NimbusSanL Regu Open CR Manual

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Package ‘openCR’
May 25, 2018
Type Package
Title Open Population Capture-Recapture
Version 1.2.0
Depends R (>= 3.2.0), secr (>= 3.1.6)
Imports utils, MASS, nlme, parallel, stats, Rcpp (>= 0.12.14), stringr, plyr, abind, methods, RcppParallel, R2ucare
LinkingTo Rcpp, RcppParallel
Suggests knitr, RMark, rgdal
VignetteBuilder knitr
Date 2018-05-25
Description Functions for non-spatial and spatial open-population capture-recapture analysis.
License GPL (>=2)
LazyData yes
LazyDataCompression xz
SystemRequirements GNU make

R topics documented:
openCR-package
age.matrix . . . .
AIC.openCR . .
cloned.fit . . . .
derived . . . . .
dipperCH . . . .
Field vole . . . .
gonodontisCH . .
Internal . . . . .
JS.counts . . . .
JS.direct . . . . .
LLsurface . . . .
make.table . . . .
Microtus . . . . .
miscellaneous . .
moving.fit . . . .
openCR.design .

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2
3
4
6
7
9
10
13
14
16
18
19
20
21
23
24
26

2

openCR-package
openCR.fit . . . . . . .
openCR.make.newdata
par.openCR.fit . . . . .
plot.openCR . . . . . .
plotKernel . . . . . . .
PPNpossums . . . . .
predict.openCR . . . .
print.derivedopenCR .
print.openCR . . . . .
read.inp . . . . . . . .
simulation . . . . . . .
squeeze . . . . . . . .
ucare.cjs . . . . . . . .

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Index

openCR-package

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28
33
34
35
37
38
39
40
41
42
43
46
47
49

Open Population Capture–Recapture Models

Description
Functions for non-spatial open population analysis by Cormack-Jolly-Seber (CJS) and Jolly-SeberSchwarz-Arnason (JSSA) methods, and by spatially explicit extensions of these methods. The
methods build on Schwarz and Arnason (1996), Borchers and Efford (2008) and Pledger et al.
(2010) (see vignette for more comprehensive references and likelihood). The parameterisation of
JSSA recruitment is flexible (options include population growth rate λ, per capita recruitment f and
seniority γ). Spatially explicit analyses may assume home-range centres are fixed or allow dispersal
between primary sessions according to a normal, exponential or user-defined kernel.
Details
Package:
Type:
Version:
Date:
License:

openCR
Package
1.2.0
2018-05-25
GNU General Public License Version 2 or later

Data are observations of marked individuals from a ‘robust’ sampling design (Pollock 1982). Primary sessions may include one or more secondary sessions. Detection histories are assumed to be
stored in an object of class ‘capthist’ from the package secr. Grouping of occasions into primary
and secondary sessions is coded by the ‘intervals’ attribute (zero for successive secondary sessions).
A few test datasets are provided (microtusCH, FebpossumCH, dipperCH, gonodontisCH, fieldvoleCH)
and some from secr are also suitable e.g. ovenCH and OVpossumCH.
Models are defined using symbolic formula notation. Possible predictors for include both predefined variables (b, session etc.) corresponding to ‘behaviour’ and other effects), and user-provided
covariates.
Models are fitted by numerically maximizing the likelihood. The function openCR.fit creates an
object of class openCR. Generic methods (print, AIC, etc.) are provided for each object class.

3

age.matrix

A link at the bottom of each help page takes you to the help index. The help pages are also available
as ../doc/openCR-manual.pdf.
See openCR-vignette.pdf for more.
Author(s)
Murray Efford 
References
Borchers, D. L. and Efford, M. G. (2008) Spatially explicit maximum likelihood methods for
capture–recapture studies. Biometrics 64, 377–385.
Pledger, S., Pollock, K. H. and Norris, J. L. (2010) Open capture–recapture models with heterogeneity: II. Jolly-Seber model. Biometrics 66, 883–890.
Pollock, K. H. (1982) A capture–recapture design robust to unequal probability of capture. Journal
of Wildlife Management 46, 752–757.
Schwarz, C. J. and Arnason, A. N. (1996) A general methodology for the analysis of capturerecapture experiments in open populations. Biometrics 52, 860–873.
See Also
openCR.fit, capthist, ovenCH
Examples
## a CJS model is fitted by default
openCR.fit(ovenCH)

age.matrix

Session-specific Ages

Description
A matrix showing the age of each animal at each secondary session (occasion).
Usage
age.matrix(capthist, initialage = 0, minimumage = 0, maximumage = 1, collapse = FALSE)

Arguments
capthist

single-session capthist object

initialage

numeric or character name of covariate with age at first detection (optional)

minimumage

integer minimum age

maximumage

integer maximum age

collapse

logical; if TRUE then values for each individual are collapsed as a string with
no spaces

