary.ripple, whose rows correspond to marker orders with likelihood (or
number of obligate crossovers) within some cutoff of the initial order. If no marker order, other
than the initial one, has likelihood within the specified range, the initial and next-best orders are
returned.
Author(s)
Karl W Broman, 
See Also
ripple, est.map, est.rf
Examples
## Not run: data(badorder)
rip1 <- ripple(badorder, 1, 7)
summary(rip1)
rip2 <- ripple(badorder, 1, 2, method="likelihood")
summary(rip2)
badorder <- switch.order(badorder, 1, rip2[2,])
## End(Not run)

summary.scanone

Summarize the results of a genome scans

Description
Print the rows of the output from scanone that correspond to the maximum LOD for each chromosome, provided that they exceed some specified thresholds.
Usage
## S3 method for class 'scanone'
summary(object, threshold,
format=c("onepheno", "allpheno", "allpeaks", "tabByCol", "tabByChr"),
perms, alpha, lodcolumn=1, pvalues=FALSE,
ci.function=c("lodint", "bayesint"), ...)
Arguments
object

An object output by the function scanone.

threshold

LOD score thresholds. Only peaks with LOD score above this value will be
returned. This could be a single number or (for formats other than "onepheno")
a threshold for each LOD score column. If alpha is specified, threshold should
not be.

format

Format for the output. See Details, below.

254

summary.scanone
perms

Optional permutation results used to derive thresholds or to calculate genomescan-adjusted p-values. This must be consistent with the object input, in that it
must have the same number of LOD score columns, though it can have just one
column of permutation results, in which case they are reused for all LOD score
columns in the scanone output, object. (These can also be permutation results
from scantwo, which permutations for a one-dimensional scan.)

alpha

If perms are included, this is the significance level used to calculate thresholds
for determining which peaks to pull out. If threshold is specified, alpha should
not be.

lodcolumn

If format="onepheno", this indicates the LOD score column to focus on. This
should be a single number between 1 and the number of LOD columns in the
object input.

pvalues

If TRUE, include columns with genome-scan-adjusted p-values in the results.
This requires that perms be provided.

ci.function

For formats "tabByCol" and "tabByChr", indicates the function to use to get
approximate confidence intervals for QTL location.

...

For formats "tabByCol" and "tabByChr", additional arguments are passed to
the function indicated by ci.function (for example, drop for lodint or prob
for bayesint, or expandtomarkers for either).

Details
This function is used to report loci deemed interesting from a one-QTL genome scan (by scanone).
For format="onepheno", we focus on a single LOD score column, indicated by lodcolumn. The
single largest LOD score peak on each chromosome is extracted. If threshold is specified, only
those peaks with LOD meeting the threshold will be returned. If perms and alpha are specified, a
threshold is calculated based on the permutation results in perms for the significance level alpha.
If neither threshold nor alpha are specified, the peak on each chromosome is returned. Again
note that with this format, only the LOD score column indicated by lodcolumn is considered in
deciding which chromosomes to return, but the LOD scores from other columns, at the position
with maximum LOD score in the lodcolumn column, are also returned.
For format="allpheno", we consider all LOD score columns, and pull out the position, on each
chromosome, showing the largest LOD score. The output thus may contain multiple rows for a
chromosome. Here threshold may be a vector of LOD score thresholds, one for each LOD score
column, in which case only those positions for which a LOD score column exceeded its threshold
are given. If threshold is a single number, it is applied to all of the LOD score columns. If alpha is
specified, it must be a single significance level, applied for all LOD score columns, and again perms
must be specified, and these are used to calculate the LOD score threshold for the significance level
alpha.
For format="allpeaks", the output will contain, for each chromosome, the maximum LOD score
for each LOD score column, at the position at which it achieved its maximum. Thus, the output will
contain no more than one row per chromosome, but will contain the position and maximum LOD
score for each of the LOD score columns. The arguments threshold and alpha may be specified
as for the "allpheno" format. The results for a chromosome are returned if at least one of the LOD
score columns exceeded its threshold.
For format="tabByCol", there will be a separate table for each LOD score column, with a single
peak per chromosome. Included are columns indicating chromosome, peak position, lower and
upper limits of the confidence interval calculated via lodint or bayesint, and lod score.
The output for format="tabByChr", is similar to that of format="tabByCol", but with results
organized by chromosome rather than by LOD score column.

summary.scanone

255

If pvalues=TRUE, and perms is specified, genome-scan-adjusted p-values are calculated for each
LOD score column, and there are additional columns in the output containing these p-values.
In the case that X-chromosome specific permutations were performed (with perm.Xsp=TRUE in
scanone), autosome- and X-chromosome specific thresholds and p-values are calculated by the
method in Broman et al. (2006).
Value
An object of class summary.scanone, to be printed by print.summary.scanone.
Author(s)
Karl W Broman, 
References
Broman, K. W., Sen, Ś, Owens, S. E., Manichaikul, A., Southard-Smith, E. M. and Churchill G. A.
(2006) The X chromosome in quantitative trait locus mapping. Genetics, 174, 2151–2158.
See Also
scanone, plot.scanone, max.scanone, subset.scanone, c.scanone, summary.scanoneperm
c.scanoneperm
Examples
data(fake.bc)
fake.bc <- calc.genoprob(fake.bc, step=5)
# genome scan by Haley-Knott regression
out <- scanone(fake.bc, method="hk")
# permutation tests
## Not run: operm <- scanone(fake.bc, method="hk", n.perm=1000)
# peaks for all chromosomes
summary(out)
# results with LOD >= 3
summary(out, threshold=3)
# the same, but also showing the p-values
summary(out, threshold=3, perms=operm, pvalues=TRUE)
# results with LOD meeting the 0.05 threshold from the permutation results
summary(out, perms=operm, alpha=0.05)
# the same, also showing the p-values
summary(out, perms=operm, alpha=0.05, pvalues=TRUE)
##### summary with multiple phenotype results
out2 <- scanone(fake.bc, pheno.col=1:2, method="hk")

256

summary.scanoneboot
# permutations
## Not run: operm2 <- scanone(fake.bc, pheno.col=1:2, method="hk", n.perm=1000)
# results with LOD >= 2 for the 1st phenotype and >= 1 for the 2nd phenotype
#
using format="allpheno"
summary(out2, thr=c(2, 1), format="allpheno")
# The same with format="allpeaks"
summary(out2, thr=c(2, 1), format="allpeaks")
# The same with p-values
summary(out2, thr=c(2, 1), format="allpeaks", perms=operm2, pvalues=TRUE)
# results with LOD meeting the 0.05 significance level by the permutations
#
using format="allpheno"
summary(out2, format="allpheno", perms=operm2, alpha=0.05)
# The same with p-values
summary(out2, format="allpheno", perms=operm2, alpha=0.05, pvalues=TRUE)
# The same with format="allpeaks"
summary(out2, format="allpeaks", perms=operm2, alpha=0.05, pvalues=TRUE)
# format="tabByCol"
summary(out2, format="tabByCol", perms=operm2, alpha=0.05, pvalues=TRUE)
# format="tabByChr", but using bayes intervals
summary(out2, format="tabByChr", perms=operm2, alpha=0.05, pvalues=TRUE,
ci.function="bayesint")
# format="tabByChr", but using 99% bayes intervals
summary(out2, format="tabByChr", perms=operm2, alpha=0.05, pvalues=TRUE,
ci.function="bayesint", prob=0.99)

summary.scanoneboot

Bootstrap confidence interval for QTL location

Description
Calculates a bootstrap confidence interval for QTL location, using the bootstrap results from scanoneboot.
Usage
## S3 method for class 'scanoneboot'
summary(object, prob=0.95, expandtomarkers=FALSE, ...)
Arguments
object

Output from scanoneboot.

prob
Desired coverage.
expandtomarkers
If TRUE, the interval is expanded to the nearest flanking markers.
...