4

AIC.openCR

Details
age.matrix is used by openCR.design for the predictors ‘age’ and ‘Age’.
Computations use the intervals attribute of capthist, which may be non-integer.
Ages are inferred for occasions before first detection, back to the minimum age.
Value
Either a numeric matrix with dimensions (number of animals, number of secondary occasions) or
if collapse = TRUE a character matrix with one column.
See Also
openCR.design
Examples
age.matrix(join(ovenCH), maximumage = 2, collapse = TRUE)

AIC.openCR

Compare openCR Models

Description
Terse report on the fit of one or more spatially explicit capture–recapture models. Models with
smaller values of AIC (Akaike’s Information Criterion) are preferred.
Usage
## S3 method for class 'openCR'
AIC(object, ..., sort = TRUE, k = 2, dmax = 10, use.rank = FALSE,
svtol = 1e-5, criterion = c('AIC','AICc'))
## S3 method for class 'openCRlist'
AIC(object, ..., sort = TRUE, k = 2, dmax = 10, use.rank = FALSE,
svtol = 1e-5, criterion = c('AIC','AICc'))
## S3 method for class 'openCR'
logLik(object, ...)

Arguments
object

openCR object output from the function openCR.fit, or openCRlist

...

other openCR objects

sort

logical for whether rows should be sorted by ascending AICc

k

numeric, the penalty per parameter to be used; always k = 2 in this method

dmax

numeric, the maximum AIC difference for inclusion in confidence set

5

AIC.openCR
use.rank

logical; if TRUE the number of parameters is based on the rank of the Hessian
matrix

svtol

minimum singular value (eigenvalue) of Hessian used when counting non-redundant
parameters

criterion

character, criterion to use for model comparison and weights

Details
Models to be compared must have been fitted to the same data and use the same likelihood method
(full vs conditional).
AIC with small sample adjustment is given by
AICc = −2 log(L(θ̂)) + 2K +

2K(K + 1)
n−K −1

where K is the number of "beta" parameters estimated. The sample size n is the number of individuals observed at least once (i.e. the number of rows in capthist).
Model weights are calculated as
exp(−∆i /2)
wi = P
exp(−∆i /2)
Models for which dAIC > dmax are given a weight of zero and are excluded from the summation.
Model weights may be used to form model-averaged estimates of real or beta parameters with
model.average (see also Buckland et al. 1997, Burnham and Anderson 2002).
The argument k is included for consistency with the generic method AIC.
Value
A data frame with one row per model. By default, rows are sorted by ascending AIC.
model

character string describing the fitted model

npar

number of parameters estimated

rank

rank of Hessian

logLik

maximized log likelihood

AIC

Akaike’s Information Criterion

AICc

AIC with small-sample adjustment of Hurvich & Tsai (1989)

dAICc

difference between AICc of this model and the one with smallest AIC

AICwt

AICc model weight

logLik.openCR returns an object of class ‘logLik’ that has attribute df (degrees of freedom =
number of estimated parameters).
Note
The default criterion is AIC, not AICc as in secr 3.1.
Computed values differ from MARK for various reasons. MARK uses the number of observations,
not the number of capture histories when computing AICc. It is also likely that MARK will count
parameters differently.
It is not be meaningful to compare models by AIC if they relate to different data.
The issue of goodness-of-fit and possible adjustment of AIC for overdispersion has yet to be addressed (cf QAIC in MARK).

6

cloned.fit

References
Buckland S. T., Burnham K. P. and Augustin, N. H. (1997) Model selection: an integral part of
inference. Biometrics 53, 603–618.
Burnham, K. P. and Anderson, D. R. (2002) Model Selection and Multimodel Inference: A Practical
Information-Theoretic Approach. Second edition. New York: Springer-Verlag.
Hurvich, C. M. and Tsai, C. L. (1989) Regression and time series model selection in small samples.
Biometrika 76, 297–307.
See Also
AIC, openCR.fit, print.openCR, LR.test
Examples
## Not run:
m1 <- openCR.fit(ovenCH, type = 'JSSAf')
m2 <- openCR.fit(ovenCH, type = 'JSSAf', model = list(p~session))
AIC(m1, m2)
## End(Not run)

cloned.fit

Cloning to Evaluate Identifiability

Description
The identifiability of parameters may be examined by refitting a model with cloned data (each
capture history replicated nclone times). For identifiable parameters the estimated variances are
proportional to 1/nclone.
Usage
cloned.fit(object, nclone = 100, newdata = NULL, linkscale = FALSE)

Arguments
object
nclone
newdata
linkscale

previously fitted openCR object
integer number of times to replicate each capture history
optional dataframe of values at which to evaluate model
logical; if TRUE then comparison uses SE of linear predictors

Details
The key output is the ratio of SE for estimates from the uncloned and cloned datasets, adjusted for
the level of cloning (nclone). For identifiable parameters the ratio is expected to be 1.0.
Cloning is not implemented for spatial models.
The comparison may be done either on the untransformed scale (using approximate SE) or on the
link scale.