Ignored at this point.

summary.scanoneperm

257

Value
An object of class scanone, indicating the position with the maximum LOD, and indicating endpoints for the estimated bootstrap confidence interval.
Author(s)
Karl W Broman, 
See Also
scanoneboot, plot.scanoneboot, lodint, bayesint
Examples
## Not run: data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=1, err=0.001)
bootoutput <- scanoneboot(fake.f2, chr=13, method="hk")
summary(bootoutput)
## End(Not run)

summary.scanoneperm

LOD thresholds from scanone permutation results

Description
Print the estimated genome-wide LOD thresholds on the basis of permutation results from scanone
(with n.perm > 0).
Usage
## S3 method for class 'scanoneperm'
summary(object, alpha=c(0.05, 0.10),
controlAcrossCol=FALSE, ...)
Arguments
object

Output from the function scanone with n.perm > 0.

alpha

Genome-wide significance levels.

controlAcrossCol
If TRUE, control error rate not just across the genome but also across the columns
of LOD scores.
...

Ignored at this point.

258

summary.scanoneperm

Details
If there were autosomal data only or scanone was run with perm.Xsp=FALSE, genome-wide LOD
thresholds are given; these are the 1-α quantiles of the genome-wide maximum LOD scores from
the permutations.
If there were autosomal and X chromosome data and scanone was run with perm.Xsp=TRUE,
autosome- and X-chromsome-specific LOD thresholds are given, by the method described in Broman et al. (2006). Let LA and LX be total the genetic lengths of the autosomes and X chromosome,
respectively, and let LT = LA + LX Then in place of α, we use
αA = 1 − (1 − α)LA /LT
as the significance level for the autosomes and
αX = 1 − (1 − α)LX /LT
as the significance level for the X chromosome. The result is a list with two matrices, one for the
autosomes and one for the X chromosome.
If controlAcrossCol=TRUE, we use a trick to control the error rate not just across the genome but
also across the LOD score columns. Namely, we convert each column of permutation results to
ranks, and then for each permutation replicate we find the maximum rank across the columns. We
then find the appropriate quantile of the maximized ranks, and then backtrack to the corresponding
LOD score within each of the columns. See Burrage et al. (2010), right column on page 118.
Value
An object of class summary.scanoneperm, to be printed by print.summary.scanoneperm. If there
were X chromosome data and scanone was run with perm.Xsp=TRUE, there are two matrices in the
results, for the autosome and X-chromosome LOD thresholds.
Author(s)
Karl W Broman, 
References
Broman KW, Sen Ś, Owens SE, Manichaikul A, Southard-Smith EM, Churchill GA (2006) The X
chromosome in quantitative trait locus mapping. Genetics, 174, 2151–2158.
Burrage LC, Baskin-Hill AE, Sinasac DS, Singer JB, Croniger CM, Kirby A, Kulbokas EJ, Daly
MJ, Lander ES, Broman KW, Nadeau JH (2010) Genetic resistance to diet-induced obesity in chromosome substitution strains of mice. Mamm Genome, 21, 115–129.
Churchill GA, Doerge RW (1994) Empirical threshold values for quantitative trait mapping. Genetics 138, 963–971.
See Also
scanone, summary.scanone, plot.scanoneperm
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=2.5)

summary.scanPhyloQTL

259

operm1 <- scanone(fake.f2, n.perm=100, method="hk")
summary(operm1)
operm2 <- scanone(fake.f2, n.perm=100, method="hk", perm.Xsp=TRUE)
summary(operm2)
# Add noise column
fake.f2$pheno$noise <- rnorm(nind(fake.f2))
operm3 <- scanone(fake.f2, pheno.col=c("phenotype", "noise"), n.perm=10, method="hk")
summary(operm3)
summary(operm3, controlAcrossCol=TRUE, alpha=c(0.05, 0.36))

summary.scanPhyloQTL

Summarize the results a genome scan to map a QTL to a phylogenetic
tree

Description
Print the maximum LOD scores for each partition on each chromosome, from the results of scanPhyloQTL.
Usage
## S3 method for class 'scanPhyloQTL'
summary(object, format=c("postprob", "lod"),
threshold, ...)
Arguments
object

An object output by the function scanPhyloQTL.

format

Indicates whether to provide LOD scores or approximate posterior probabilities;
see Details below.

threshold

A threshold determining which chromosomes should be output; see Details below.

...

Ignored at this point.

Details
This function is used to report chromosomes deemed interesting from a one-QTL genome scan to
map QTL to a phylogenetic tree (by scanPhyloQTL).
For format="lod", the output contains the maximum LOD score for each partition on each chromosome (which do not necessarily occur at the same position). The position corresponds to the
peak location for the partition with the largest LOD score on that chromosome. The last column is
the overall maximum LOD (across partitions) on that chromosome. The second-to-last column is
the inferred partition (i.e., that with the largest LOD score. The third-to-last column is the difference
between the LOD score for the best partition and that for the second-best.
For format="postprob", the final column contains the maximum LOD score across partitions.
But instead of providing the LOD scores for each partition, these are converted to approximate
posterior probabilities under the assumption of a single diallelic QTL on that chromosome: on each
chromosome, we take 10LOD for the partitions and rescale them to sum to 1.
The threshold argument is applied to the last column (the maximum LOD score across partitions).

260

summary.scanPhyloQTL

Value
An object of class summary.scanPhyloQTL, to be printed by print.summary.scanPhyloQTL.
Author(s)
Karl W Broman, 
References
Broman, K. W., Kim, S., An\’e, C. and Payseur, B. A. Mapping quantitative trait loci to a phylogenetic tree. In preparation.
See Also
scanPhyloQTL, plot.scanPhyloQTL, max.scanPhyloQTL, summary.scanone, inferredpartitions,
simPhyloQTL
Examples
## Not run:
# example map; drop X chromosome
data(map10)
map10 <- map10[1:19]
# simulate data
x <- simPhyloQTL(4, partition="AB|CD", crosses=c("AB", "AC", "AD"),
map=map10, n.ind=150,
model=c(1, 50, 0.5, 0))
# run calc.genoprob on each cross
x <- lapply(x, calc.genoprob, step=2)
# scan genome, at each position trying all possible partitions
out <- scanPhyloQTL(x, method="hk")
# maximum peak
max(out, format="lod")
# approximate posterior probabilities at peak
max(out, format="postprob")
# all peaks above a threshold for LOD(best) - LOD(2nd best)
summary(out, threshold=1, format="lod")
# all peaks above a threshold for LOD(best), showing approx post'r prob
summary(out, format="postprob", threshold=3)
# plot of results
plot(out)
## End(Not run)

summary.scantwo

summary.scantwo

261

Summarize the results of a two-dimensional genome scan

Description
Summarize the interesting aspects of the results of scantwo.
Usage
## S3 method for class 'scantwo'
summary(object, thresholds,
what=c("best", "full", "add", "int"),
perms, alphas, lodcolumn=1, pvalues=FALSE,
allpairs=TRUE, ...)
Arguments
object

An object of class scantwo, the output of the function scantwo.

thresholds

A vector of length 5, giving LOD thresholds for the full, conditional-interactive,
interaction, additive, and conditional-additive LOD scores. See Details, below.

what

Indicates for which LOD score the maximum should be reported. See Details,
below.

perms

Optional permutation results used to derive thresholds or to calculate genomescan-adjusted p-values. This must be consistent with the object input, in that it
must have the same number of LOD score columns, though it can have just one
column of permutation results, in which case they are assumed to apply to any
chosen LOD score column.

alphas

If perms are included, these are the significance levels used to calculate thresholds for determining which peaks to pull out. It should be a vector of length 5,
giving significance levels for the full, conditional-interactive, interaction, additive, and conditional-additive LOD scores. (It can also be a single number, in
which case it is assumed that the same value is used for all five LOD scores.) If
thresholds is specified, alphas should not be.

lodcolumn

If the scantwo results contain LOD scores for multiple phenotypes, this argument indicates which to use in the summary. Only one LOD score column may
be considered at a time.

pvalues

If TRUE, include columns with genome-scan-adjusted p-values in the results.
This requires that perms be provided.

allpairs

If TRUE, all pairs of chromosomes are considered. If FALSE, only self-self
pairs are considered, so that one may more conveniently check for possible
linked QTL.

...

Ignored at this point.

Details
If what="best", we calculate, for each pair of chromosomes, the maximum LOD score for the
full model (two QTL plus interaction) and the maximum LOD score for the additive model. The
difference between these is a LOD score for a test for interaction. We also calculate the difference

262

summary.scantwo
between the maximum full LOD and the maximum single-QTL LOD score for the two chromosomes; this is the LOD score for a test for a second QTL, allowing for epistasis, which we call
either the conditional-interactive or "fv1" LOD score. Finally, we calculate the difference between
the maximum additive LOD score and the maximum single-QTL LOD score for the two chromosomes; this is the LOD score for a test for a second QTL, assuming that the two QTL act additively,
which we call either the conditional-additive or "av1" LOD score. Note that the maximum full LOD
and additive LOD are allowed to occur in different places.
If what="full", we find the maximum full LOD and extract the additive LOD at the corresponding
pair of positions; we derive the other three LOD scores for that fixed pair of positions.
If what="add", we find the maximum additive LOD and extract the full LOD at the corresponding
pair of positions; we derive the other three LOD scores for that fixed pair of positions.
If what="int", we find the pair of positions for which the difference between the full and additive
LOD scores is largest, and then calculate the five LOD scores at that pair of positions.
If thresholds or alphas is provided (and note that when alphas is provided, perms must also),
we extract just those pairs of chromosomes for which either (a) the full LOD score exceeds its
thresholds and either the conditional-interactive LOD or the interaction LOD exceed their threshold,
or (b) the additive LOD score exceeds its threshold and the conditional-additive LOD exceeds its
threshold. The thresholds or alphas must be given in the order full, cond-int, int, add, cond-add.
Thresholds may be obtained by a permutation test with scantwo, but these are extremely timeconsuming. For a mouse backcross, we suggest the thresholds (6.0, 4.7, 4.4, 4.7, 2.6) for the full,
conditional-interactive, interaction, additive, and conditional-additive LOD scores, respectively. For
a mouse intercross, we suggest the thresholds (9.1, 7.1, 6.3, 6.3, 3.3) for the full, conditionalinteractive, interaction, additive, and conditional-additive LOD scores, respectively. These were
obtained by 10,000 simulations of crosses with 250 individuals, markers at a 10 cM spacing, and
analysis by Haley-Knott regression.

Value
An object of class summary.scantwo, to be printed by print.summary.scantwo;
Output of addpair
Note that, for output from addpair in which the new loci are indicated explicitly in the formula,
the summary provided by summary.scantwo is somewhat special.
All arguments except allpairs and thresholds (and, of course, the input object) are ignored.
If the formula is symmetric in the two new QTL, the output has just two LOD score columns:
lod.2v0 comparing the full model to the model with neither of the new QTL, and lod.2v1 comparing the full model to the model with just one new QTL.
If the formula is not symmetric in the two new QTL, the output has three LOD score columns:
lod.2v0 comparing the full model to the model with neither of the new QTL, lod.2v1b comparing
the full model to the model in which the first of the new QTL is omitted, and lod.2v1a comparing
the full model to the model with the second of the new QTL omitted.
The thresholds argument should have length 1 or 2, rather than the usual 5. Rows will be retained
if lod.2v0 is greater than thresholds[1] and lod.2v1 (or either of lod.2v1a or lod.2v1b) is
greater than thresholds[2]. (If a single thresholds is given, we assume that thresholds[2]==0.)
The older version
The previous version of this function is still available, though it is now named summaryScantwoOld.

summary.scantwo

263

We much prefer the revised function. However, while we are confident that this function (and the
permutations in scantwo) are calculating the relevant statistics, the appropriate significance levels
for these relatively complex series of statistical tests is not yet completely clear.
Author(s)
Karl W Broman, 
See Also
scantwo, plot.scantwo, max.scantwo, condense.scantwo
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=5)
out.2dim <- scantwo(fake.f2, method="hk")
# All pairs of chromosomes
summary(out.2dim)
# Chromosome pairs meeting specified criteria
summary(out.2dim, thresholds=c(9.1, 7.1, 6.3, 6.3, 3.3))
# Similar, but ignoring the interaction LOD score in the rule
summary(out.2dim, thresholds=c(9.1, 7.1, Inf, 6.3, 3.3))
# Pairs having largest interaction LOD score, if it's > 4
summary(out.2dim, thresholds=c(0, Inf, 4, Inf, Inf), what="int")
# permutation test to get thresholds; run in two batches
#
and then combined with c.scantwoperm
## Not run: operm.2dimA <- scantwo(fake.f2, method="hk", n.perm=500)
operm.2dimB <- scantwo(fake.f2, method="hk", n.perm=500)
operm.2dim <- c(operm.2dimA, operm.2dimB)
## End(Not run)
# estimated LOD thresholds
summary(operm.2dim)
# Summary, citing significance levels and so estimating thresholds
#
from the permutation results
summary(out.2dim, perms=operm.2dim, alpha=rep(0.05, 5))
# Similar, but ignoring the interaction LOD score in the rule
summary(out.2dim, perms=operm.2dim, alpha=c(0.05, 0.05, 0, 0.05, 0.05))
# Similar, but also getting genome-scan-adjusted p-values
summary(out.2dim, perms=operm.2dim, alpha=c(0.05, 0.05, 0, 0.05, 0.05),
pvalues=TRUE)

264

summary.scantwoperm

summary.scantwoperm

LOD thresholds from scantwo permutation results

Description
Print the estimated genome-wide LOD thresholds on the basis of permutation results from scantwo
(with n.perm > 0).
Usage
## S3 method for class 'scantwoperm'
summary(object, alpha=c(0.05, 0.10), ...)
Arguments
object

Output from the function scantwo with n.perm > 0.

alpha

Genome-wide significance levels.

...

Ignored at this point.

Details
We take the 1 − α quantiles of the individual LOD scores.
In the case of X-chr-specific permutations, we use the combined length of the autosomes, LA , and
the length of the X chromosome, LX , and calculate the area of the A:A, A:X, and X:X regions as
L2A /2, LA LX , and L2X /2, and then use the nominal significance levels of 1 − (1 − α)p , where p is
the proportional area for that region.
Value
An object of class summary.scantwoperm, to be printed by print.summary.scantwoperm.
Author(s)
Karl W Broman, 
References
Churchill, G. A. and Doerge, R. W. (1994) Empirical threshold values for quantitative trait mapping.
Genetics 138, 963–971.
See Also
scantwo, summary.scantwo, plot.scantwoperm
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=0)
## Not run: operm <- scantwo(fake.f2, n.perm=100, method="hk")
summary(operm)

summaryMap

summaryMap

265

Print summary of a genetic map

Description
Print summary information about a map object.

Usage
## S3 method for class 'map'
summary(object, ...)
summaryMap(object, ...)