7

derived
Value
Dataframe with columns* –
estimate

original estimate

SE.estimate

original SE

estimate.xxx
cloned estimate (xxx = nclone)
SE.estimate.xxx
cloned SE
SE.ratio

SE.estimate / SE.estimate.xxx / sqrt(nclone)

* ‘estimate’ becomes ‘beta’ when linkscale = TRUE.
References
Lele, S.R., Nadeem, K. and Schmuland, B. (2010) Estimability and likelihood inference for generalized linear mixed models using data cloning. Journal of the American Statistical Association 105,
1617–1625.
See Also
openCR.fit
Examples
fit <- openCR.fit(dipperCH)
cloned.fit(fit)

derived

Derived Parameters From openCR Models

Description
For ..CL openCR models, compute the superpopulation size or density. For all openCR models,
compute the time-specific population size or density from the estimated superpopulation size and
the turnover parameters.
Usage
## S3 method for class 'openCR'
derived(object, newdata = NULL, all.levels = FALSE, Dscale = 1,
HTbysession = FALSE, ...)
## S3 method for class 'openCRlist'
derived(object, newdata = NULL, all.levels = FALSE, Dscale = 1,
HTbysession = FALSE, ...)
openCR.esa(object, bysession = FALSE)
openCR.pdot(object, bysession = FALSE)

8

derived

Arguments
object

fitted openCR model

newdata

optional dataframe of values at which to evaluate model

all.levels

logical; passed to openCR.make.newdata if newdata not specified

Dscale

numeric to scale density

HTbysession

logical; Horvitz-Thompson estimates by session (see Details)

...

other arguments (not used)

bysession

logical; if TRUE then esa or pdot is computed separately for each session

Details
Derived estimates of density and superD are multiplied by Dscale. Use Dscale = 1e4 for animals
per 100 sq. km. openCR.esa and openCR.pdot are used internally by derived.openCR.
If HTbysession then a separate H-T estimate is derived for each primary session; otherwise a HT estimate of the superpopulation is used in combination with turnover parameters (phi, beta) to
obtain session-specific estimates. Results are often identical.
The output is an object with its own print method (see print.derivedopenCR).
The code does not yet allow user-specified newdata.
Value
derived returns an object of class c(“derivedopenCR",“list"), list with these components:
totalobserved

number of different individuals detected

parameters

character vector; names of parameters in model (excludes derived parameters)

superN

superpopulation size (non-spatial models only)

superD

superpopulation density (spatial models only)

estimates

data frame of counts and estimates

Dscale

numeric multiplier for printing densities

If newdata has multiple levels then the value is a list of such objects, one for each level.
openCR.pdot returns a vector of experiment-wide detection probabilities under the fitted model
(one for each detected animal).
openCR.esa returns a vector of effective sampling areas under the fitted model (one for each detected animal).
See Also
openCR.fit, print.derivedopenCR
Examples
# override default method to get true ML for L1
L1CL <- openCR.fit(ovenCH, type = 'JSSAlCL', method = 'Nelder-Mead')
predict(L1CL)
derived(L1CL)
## Not run:

9

dipperCH
## compare to above
L1 <- openCR.fit(ovenCH, type = 'JSSAl', method = 'Nelder-Mead')
predict(L1)
derived(L1)
## End(Not run)

dipperCH

Dippers

Description
Lebreton et al. (1992) demonstrated Cormack-Jolly-Seber methods with a dataset on European
Dipper (*Cinclus cinclus*) collected by Marzolin (1988) and the data have been much used since
then. Dippers were captured annually over 1981–1987. We use the version included in the RMark
package (Laake 2013).
Usage
dipperCH

Format
The format is a single-session secr capthist object. As these are non-spatial data, the traps attribute
is NULL.
Details
Dippers were sampled in 1981–1987.
Source
MARK example dataset ‘ed.inp’. Also RMark (Laake 2013). See Examples.
References
Laake, J. L. (2013). RMark: An R Interface for Analysis of Capture–Recapture Data with MARK.
AFSC Processed Report 2013-01, 25p. Alaska Fisheries Science Center, NOAA, National Marine
Fisheries Service, 7600 Sand Point Way NE, Seattle WA 98115.
Lebreton, J.-D., Burnham, K. P., Clobert, J., and Anderson, D. R. (1992) Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecological
Monographs 62, 67–118.
Marzolin, G. (1988) Polygynie du Cincle plongeur (*Cinclus cinclus*) dans les c?tes de Lorraine.
L’Oiseau et la Revue Francaise d’Ornithologie 58, 277–286.
See Also
read.inp

10

Field vole

Examples
m.array(dipperCH)
## Not run:
# From file 'ed.inp' in MARK input format
datadir <- system.file('extdata', package = 'openCR')
dipperCH <- read.inp(paste0(datadir, '/ed.inp'), grouplabel='sex',
grouplevels = c('Male','Female'))
sessionlabels(dipperCH) <- 1981:1987
# labels only
# or extracted from the RMark package with this code
if (require(RMark)) {
if (all (nchar(Sys.which(c('mark.exe','mark64.exe', 'mark32.exe'))) < 2))
stop ("MARK executable not found; set e.g. MarkPath <- 'c:/Mark/'")
data(dipper)
# retrieve dataframe of dipper capture histories
dipperCH2 <- unRMarkInput(dipper) # convert to secr capthist object
sessionlabels(dipperCH2) <- 1981:1987 # labels only
}
else message ("RMark not found")
# The objects dipperCH and dipperCH2 differ in the order of factor levels for 'sex'
## End(Not run)

Field vole

Kielder Field Voles

Description
Captures of Microtus agrestis on a large grid in a clearcut within Kielder Forest, northern England,
June–August 2000 (Ergon and Gardner 2014). Robust-design data from four primary sessions of
3–5 secondary sessions each.
Usage
fieldvoleCH

Format
The format is a multi-session secr capthist object. Attribute ‘ampm’ codes for type of secondary
session (am, pm).
Details
Ergon and Lambin (2013) provided a robust design dataset from a trapping study on field voles
Microtus agrestis in a clearcut within Kielder Forest, northern England – see also Ergon et al.
(2011), Ergon and Gardner (2014) and Reich and Gardner (2014). The study aimed to describe sex

Field vole

11

differences in space-use, survival and dispersal among adult voles. Data were from one trapping
grid in summer 2000.
Trapping was on a rectangular grid of 192 multi-catch (Ugglan Special) traps at 7-metre spacing.
Traps were baited with whole barley grains and carrots; voles were marked with individually numbered ear tags.
Four trapping sessions were conducted at intervals of 21 to 23 days between 10 June and 15 August.
Traps were checked at about 12 hour intervals (6 am and 6 pm).
The attribute ‘ampm’ is a data.frame with a vector of codes, one per secondary session, to separate
am and pm trap checks (1 = evening, 2 = morning). The four primary sessions had respectively 3,
5, 4 and 5 trap checks.
Ergon and Gardner (2014) restricted their analysis to adult voles (118 females and 40 males). Histories of five voles (ma193, ma239, ma371, ma143, ma348) were censored part way through the
study because they died in traps (T. Ergon pers. comm.).
Source
Data were retrieved from DRYAD (Ergon and Lambin (2013) for openCR. Code for translating the
DRYAD ASCII file into a capthist object is given in Examples.
References
Efford, M. G. (2017) Multi-session models in secr 3.0. https://www.otago.ac.nz/density/pdfs/secrmultisession.pdf
Ergon, T., Ergon, R., Begon, M., Telfer, S. and Lambin, X. (2011) Delayed density- dependent
onset of spring reproduction in a fluctuating population of field voles. Oikos 120, 934–940.
Ergon, T. and Gardner, B. (2014) Separating mortality and emigration: modelling space use, dispersal and survival with robust-design spatial capture–recapture data. Methods in Ecology and
Evolution 5, 1327–1336.
Ergon, T. and Lambin, X. (2013) Data from: Separating mortality and emigration: Modelling space
use, dispersal and survival with robust-design spatial capture–recapture data. Dryad Digital Repository. URL http://dx.doi.org/10.5061/dryad.r17n5.
Reich, B. J. and Gardner, B. (2014) A spatial capture–recapture model for territorial species. Environmetrics 25, 630–637.
Examples
summary(fieldvoleCH, terse = TRUE)
m.array(fieldvoleCH)
JS.counts(fieldvoleCH)
maleCH <- subset(fieldvoleCH, function(x) covariates(x) == 'M')
fit <- openCR.fit(maleCH)
predict(fit)
attr(fieldvoleCH, 'ampm')
## Not run:
# Read data object from DRYAD ASCII file
datadir <- system.file('extdata', package = 'openCR')