Arguments
object

An object of class map, which is a list of vectors (or, for a sex-specific map,
2-row matrices), each specifying the locations of the markers. The object can
also be of class cross, in which case the function pull.map is used to extract
the genetic map from the object.

...

Ignored at this point.

Value
An object of class summary.map, which is just a data.frame containing the number of markers,
length, the average inter-marker spacing, and the maximum distance between markers, for each
chromosome and overall. An attribute sexsp indicates whether the map was sex-specific.

Author(s)
Karl W Broman, 

See Also
chrlen, pull.map, summary.cross

Examples
data(map10)
summary(map10)

266

summaryScantwoOld

summaryScantwoOld

Summarize the results of a two-dimensional genome scan

Description
Summarize the interesting aspects of the results of scantwo; this is the version of summary.scantwo
that was included in R/qtl version 1.03 and earlier.
Usage
summaryScantwoOld(object, thresholds = c(0, 0, 0), lodcolumn=1,
type = c("joint","interaction"), ...)
Arguments
object

An object of class scantwo, the output of the function scantwo.

thresholds

A vector of length three, giving LOD thresholds for the joint LOD, interaction
LOD and single-QTL conditional LOD. Negative threshold values are taken relative to the maximum joint, interaction, or individual QTL LOD, respectively.

lodcolumn

If the scantwo results contain LOD scores for multiple phenotypes, this argument indicates which to use in the summary.

type

Indicates whether to pick peaks with maximal joint or interaction LOD.

...

Ignored at this point.

Details
For each pair of chromosomes, the pair of loci for which the LOD score (either joint or interaction
LOD, according to the argument type) is a maximum is considered. The pair is printed only if its
joint LOD score exceeds the joint threshold and either (a) the interaction LOD score exceeds its
threshold or (b) both of the loci have conditional LOD scores that are above the conditional LOD
threshold, where the conditional LOD score for locus q1 , LOD(q1 |q2 ), is the log10 likelihood ratio
comparing the model with q1 and q2 acting additively to the model with q2 alone.
In the case the results of scanone are not available, the maximum locus pair for each chromosome
is printed whenever its joint LOD exceeds the joint LOD threshold.
The criterion used in this summary is due to Gary Churchill and Śaunak Sen, and deserves careful
consideration and possible revision.
Value
An object of class summary.scantwo.old, to be printed by print.summary.scantwo.old. Pairs
of loci meeting the specified criteria are printed, with their joint LOD, interaction LOD, and the
conditional LOD for each locus, along with single-point P-values calculated by the χ2 approximation. P-values are printed as − log10 (P ).
If the input scantwo object does not include the results of scanone, the interaction and conditional
LOD thresholds are ignored, and all pairs of loci for which the joint LOD exceeds its threshold are
printed, though without their conditional LOD scores.

switch.order

267

Author(s)
Hao Wu; Karl W Broman, ; Brian Yandell
See Also
summary.scantwo, scantwo, plot.scantwo, max.scantwo
Examples
data(fake.f2)
fake.f2 <- calc.genoprob(fake.f2, step=5)
out.2dim <- scantwo(fake.f2, method="hk")
# All pairs of loci
summaryScantwoOld(out.2dim)
# Pairs meeting specified criteria
summaryScantwoOld(out.2dim, c(7, 3, 3))
# Pairs with both conditional LODs > 2
summaryScantwoOld(out.2dim,c(0,1000,2))
# Pairs with interaction LOD is above 3
summaryScantwoOld(out.2dim,c(0,3,1000))

switch.order

Switch the order of markers on a chromosome

Description
Switch the order of markers on a specified chromosome to a specified new order.
Usage
switch.order(cross, chr, order, error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
maxit=4000, tol=1e-6, sex.sp=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

The chromosome for which the marker order is to be switched. Only one chromosome is allowed. (This should be a character string referring to the chromosomes by name.)

order

A vector of numeric indices defining the new marker order. The vector may have
length two more than the number of markers, for easy in use with the output of
the function ripple.

error.prob

Assumed genotyping error rate (passed to est.map).

map.function

Map function to be used (passed to est.map).

maxit

Maximum number of EM iterations to perform.

268

switchAlleles
tol

Tolerance for determining convergence.

sex.sp

Indicates whether to estimate sex-specific maps; this is used only for the 4-way
cross.

Value
The input cross object, but with the marker order on the specified chromosome updated, and with
any derived data removed (except for recombination fractions, if present, which are not removed);
the genetic map for the relevant chromosome is re-estimated.
Author(s)
Karl W Broman, 
See Also
flip.order, ripple, clean.cross
Examples
data(fake.f2)
fake.f2 <- switch.order(fake.f2, 1, c(1,3,2,4:7))

switchAlleles

Switch alleles at selected markers

Description
Switch alleles at selected markers in a cross object.
Usage
switchAlleles(cross, markers, switch=c("AB", "CD", "ABCD", "parents"))
Arguments
cross

An object of class cross. See read.cross for details.

markers

Names of markers whose alleles are to be switched.

switch

For a 4-way cross, indicates how to switch the alleles (A for B, C for D, both A
for B and C for D), or both A for C and B for D (parents).

Details
For a backcross, we exchange homozygotes (AA) and heterozygotes (AB).
For doubled haploids and recombinant inbred lines, we exchange the two homozygotes.
For an intercross, we exchange the two homozygotes, and exchange C (i.e., not AA) and D (i.e., not
BB). (The heterozygotes in an intercross are left unchanged.)
For a 4-way cross, we consider the argument switch, and the exchanges among the genotypes are
more complicated.

table2map

269

Value
The input cross object, with alleles at selected markers switched.
Author(s)
Karl W Broman, 
See Also
checkAlleles, est.rf, geno.crosstab
Examples
data(fake.f2)
geno.crosstab(fake.f2, "D5M391", "D5M81")
# switch homozygotes at marker D5M391
fake.f2 <- switchAlleles(fake.f2, "D5M391")
geno.crosstab(fake.f2, "D5M391", "D5M81")
## Not run: fake.f2 <- est.rf(fake.f2)
checkAlleles(fake.f2)
## End(Not run)

table2map

Convert a table of marker positions to a map object.

Description
Convert a data frame with marker positions to a map object.
Usage
table2map(tab)
Arguments
tab

A data frame with two columns: chromosome and position. The row names are
the marker names.

Value
A map object: a list whose components (corresponding to chromosomes) are vectors of marker
positions.
Author(s)
Karl W Broman, 

270

top.errorlod

See Also
map2table, pull.map, est.map
Examples
tab <- data.frame(chr=c(1,1,1,1,2,2,2,2,3,3,3,3),
pos=c(0,2,4,8,0,2,4,8,0,2,4,8))
rownames(tab) <- paste0("marker", 1:nrow(tab))
map <- table2map(tab)

top.errorlod

List genotypes with large error LOD scores

Description
Prints those genotypes with error LOD scores above a specified cutoff.
Usage
top.errorlod(cross, chr, cutoff=4, msg=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

cutoff

Only those genotypes with error LOD scores above this cutoff will be listed.

msg

If TRUE, print a message if there are no apparent errors.

Value
A data.frame with 4 columns, whose rows correspond to the genotypes that are possibly in error.
The four columns give the chromosome number, individual number, marker name, and error LOD
score.
Author(s)
Karl W Broman, 
See Also
calc.errorlod, plotGeno, plotErrorlod

totmar

271

Examples
data(hyper)
# Calculate error LOD scores
hyper <- calc.errorlod(hyper,error.prob=0.01)
# Print those above a specified cutoff
top.errorlod(hyper,cutoff=4)

totmar

Determine the total number of markers

Description
Determine the total number of markers in a cross or map object.
Usage
totmar(object)
Arguments
object

An object of class cross (see read.cross for details) or map (see sim.map for
details).