12

Field vole
EG <- dget(paste0(datadir,'/ergonandgardner2013.rdat'))
# construct capthist object
onesession <- function (sess) {
mat <- EG$H[,,sess]
id <- as.numeric(row(mat))
occ <- as.numeric(col(mat))
occ[mat<0] <- -occ[mat<0]
trap <- abs(as.numeric(mat))
matrow <- rownames(mat)
df <- data.frame(session = rep(sess, length(id)),
ID = matrow[id],
occ = occ,
trapID = trap,
sex = c('F','M')[EG$gr],
row.names = 1:length(id))
# retain captures (trap>0)
df[df$trapID>0, , drop = FALSE]
}
tr <- read.traps(data = data.frame(EG$X), detector = "multi")
# recode matrix as mixture of zeros and trap numbers
EG$H <- EG$H-1
# code censored animals with negative trap number
# two ways to recognise censoring
censoredprimary <- which(EG$K < 4)
censoredsecondary <- which(apply(EG$J,1,function(x) any(x-c(3,5,4,5) < 0)))
censored <- unique(c(censoredprimary, censoredsecondary))
rownames(EG$H)[censored]
# [1] "ma193" "ma239" "ma371" "ma143" "ma348"
censorocc <- apply(EG$H[censored,,], 1, function(x) which.max(cumsum(x)))
censor3 <- ((censorocc-1) %/% 5)+1
# session
censor2 <- censorocc - (censor3-1) * 5 # occasion within session
censori <- cbind(censored, censor2, censor3)
EG$H[censori] <- -EG$H[censori]
lch <- lapply(1:4, onesession)
ch <- make.capthist(do.call(rbind,lch), tr=tr, covnames='sex')
# apply intervals in months
intervals(ch) <- EG$dt
fieldvoleCH <- ch
# extract time covariate - each secondary session was either am (2) or pm (1)
# EG$tod
# 1 2 3 4 5
# 1 2 1 2 NA NA
# 2 2 1 2 1 1
# 3 2 1 2 1 NA
# 4 2 1 2 1 2
# Note consecutive pm trap checks in session 2
ampm <- split(EG$tod, 1:4)
ampm <- lapply(ampm, na.omit)
attr(fieldvoleCH, 'ampm') <- data.frame(ampm = unlist(ampm))

13

gonodontisCH

## End(Not run)

gonodontisCH

Gonodontis Moths

Description
Non-spatial open-population capture–recapture data of Bishop et al. (1978) for nonmelanic male
Gonodontis bidentata at Cressington Park, northwest England.
Usage
gonodontisCH
Format
The format is a single-session secr capthist object. As these are non-spatial data, the traps attribute
is NULL.
Details
The data are from a study of the relative fitness of melanic and nonmelanic morphs of the moth
Gonodontis bidentata at several sites in England (Bishop et al. 1978). Crosbie (1979; see also
Crosbie and Manly 1985) selected a subset of the Bishop et al. data (nonmelanic males from
Cressington Park) to demonstrate innovations in Jolly-Seber modelling, and the same data were
used by Link and Barker (2005) and Schofield and Barker (2008). The present data are those used
by Crosbie (1979) and Link and Barker (2005).
Male moths were attracted to traps which consisted of a cage containing phermone-producing females surrounded by an enclosure which the males could enter but not leave. New virgin females
were usually added every 1 to 4 days. Moths were marked at each capture with a date-specific mark
in enamel paint or felt-tip pen on the undersurface of the wing. Thus, although moths at Cressington
Park were not marked individually, each moth was a flying bearer of its own capture history.
The data comprise 689 individual capture histories for moths captured at 8 traps operated over 17
days (24 May–10 June 1970). The traps were in a square that appears have been about 40 m on
a side. The location of captures is not included in the published data. All captured moths appear
to have been marked and released (i.e. there were no removals recorded). All captures on Day 17
were recaptures; it is possible that unmarked moths were not recorded on that day.
Both Table 1 and Appendix 1 (microfiche) of Bishop et al. (1978) refer to 690 capture histories
of nonmelanics at Cressington Park. In the present data there are only 689, and there are other
minor discrepancies. Also, Crosbie and Manly (1985: Table 1) refer to 82 unique capture histories
(“distinct cmr patterns”) when there are only 81 in the present dataset (note that two moths share
00000000000000011).
Source
Richard Barker provided an electronic copy of the data used by Link and Barker (2005), copied
from Crosbie (1979).

14

Internal

References
Bishop, J. A., Cook, L. M., and Muggleton, J. (1978). The response of two species of moth to industrialization in northwest England. II. Relative fitness of morphs and population size. Philosophical
Transactions of the Royal Society of London B281, 517–540.
Crosbie, S. F. (1979) The mathematical modelling of capture–mark–recapture experiments on animal populations. Ph.D. Thesis, University of Otago, Dunedin, New Zealand.
Crosbie, S. F. and Manly, B. F. J. (1985) Parsimonious modelling of capture–mark–recapture studies. Biometrics 41, 385–398.
Link, W. A. and Barker, R. J. (2005) Modeling association among demographic parameters in
analysis of open-population capture–recapture data. Biometrics 61, 46–54.
Schofield, M. R. and Barker, R. J. (2008) A unified capture–recapture framework. Journal of Agricultural Biological and Environmental Statistics 13, 458–477.
Examples
summary(gonodontisCH)
m.array(gonodontisCH)
## Not run:
# compare default (CJS) estimates from openCR, MARK
fit <- openCR.fit(gonodontisCH)
predict(fit)
if (require(RMark)) {
if (all (nchar(Sys.which(c('mark.exe','mark64.exe', 'mark32.exe'))) < 2))
stop ("MARK executable not found; set e.g. MarkPath <- 'c:/Mark/'")
mothdf <- RMarkInput(gonodontisCH)
mark(mothdf)
cleanup(ask = FALSE)
}
else message ("RMark not found")

## End(Not run)

Internal

Internal Functions

Description
Functions called by openCR.fit when details$R == TRUE, and some others
Usage
prwi (type, n, x, jj, cumss, nmix, w, fi, li, openval, PIA, PIAJ, intervals, CJSp1)
prwisecr (type, n, x, nc, jj, kk, mm, nmix, cumss, w, fi, li, gk, openval,

15

Internal

PIA, PIAJ, binomN, Tsk, intervals, CJSp1, moveargsi, movemodel, usermodel,
kernel = NULL, mqarray = NULL, cellsize = NULL)
PCH1 (type, x, nc, cumss, nmix, openval0, PIA0, PIAJ, intervals)
PCH1secr (type, individual, x, nc, jj, cumss, kk, mm, openval0, PIA0, PIAJ, gk0,
binomN, Tsk, intervals, moveargsi, movemodel, usermodel, kernel, mqarray, cellsize)
pradelloglik (type, w, openval, PIAJ, intervals)
cyclic.fit (..., maxcycle = 10, tol = 1e-5, trace = FALSE)

Arguments
type

character

n

integer index of capture history

x

integer index of latent class

jj

integer number of primary sessions

cumss

integer vector cumulative number of secondary sessions at start of each primary
session

nmix

integer number of latent classes

w

array of capture histories

fi

integer first primary session

li

integer last primary session

openval

dataframe of real parameter values (one unique combination per row)

PIA

parameter index array (secondary sessions)

PIAJ

parameter index array (primary sessions)

intervals

integer vector

CJSp1

logical; should CJS likelihood include first primary session?

moveargsi

integer 2-vector for index of move.a, move.b (negative if unused)

movemodel

character

usermodel

function to fill kernel

kernel

dataframe with columns x,y relative coordinates of kernel cell centres

mqarray

integer matrix

cellsize

numeric length of side of kernel cell

gk

real array

Tsk

array detector usage

openval0

openval for naive animals

PIA0

PIA for naive animals

individual

logical; TRUE if model uses individual covariates

gk0

gk for naive animals

nc

number of capture histories

kk

number of detectors

16

JS.counts
mm

number of points on habitat mask

binomN

code for distribution of counts (see secr.fit)

...

named arguments passed to openCR.fit or predict (see extractFocal)

maxcycle

integer maximum number of cycles (maximizations of a given parameter)

tol

absolute tolerance for improvement in log likelihood

trace

logical; if TRUE a status message is given at each maximization

Details
cyclic.fit implements cyclic fixing more or less as described by Schwarz and Arnason (1996)
and used by Pledger et al. (2010). The intention is to speed up maximization when there are many
(beta) parameters. However, fitting is slower than with a single call to openCR.fit, and the function
is here only as a curiosity (it is not exported in 1.2.0).
Value
cyclic.fit returns a fitted model object of class ‘openCR’.
Other functions return numeric components of the log likelihood.
References
Pledger, S., Pollock, K. H. and Norris, J. L. (2010) Open capture–recapture models with heterogeneity: II. Jolly-Seber model. Biometrics 66, 883–890.
Schwarz, C. J. and Arnason, A. N. (1996) A general methodology for the analysis of capturerecapture experiments in open populations. Biometrics 52, 860–873.
See Also
openCR.fit
Examples
## Not run:
openCR:::cyclic.fit(capthist = dipperCH, model = list(p~t, phi~t), tol = 1e-5, trace = TRUE)

## End(Not run)

JS.counts

Summarise Non-spatial Open-population Data

Description
Simple conventional summaries of data held in secr ‘capthist’ objects.

17

JS.counts
Usage

JS.counts(object, primary.only = TRUE)
m.array(object, primary.only = TRUE, never.recaptured = TRUE, last.session = TRUE)
bd.array(beta, phi)

Arguments
object

secr capthist object or similar

primary.only
logical; if TRUE then counts are tabuated for primary sessions
never.recaptured
logical; if TRUE then a column is added for animals never recaptured
last.session

logical; if TRUE releases are reported for the last session

beta

numeric vector of entry probabilities, one per primary session

phi

numeric vector of survival probabilities, one per primary session

Details
The input is a capthist object representing a multi-session capture–recapture study. This may be
(i) a single-session capthist in which occasions are understood to represent primary sessions, or (ii)
a multi-session capthist object that is automatically converted to a single session object with join
(any secondary sessions (occasions) are first collapsed with reduce(object, by = 'all')*).
The argument primary.only applies for single-session input with a robust-design structure defined
by the intervals. last.session results in a final row with no recaptures.
If the covariates attribute of object includes a column named ‘freq’ then this is used to expand the
capture histories.
Conventional Jolly–Seber estimates may be computed with JS.direct.
bd.array computes the probability of each possible combination of birth and death times (strictly,
the primary session at which an animal was first and last available for detection), given the parameter
vectors beta and phi. These cell probabilities are integral to JSSA models.
* this may fail with nonspatial data.
Value
For JS.counts, a data.frame where rows correspond to sessions and columns hold counts as follows
–
n

number of individuals detected

R

number of individuals released

m

number of previously marked individuals

r

number of released individuals detected in later sessions

z

number known to be alive (detected before and after) but not detected in current
session

For m.array, a table object with rows corresponding to release cohorts and columns corresponding
to first–recapture sessions. The size of the release cohort is shown in the first column. Cells in the
lower triangle have value NA and print as blank by default.