Value
The total number of markers in the input.
Author(s)
Karl W Broman, 
See Also
read.cross, plot.cross, summary.cross, nind, nchr, nmar, nphe
Examples
data(fake.f2)
totmar(fake.f2)
map <- pull.map(fake.f2)
totmar(map)

272

transformPheno

transformPheno

Transformation of the phenotypes in a cross object

Description
Transform phenotypes in a cross object; by default use a logarithmic transformation, though any
function may be used.
Usage
transformPheno(cross, pheno.col=1, transf=log, ...)
Arguments
cross

An object of class cross. See read.cross for details.

pheno.col

A vector of numeric indices or character strings (indicating phenotypes by name)
of phenotypes to be transformed.

transf

The function to use in the transformation.

...

Additional arguments, to be passed to transf.

Value
The input cross object with the transformed phenotypes
Author(s)
Danny Arends 
See Also
mqmscan, scanone
Examples
data(multitrait)
# Log transformation of all phenotypes
multitrait.log <- transformPheno(multitrait, pheno.col=1:nphe(multitrait))
# Square-root transformation of all phenotypes
multitrait.sqrt <- transformPheno(multitrait, pheno.col=1:nphe(multitrait),
transf=sqrt)

tryallpositions

tryallpositions

273

Test all possible positions for a marker

Description
Try all possible positions for a marker, keeping all other markers fixed, and evaluate the log likelihood and estimate the chromosome length.
Usage
tryallpositions(cross, marker, chr, error.prob=0.0001,
map.function=c("haldane","kosambi","c-f","morgan"),
m=0, p=0, maxit=4000, tol=1e-6, sex.sp=TRUE,
verbose=TRUE)
Arguments
cross

An object of class cross. See read.cross for details.

marker

Character string with name of the marker to move about.

chr

A vector specifying which chromosomes to test for the position of the marker.
This should be a vector of character strings referring to chromosomes by name;
numeric values are converted to strings. Refer to chromosomes with a preceding
- to have all chromosomes but those considered. A logical (TRUE/FALSE)
vector may also be used.

error.prob

Assumed genotyping error rate used in the calculation of the penetrance Pr(observed
genotype | true genotype).

map.function

Indicates whether to use the Haldane, Kosambi, Carter-Falconer, or Morgan map
function when converting genetic distances into recombination fractions. (Ignored if m > 0.)

m

Interference parameter for the chi-square model for interference; a non-negative
integer, with m=0 corresponding to no interference. This may be used only for
a backcross or intercross.

p

Proportion of chiasmata from the NI mechanism, in the Stahl model; p=0 gives
a pure chi-square model. This may be used only for a backcross or intercross.

maxit

Maximum number of EM iterations to perform.

tol

Tolerance for determining convergence.

sex.sp

Indicates whether to estimate sex-specific maps; this is used only for the 4-way
cross.

verbose

If TRUE, print information on progress.

Value
A data frame (actually, an object of class "scanone", so that one may use plot.scanone, summary.scanone,
etc.) with each row being a possible position for the marker. The first two columns are the chromosome ID and position. The third column is a LOD score comparing the hypotheses that the marker
is in that position versus the hypothesis that it is not linked to that chromosome.
In the case of a 4-way cross, with sex.sp=TRUE, there are two additional columns with the estimated
female and male genetic lengths of the respective chromosome, when the marker is in that position.

274

typingGap
With sex.sp=FALSE, or for other types of crosses, there is one additional column, with the estimated
genetic length of the respective chromosome, when the marker is in that position.
The row names indicate the nearest flanking markers for each interval.

Author(s)
Karl W Broman, 
See Also
droponemarker, est.map, ripple, est.rf, switch.order, movemarker
Examples
data(fake.bc)
tryallpositions(fake.bc, "D7M301", 7, error.prob=0, verbose=FALSE)

typingGap

Maximum distance between genotyped markers

Description
Calculates, for each individual on each chromosome, the maximum distance between genotyped
markers.
Usage
typingGap(cross, chr, terminal=FALSE)
Arguments
cross

An object of class cross. See read.cross for details.

chr

Optional vector indicating the chromosomes to consider. This should be a vector of character strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding - to have all chromosomes but those considered. A logical (TRUE/FALSE) vector may also be
used.

terminal

If TRUE, just look at terminal typing gaps (from the terminal markers to the first
typed marker).

Details
We consider not just the distances between internal genotypes, but also distances from the beginning
of the chromosome to the first typed marker, and similarly for the end of the chromosome. (The
start and end of a chromosome are taken to be the locations of the initial and final markers.) If
terminal=TRUE, we look only at those beginning and end distances.
Value
A matrix with rows corresponding to individuals and columns corresponding to chromosomes. (If
there is just one chromosome, it is a numeric vector rather than a matrix.)

write.cross

275

Author(s)
Karl W Broman, 
See Also
ntyped, nmissing, locateXO
Examples
data(hyper)
plot(typingGap(hyper, chr=5),
ylab="Maximum gap between typed markers (cM)",
ylim=c(0, diff(range(pull.map(hyper,chr=5)[[1]]))))
plot(typingGap(hyper, chr=4),
ylab="Maximum gap between typed markers (cM)",
ylim=c(0, diff(range(pull.map(hyper,chr=4)[[1]]))))
plot(typingGap(hyper, chr=4, terminal=TRUE),
ylab="Maximum gap between chr end and typed marker (cM)",
ylim=c(0, diff(range(pull.map(hyper,chr=4)[[1]]))))

write.cross

Write data for a QTL experiment to a file

Description
Data for a QTL experiment is written to a file (or files).
Usage
write.cross(cross, format=c("csv", "csvr", "csvs", "csvsr",
"mm", "qtlcart", "gary", "qtab",
"mapqtl", "tidy"),
filestem="data", chr, digits=NULL, descr)
Arguments
cross
format
filestem

chr

digits
descr

An object of class cross. See read.cross for details.
Specifies whether to write the data in comma-delimited, rotated comma-delimited,
Mapmaker, QTL Cartographer, Gary Churchill’s, QTAB, MapQTL format.
A character string giving the first part of the output file names (the bit before the
dot). In Windows, use forward slashes ("/") or double backslashes ("\\") to
specify directory trees.
A vector specifying for which chromosomes genotype data should be written.
This should be a vector of character strings referring to chromosomes by name;
numeric values are converted to strings. Refer to chromosomes with a preceding
- to have all chromosomes but those considered. A logical (TRUE/FALSE)
vector may also be used.
Number of digits to which phenotype values and genetic map positions should
be rounded. If NULL (the default), they are not rounded.
Character string description; used only with format="qtab".

276

write.cross

Details
Comma-delimited formats: a single csv file is created in the formats "csv" or "csvr". Two files
are created (one for the genotype data and one for the phenotype data) for the formats "csvs" and
"csvsr"; if filestem="file", the two files will be names "file_gen.csv" and "file_phe.csv".
See the help file for read.cross for details on these formats.
Mapmaker format: Data is written to two files. Suppose filestem="file". Then "file.raw" will
contain the genotype and phenotype data, and "file.prep" will contain the necessary code for
defining the chromosome assignments, marker order, and inter-marker distances.
QTL Cartographer format: Data is written to two files. Suppose filestem="file". Then "file.cro"
will contain the genotype and phenotype data, and "file.map" will contain the genetic map information. Note that cross types are converted to QTL Cartographer cross types as follows: riself to
RF1, risib to RF2, bc to B1 and f2 to RF2.
Gary’s format: Data is written to six files. They are:
"geno.data" - genotype data;
"pheno.data" - phenotype data;
"chrid.dat" - the chromosome identifier for each marker;
"mnames.txt" - the marker names;
"markerpos.txt" - the marker positions;
"pnames.txt" - the phenotype names
QTAB format: See documentation.
MapQTL format: See documentation.
Tidy format: Data is written to three files, "stem_gen.csv", "stem_phe.csv", and "stem_map.csv"
(where stem is taken from the filestem argument.
Author(s)
Karl W Broman, ; Hao Wu; Brian S. Yandell; Danny Arends;
Aaron Wolen
See Also
read.cross
Examples
## Not run: data(fake.bc)
# comma-delimited format
write.cross(fake.bc, "csv", "Data/fakebc", c(1,5,13))
# rotated comma-delimited format
write.cross(fake.bc, "csvr", "Data/fakebc", c(1,5,13))
# split comma-delimited format
write.cross(fake.bc, "csvs", "Data/fakebc", c(1,5,13))
# split and rotated comma-delimited format
write.cross(fake.bc, "csvsr", "Data/fakebc", c(1,5,13))
# Mapmaker format
write.cross(fake.bc, "mm", "Data/fakebc", c(1,5,13))

xaxisloc.scanone

277

# QTL Cartographer format
write.cross(fake.bc, "qtlcart", "Data/fakebc", c(1,5,13))
# Gary's format
write.cross(fake.bc, "gary", c(1,5,13))
## End(Not run)

xaxisloc.scanone

Get x-axis locations in scanone plot

Description
Get x-axis locations for given cM positions on given chromosomes in a plot from plot.scanone)
Usage
xaxisloc.scanone(out, thechr, thepos, chr, gap=25)
Arguments
out

An object of class "scanone", as output by scanone. This must be identical to
what was used in the call to plot.scanone.

thechr

Chromosome IDs at which x-axis locations are to be determined.

thepos

Chromosome positions at which x-axis locations are to be determined.

chr

Optional vector specifying which chromosomes were plotted. This must be
identical to what was used in the call to plot.scanone.

gap

Gap separating chromosomes (in cM). This must be identical to what was used
in the call to plot.scanone.

Details
This function allows you to identify the x-axis locations in a plot of genome scan results, produced
by plot.scanone. This is useful for adding annotations, such as text or arrows.
The arguments out, chr, and gap must match what was used in the call to plot.scanone.
The arguments thechr and thepos indicate the genomic positions for which x-axis locations are
desired. If they both have length > 1, they must have the same length. If one has length > 1 and one
has length 1, the one with length 1 is expanded to match.
Value
A numeric vector of x-axis locations.
Author(s)
Karl W Broman, 
See Also
plot.scanone, add.threshold

278

xaxisloc.scanone

Examples
data(hyper)
hyper <- calc.genoprob(hyper)
out <- scanone(hyper, method="hk")
plot(out, chr=c(1, 4, 6, 15))
# add arrow and text to indicate peak LOD score
mxout <- max(out)
x <- xaxisloc.scanone(out, mxout$chr, mxout$pos, chr=c(1,4,6,15))
arrows(x+30, mxout$lod, x+5, mxout$lod, len=0.1, col="blue")
text(x+35, mxout$lod, "the peak", col="blue", adj=c(0, 0.5))

Index
plot.scanoneboot, 160
plot.scanoneperm, 161
plot.scanPhyloQTL, 162
plot.scantwo, 163
plot.scantwoperm, 166
plotErrorlod, 167
plotGeno, 168
plotInfo, 170
plotLodProfile, 171
plotMap, 173
plotMissing, 175
plotModel, 176
plotPheno, 177
plotPXG, 178
plotRF, 180
xaxisloc.scanone, 277
∗Topic manip
c.cross, 32
c.scanone, 33
c.scanoneperm, 34
c.scantwo, 35
c.scantwoperm, 36
cbind.scanoneperm, 41
cbind.scantwoperm, 42
clean.cross, 47
clean.scantwo, 48
convert.map, 53
convert.scanone, 54
convert.scantwo, 55
convert2riself, 56
convert2risib, 57
convert2sa, 58
drop.dupmarkers, 60
drop.markers, 60
drop.nullmarkers, 61
findDupMarkers, 81
flip.order, 87
interpPositions, 98
jittermap, 99
movemarker, 113
pickMarkerSubset, 154
pull.markers, 186
replace.map, 200

∗Topic IO
read.cross, 188
readMWril, 195
write.cross, 275
∗Topic arith
arithscan, 26
arithscanperm, 27
∗Topic datagen
sim.cross, 230
sim.map, 234
simFounderSnps, 235
simPhyloQTL, 236
∗Topic datasets
badorder, 28
bristle3, 30
bristleX, 31
fake.4way, 72
fake.bc, 73
fake.f2, 74
hyper, 95
listeria, 100
locations, 102
map10, 105
mapthis, 107
multitrait, 144
∗Topic hplot
add.cim.covar, 10
add.threshold, 11
effectplot, 64
effectscan, 67
geno.image, 91
mqmplot.cistrans, 126
mqmplot.clusteredheatmap, 127
mqmplot.cofactors, 129
mqmplot.directedqtl, 130
mqmplot.heatmap, 131
mqmplot.multitrait, 132
mqmplot.permutations, 133
mqmplot.singletrait, 134
plot.cross, 155
plot.qtl, 156
plot.rfmatrix, 157
plot.scanone, 158
279

280
replacemap.scanone, 201
replacemap.scantwo, 202
strip.partials, 243
subset.cross, 244
subset.map, 245
subset.scanone, 246
subset.scanoneperm, 247
subset.scantwo, 248
subset.scantwoperm, 249
switch.order, 267
∗Topic models
A starting point, 6
addcovarint, 12
addint, 14
addpair, 18
addqtl, 20
cim, 45
fitqtl, 82
fitstahl, 85
MQM, 114
mqmautocofactors, 118
mqmfind.marker, 120
mqmpermutation, 122
mqmprocesspermutation, 135
mqmscan, 136
mqmscanall, 138
mqmscanfdr, 140
mqmsetcofactors, 141
scanone, 206
scanonevar, 216
scanPhyloQTL, 219
scanqtl, 221
scantwo, 223
scantwopermhk, 227
stepwiseqtl, 239
∗Topic print
chrlen, 44
condense.scantwo, 52
inferredpartitions, 97
max.scanone, 109
max.scanPhyloQTL, 110
max.scantwo, 112
nchr, 145
nind, 146
nmar, 146
nphe, 148
nqtl, 149
qtlversion, 188
summary.cross, 250
summary.fitqtl, 250
summary.qtl, 251
summary.ripple, 252

INDEX
summary.scanone, 253
summary.scanoneperm, 257
summary.scanPhyloQTL, 259
summary.scantwo, 261
summary.scantwoperm, 264
summaryMap, 265
summaryScantwoOld, 266
top.errorlod, 270
totmar, 271
∗Topic univar
plotInfo, 170
∗Topic utilities
addloctocross, 16
addmarker, 17
addtoqtl, 22
allchrsplits, 24
argmax.geno, 25
bayesint, 29
calc.errorlod, 37
calc.genoprob, 38
calc.penalties, 40
checkAlleles, 43
chrnames, 45
cleanGeno, 49
comparecrosses, 50
comparegeno, 50
compareorder, 51
countXO, 59
dropfromqtl, 62
droponemarker, 63
est.map, 69
est.rf, 71
fill.geno, 75
find.flanking, 76
find.marker, 77
find.markerindex, 78
find.markerpos, 78
find.pheno, 79
find.pseudomarker, 80
formLinkageGroups, 88
formMarkerCovar, 89
geno.crosstab, 90
geno.table, 92
getid, 93
groupclusteredheatmap, 94
inferFounderHap, 96
locateXO, 101
lodint, 103
makeqtl, 104
map2table, 106
markerlrt, 108
markernames, 108