18

JS.direct

See Also
join, JS.direct
Examples
JS.counts(ovenCH)
m.array(ovenCH)
## probabilities of b,d pairs
fit <- openCR.fit(ovenCH, type = 'JSSAbCL')
beta <- predict(fit)$b$estimate
phi <- predict(fit)$phi$estimate
bd.array(beta, phi)

Jolly–Seber Estimates

JS.direct

Description
Non-spatial open-population estimates using the conventional closed-form Jolly–Seber estimators
(Pollock et al. 1990).
Usage
JS.direct(object)

Arguments
object

secr capthist object or similar

Details
Estimates are the session-specific Jolly-Seber estimates with no constraints.
The reported SE of births (B) differ slightly from those in Pollock et al. (1990), and may be in error.
Value
A dataframe in which the first 5 columns are summary statistics (counts from JS.counts) and the
remaining columns are estimates:
p

capture probability

N

population size

phi

probability of survival to next sample time

B

number of recruits at next sample time

Standard errors are in fields prefixed ‘se’; for N and B these include only sampling variation and
omit population stochasticity. The covariance of successive phi-hat is in the field ‘covphi’.

19

LLsurface
References

Pollock, K. H., Nichols, J. D., Brownie, C. and Hines, J. E. (1990) Statistical inference for capture–
recapture experiments. Wildlife Monographs 107. 97pp.
See Also
JS.counts
Examples
# cf Pollock et al. (1990) Table 4.8
JS.direct(microtusCH)

LLsurface

Plot Likelihood Surface

Description
Calculate log likelihood over a grid of values of two beta parameters from a fitted openCR model
and optionally make an approximate contour plot of the log likelihood surface.
This is a method for the generic function LLsurface defined in secr.
Usage
## S3 method for class 'openCR'
LLsurface(object, betapar = c("phi", "sigma"), xval = NULL, yval = NULL,
centre = NULL, realscale = TRUE, plot = TRUE, plotfitted = TRUE, ncores = 1, ...)

Arguments
object

openCR object output from openCR.fit

betapar

character vector giving the names of two beta parameters

xval

vector of numeric values for x-dimension of grid

yval

vector of numeric values for y-dimension of grid

centre

vector of central values for all beta parameters

realscale

logical. If TRUE input and output of x and y is on the untransformed (inverselink) scale.

plot

logical. If TRUE a contour plot is produced

plotfitted

logical. If TRUE the MLE from object is shown on the plot (+)

ncores

integer number of cores available for parallel processing

...

other arguments passed to contour

20

make.table

Details
centre is set by default to the fitted values of the beta parameters in object. This has the effect of
holding parameters other than those in betapar at their fitted values.
If xval or yval is not provided then 11 values are set at equal spacing between 0.8 and 1.2 times
the values in centre (on the ‘real’ scale if realscale = TRUE and on the ‘beta’ scale otherwise).
Contour plots may be customized by passing graphical parameters through the . . . argument.
If ncores > 1 the parallel package is used to create processes on multiple cores (see Parallel for
more).
Value
Invisibly returns a matrix of the log likelihood evaluated at each grid point
Note
LLsurface.openCR works for named ‘beta’ parameters rather than ‘real’ parameters. The default
realscale = TRUE only works for beta parameters that share the name of the real parameter to
which they relate i.e. the beta parameter for the base level of the real parameter. This is because
link functions are defined for real parameters not beta parameters.
The contours are approximate because they rely on interpolation.
See Also
LLsurface.secr
Examples
# not yet

make.table

Tabulate Estimates From Multiple Models

Description
Session-specific estimates of real parameters (p, phi, etc.) are arranged in a rectangular table.
Usage
make.table(fits, parm = "phi", fields = "estimate", ...)

Arguments
fits

openCRlist object

parm

character name of real parameter estimate to tabulate

fields

character column from predict (estimate, SE.estimate, lcl, ucl)

...

arguments passed to predict.openCRlist

21

Microtus
Details
The input will usually be from par.openCR.fit.
Value
A table object.
See Also
par.openCR.fit, openCRlist
Examples
arglist <- list(constant = list(capthist=ovenCHp, model=phi~1),
session.specific = list(capthist=ovenCHp, model=phi~session))
fits <- par.openCR.fit(arglist, trace = FALSE)
print(make.table(fits), na=".")