INDEX
mqmaugment, 116
mqmextractmarkers, 119
mqmgetmodel, 121
mqmplot.circle, 124
mqmtestnormal, 143
nmissing, 147
nqrank, 148
ntyped, 150
nullmarkers, 151
orderMarkers, 151
phenames, 153
pull.argmaxgeno, 181
pull.draws, 182
pull.geno, 183
pull.genoprob, 184
pull.map, 185
pull.pheno, 186
pull.rf, 187
reduce2grid, 196
refineqtl, 197
reorderqtl, 199
replaceqtl, 203
rescalemap, 204
ripple, 205
scanoneboot, 214
shiftmap, 229
sim.geno, 233
simulatemissingdata, 238
summary.scanoneboot, 256
switchAlleles, 268
table2map, 269
transformPheno, 272
tryallpositions, 273
typingGap, 274
+.scanone, 211
+.scanone (arithscan), 26
+.scanoneperm (arithscanperm), 27
+.scantwo (arithscan), 26
+.scantwoperm (arithscanperm), 27
-.scanone (arithscan), 26
-.scanoneperm (arithscanperm), 27
-.scantwo (arithscan), 26
-.scantwoperm (arithscanperm), 27
.Rprofile, 6
[.cross (subset.cross), 244
[.map (subset.map), 245
[.scanoneperm (subset.scanoneperm), 247
[.scantwoperm (subset.scantwoperm), 249
A starting point, 6
abline, 11
add.cim.covar, 10, 47
add.threshold, 11, 159, 277

281
addcovarint, 12, 15
addint, 13, 14, 20, 22
addloctocross, 16, 125
addmarker, 17
addpair, 13, 15, 18, 22, 113, 165, 242, 262
addqtl, 13, 15, 20, 20, 242
addtoqtl, 20, 22, 22, 62, 84, 105, 149, 199,
203
allchrsplits, 24
argmax.geno, 25, 39, 47, 75, 76, 87, 96, 181,
182, 200, 231, 234
arithscan, 26
arithscanperm, 27
attr, 84, 138
badorder, 28, 71, 108, 181
barplot, 177, 178
bayesint, 29, 103, 215, 216, 254, 257
bristle3, 30, 72–74, 95, 100
bristleX, 31, 31, 32, 72–74, 95, 100
c.cross, 32, 194
c.scanone, 33, 36, 41, 42, 255
c.scanoneperm, 34, 42, 247, 255
c.scantwo, 35
c.scantwoperm, 35, 36, 42, 226, 228, 249
calc.errorlod, 7, 37, 39, 49, 87, 168, 169,
270
calc.genoprob, 7, 8, 18, 21, 26, 33, 35, 38,
47, 60, 61, 76, 80, 87, 89, 96, 104,
105, 113, 170, 171, 184, 186, 196,
197, 200, 208, 211, 217, 221, 224,
225, 231, 234
calc.penalties, 40, 241, 242
cbind.scanone (c.scanone), 33
cbind.scanoneperm, 34, 35, 41, 247
cbind.scantwo (c.scantwo), 35
cbind.scantwoperm, 37, 42
checkAlleles, 43, 71, 269
chrlen, 44, 265
chrnames, 45, 109, 153
cim, 10, 45, 123, 140
clean, 99
clean.cross, 47, 60, 61, 186, 194, 268
clean.scantwo, 47, 48, 224
cleanGeno, 38, 49, 59, 102
colors, 159, 163
comparecrosses, 50
comparegeno, 50
compareorder, 51
condense.scantwo, 52, 263
contour, 164
convert.map, 53

282
convert.scanone, 54, 56
convert.scantwo, 55, 55
convert2riself, 56, 57
convert2risib, 56, 57
convert2sa, 58
countXO, 49, 59, 102, 152
data, 6
drop.dupmarkers, 60
drop.markers, 17, 47, 60, 60, 61, 64, 81, 93,
154, 186, 244
drop.nullmarkers, 7, 47, 60, 61, 61, 81, 93,
151, 186
dropfromqtl, 23, 62, 84, 105, 149, 199, 203
droponemarker, 63, 274
effectplot, 64, 68, 77, 80, 179
effectscan, 66, 67, 179
est.map, 7, 25, 29, 54, 58, 64, 69, 71, 86, 106,
107, 137, 152, 174, 189, 200–202,
204–206, 229, 253, 267, 270, 274
est.rf, 7, 25, 29, 43, 64, 70, 71, 87, 88, 107,
108, 113, 157, 181, 187, 188, 206,
253, 269, 274
example, 6
fake.4way, 31, 32, 72, 73, 74, 95, 100, 232
fake.bc, 31, 32, 72, 73, 74, 95, 100, 232
fake.f2, 31, 32, 72, 73, 74, 95, 100, 107, 232
fill.geno, 26, 46, 47, 75, 89, 96, 117
find.flanking, 76, 77, 79, 80, 179
find.marker, 66, 76, 77, 79, 80, 90, 179
find.markerindex, 78
find.markerpos, 76–78, 78, 80
find.pheno, 79
find.pseudomarker, 66, 76, 77, 79, 80
findDupMarkers, 81
fitqtl, 13, 15, 20, 22, 23, 62, 82, 104, 105,
149, 199, 203, 222, 242, 250, 251
fitstahl, 70, 85
flip.order, 87, 268
formLinkageGroups, 88, 107, 152
formMarkerCovar, 89
formula, 12, 14, 18, 21, 82, 198, 221
geno.crosstab, 43, 90, 269
geno.image, 91, 176
geno.table, 61, 90, 92, 171, 186
getid, 93
groupclusteredheatmap, 94
heatmap, 128
help.start, 6

INDEX
hist, 160, 161, 166, 177, 178
hyper, 6, 31, 32, 72–74, 95, 100
image, 91, 131, 165, 167, 168, 175, 176, 180,
181
inferFounderHap, 96
inferredpartitions, 97, 111, 163, 220, 237,
260
interpPositions, 98
jittermap, 99
listeria, 31, 32, 72–74, 95, 100
locateXO, 49, 59, 101, 275
locations, 102
lodint, 30, 103, 215, 216, 254, 257
makeqtl, 12–15, 18, 20–23, 62, 82, 84, 104,
122, 149, 156, 157, 173, 176, 177,
197–199, 203, 222, 239, 242, 251,
252
map10, 105
map2table, 70, 106, 185, 270
mapthis, 107
markerlrt, 87, 108
markernames, 45, 108, 153
max.scanone, 8, 109, 111, 211, 255
max.scanPhyloQTL, 97, 110, 163, 220, 237,
260
max.scantwo, 9, 19, 53, 112, 226, 263, 267
movemarker, 25, 52, 64, 113, 274
MQM, 16, 94, 114, 115, 117–120, 122, 124, 125,
127–135, 138, 139, 141–143, 238
mqmaugment, 16, 94, 115, 116, 117–120, 122,
124, 125, 127–135, 138, 139,
141–143, 239
mqmautocofactors, 16, 94, 115, 117, 118,
118, 119, 120, 122–125, 127–136,
138, 139, 141–143, 239
mqmextractmarkers, 119
mqmfind.marker, 120
mqmgetmodel, 121, 138
mqmpermutation, 16, 94, 115, 117–120, 122,
122, 124, 125, 127–133, 135, 138,
139, 141–143, 239
mqmplot.circle, 124
mqmplot.cistrans, 16, 126
mqmplot.clusteredheatmap, 94, 127
mqmplot.cofactors, 129
mqmplot.directedqtl, 130
mqmplot.heatmap, 131
mqmplot.multitrait, 132
mqmplot.permutations, 133

INDEX
mqmplot.singletrait, 134, 137
mqmprocesspermutation, 120, 135
mqmscan, 16, 94, 115, 117–120, 122–125,
127–135, 136, 138–143, 238, 272
mqmscanall, 16, 94, 115, 117–120, 122,
124–135, 138, 138, 139, 141–143,
239
mqmscanfdr, 140
mqmsetcofactors, 16, 94, 115, 117–120, 122,
124, 125, 127–133, 135, 136, 138,
139, 141, 141, 142, 143, 239
mqmtestnormal, 137, 143
multitrait, 102, 103, 144
nchr, 145, 146–148, 250, 271
nind, 145, 146, 147, 148, 150, 250, 271
nmar, 145, 146, 146, 148, 250, 271
nmissing, 51, 147, 150, 275
nphe, 145–147, 148, 250, 271
nqrank, 148
nqtl, 149
ntyped, 147, 150, 275
nullmarkers, 61, 151
orderMarkers, 88, 107, 151
par, 159, 163, 169
phenames, 45, 109, 153
pickMarkerSubset, 154
plot, 67, 132, 159, 172, 174, 176, 179
plot.cross, 6, 91, 145–148, 155, 174, 176,
178, 194, 250, 271
plot.map (plotMap), 173
plot.qtl, 129, 156
plot.rfmatrix, 71, 157, 181, 188
plot.scanone, 8, 10, 11, 24, 47, 64, 92, 110,
132, 134, 137, 157, 158, 162, 163,
165, 170, 171, 196, 197, 211, 255,
273, 277
plot.scanoneboot, 160, 216, 257
plot.scanoneperm, 161, 258
plot.scanPhyloQTL, 97, 111, 162, 220, 237,
260
plot.scantwo, 8, 19, 113, 163, 226, 263, 267
plot.scantwoperm, 166, 228, 264
plotErrorlod, 37, 38, 167, 190, 192, 270
plotGeno, 7, 37, 91, 168, 168, 190, 192, 270
plotInfo, 170, 243
plotLodProfile, 171, 198, 199, 242
plotMap, 6, 7, 58, 70, 106, 155–157, 173, 178,
185, 235
plotMissing, 6, 91, 155, 171, 175, 178, 243
plotModel, 176, 242

283
plotPheno, 155, 177
plotPXG, 66, 68, 76, 77, 80, 178
plotRF, 71, 108, 157, 180, 188
points, 10, 159
polyplot, 133
pull.argmaxgeno, 181, 182–184
pull.draws, 182, 182, 183, 184
pull.geno, 89, 182, 183, 184, 187
pull.genoprob, 89, 182, 183, 184
pull.map, 44, 99, 100, 106, 109, 183, 185,
187, 200, 235, 244, 265, 270
pull.markers, 17, 60, 61, 154, 186
pull.pheno, 183, 186
pull.rf, 71, 157, 181, 187
qnorm, 149
qtl-package (A starting point), 6
qtlversion, 188
rank, 149
rbind.scanoneperm, 247
rbind.scanoneperm (c.scanoneperm), 34
rbind.scantwoperm, 249
rbind.scantwoperm (c.scantwoperm), 36
read.cross, 6, 12, 14, 16–18, 21, 23–25, 29,
31, 33, 37, 38, 43, 45–47, 49–52, 56,
57, 59–61, 63, 69, 71–82, 85, 87–96,
99–101, 104, 107–109, 113, 116,
118, 120, 123, 125, 126, 128–131,
136, 139, 140, 142–148, 150–153,
155, 167, 168, 170, 175, 177, 178,
180–187, 188, 195–197, 200,
203–205, 207, 214, 216–219, 221,
223, 227, 229, 231–233, 237–239,
243, 244, 250, 267, 268, 270–276
read.csv, 17
read.table, 190, 191, 194, 195
readMWril, 195
reduce2grid, 196
refineqtl, 13, 15, 20, 22, 30, 84, 103,
171–173, 197, 222, 240, 242
reorderqtl, 23, 62, 84, 105, 149, 199, 203
replace.map, 7, 54, 70, 100, 185, 200, 204,
229, 235
replacemap.cross, 201, 202
replacemap.cross (replace.map), 200
replacemap.scanone, 201, 202
replacemap.scantwo, 201, 202
replaceqtl, 23, 62, 84, 105, 149, 199, 203
rescalemap, 99, 204
ripple, 25, 29, 52, 59, 64, 152, 181, 205, 252,
253, 267, 268, 274
rug, 166

284
save.image, 8
scanone, 7, 8, 11, 16, 22, 26–30, 33–35,
40–42, 46, 47, 54, 55, 68, 80, 89, 92,
94, 103, 109, 110, 115, 117–120,
122–125, 127–133, 135, 137–143,
157–161, 165, 196, 197, 201, 206,
215–217, 219, 220, 225, 226, 239,
246, 247, 253–255, 257, 258, 266,
272, 277
scanoneboot, 160, 214, 256, 257
scanonevar, 216
scanonevar.meanperm, 217
scanonevar.varperm, 218
scanPhyloQTL, 97, 110, 111, 162, 163, 219,
237, 259, 260
scanqtl, 13, 15, 19–22, 84, 173, 198, 199,
221, 251
scantwo, 8, 9, 18–20, 26–28, 35–37, 40–42,
48, 52, 53, 55, 56, 112, 113,
164–167, 202, 211, 223, 228, 241,
248, 249, 254, 261–264, 266, 267
scantwopermhk, 227
set.seed, 28
shapiro.test, 143
shiftmap, 99, 229
sim.cross, 29, 72–74, 86, 107, 194, 196, 230,
235–237
sim.geno, 7, 8, 18, 21, 26, 33, 35, 39, 47, 68,
75, 76, 87, 96, 104, 105, 179, 182,
196, 197, 200, 208, 211, 221, 224,
225, 231, 233
sim.map, 98, 106, 145, 146, 204, 229, 232,
234, 236, 271
simFounderSnps, 231, 232, 235
simPhyloQTL, 97, 111, 163, 220, 236, 260
simulatemissingdata, 238
stepwiseqtl, 40, 41, 177, 239
strip.partials, 243
subset.cross, 33, 93, 167–169, 190, 194,
244, 245
subset.map, 244, 245
subset.scanone, 246, 255
subset.scanoneperm, 247
subset.scantwo, 248
subset.scantwoperm, 249
summary.cross, 6, 44, 50, 60, 93, 100,
145–148, 150, 191, 194, 250, 265,
271
summary.fitqtl, 84, 250
summary.map (summaryMap), 265
summary.qtl, 105, 149, 251
summary.ripple, 206, 252

INDEX
summary.scanone, 8, 24, 34, 47, 64, 110, 157,
159, 171, 211, 217, 246, 253, 258,
260, 273
summary.scanoneboot, 160, 215, 216, 256
summary.scanoneperm, 8, 11, 35, 42, 135,
161, 211, 217, 247, 255, 257
summary.scanPhyloQTL, 97, 111, 163, 220,
237, 259
summary.scantwo, 9, 19, 36, 48, 53, 112, 113,
165, 225, 226, 248, 261, 264, 266,
267
summary.scantwoperm, 37, 42, 167, 226, 228,
249, 264
summaryMap, 44, 265
summaryScantwoOld, 262, 266
switch.order, 25, 52, 64, 87, 114, 206, 267,
274
switchAlleles, 43, 268
table2map, 106, 269
top.errorlod, 7, 37, 38, 93, 168, 169, 190,
192, 270
totmar, 145–148, 150, 250, 271
transformPheno, 272
tryallpositions, 273
typingGap, 274
write.cross, 194, 275
xaxisloc.scanone, 11, 159, 277



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