Microtus

Patuxent Meadow Voles

Description
Captures of Microtus pennsylvanicus at Patuxent Wildlife Research Center, Laurel, Maryland,
June–December 1981. Collapsed (primary session only) data for adult males and adult females,
and full robust-design data for adult males. Nichols et al. (1984) described the field methods and
analysed a superset of the present data.
Usage
microtusCH
microtusFCH
microtusMCH
microtusFMCH
microtusRDCH

Format
The format is a single-session secr capthist object. As these are non-spatial data, the traps attribute
is NULL.
Details
Voles were caught in live traps on a 10 x 10 grid with traps 7.6 m apart. Traps were baited with
corn. Traps were set in the evening, checked the following morning, and locked open during the
day. Voles were ear-tagged with individually numbered fingerling tags. The locations of captures
were not included in the published data.

22

Microtus
Data collection followed Pollock’s robust design with five consecutive days of trapping each month
for six months (27 June 1981–8 December 1981). The data are for "adult" animals only, defined
as those weighing at least 22g. Low capture numbers on the last two days of the second primary
session (occasions 9 and 10) are due to a raccoon interfering with traps (Nichols et al. 1984). Six
adult female voles and ten adult male voles were not released; their final captures are coded as -1 in
the respective capthist objects.
microtusRDCH is the full robust-design dataset for adult males ((Williams et al. 2002 Table 19.1).
microtusFCH and microtusMCH are the collapsed datasets (binary at the level of primary session)
for adult females and adult males from Williams et al. (2002 Table 17.5); microtusFMCH combines
them and includes the covariate ‘sex’.
microtusCH is a combined-sex version of the data with different lineage (see below).
The ‘intervals’ attribute was assigned for microtusRDCH to distinguish primary sesssions (interval
1 between prmary sessions; interval 0 for consecutive secondary sessions within a primary session).
True intervals (start of one primary session to start of next) were 35, 28, 35, 28 and 34 days. See
Examples to add these manually.
Williams, Nichols and Conroy (2002) presented several analyses of these data.
Program JOLLY (Hines 1988, Pollock et al. 1990) included a combined-sex version of the primarysession data that was used by Pollock et al. (1985) and Pollock et al. (1990)*. The numbers of voles
released each month in the JOLLY dataset JLYEXMPL differ by 0–3 from the sum of the male and
female data from Williams et al. (2002) (see Examples). Some discrepancies may have been due to
voles for which sex was not recorded. The JOLLY version matches Table 1 of Nichols et al. (1984).
The JOLLY version is distributed here as the object microtusCH.
Differing selections of data from the Patuxent study were analysed by Nichols et al. (1992) and
Bonner and Schwarz (2006).
* There is a typographic error in Table 4.7 of Pollock et al. (1990): ri for the first period should be
89.

Source
Object
microtusCH
microtusFCH
microtusMCH
microtusFMCH
microtusRDCH

Source
Text file JLYEXMPL distributed with Program JOLLY (Hines 1988; see also Examples)
Table 17.5 in Williams, Nichols and Conroy (2002)
Table 17.5 in Williams, Nichols and Conroy (2002)
Table 17.5 in Williams, Nichols and Conroy (2002)
Table 19.1 in Williams, Nichols and Conroy (2002) provided as text file by Jim Hines

References
Bonner, S. J. and Schwarz, C. J. (2006) An extension of the Cormack–Jolly–Seber model for continuous covariates with application to Microtus pennsylvanicus. Biometrics 62, 142–149.
Hines, J. E. (1988) Program "JOLLY". Patuxent Wildlife Research Center. https://www.mbrpwrc.usgs.gov/software/jolly.shtml
Nichols, J. D., Pollock, K. H., Hines, J. E. (1984) The use of a robust capture-recapture design in
small mammal population studies: a field example with Microtus pennsylvanicus. Acta Theriologica 29, 357–365.

23

miscellaneous

Nichols, J. D., Sauer, J. R., Pollock, K. H., and Hestbeck, J. B. (1992) Estimating transition probabilities for stage-based population projection matrices using capture–recapture data. Ecology 73,
306–312.
Pollock, K. H., Hines, J. E. and Nichols, J. D. (1985) Goodness-of-fit tests for open capture–
recapture models. Biometrics 41, 399–410.
Pollock, K. H., Nichols, J. D., Brownie, C. and Hines, J. E. (1990) Statistical inference for capture–
recapture experiments. Wildlife Monographs 107. 97pp.
Williams, B. K., Nichols, J. D. and Conroy, M. J. (2002) Analysis and management of animal
populations. Academic Press.
Examples
# cf Williams, Nichols and Conroy Table 17.6
m.array(microtusFCH)
m.array(microtusMCH)
# cf Williams, Nichols and Conroy Fig. 17.2
fitfm <- openCR.fit(microtusFMCH, model = list(p~1, phi ~ session + sex))
maledat <- expand.grid(sex = factor('M', levels = c('F','M')), session = factor(1:6))
plot(fitfm, ylim=c(0,1), type = 'o')
plot(fitfm, newdata = maledat, add = TRUE, xoffset = 0.1, pch = 16, type = 'o')
# adjusting for variable interval
intervals(microtusCH) <- c(35,28,35,28,34) / 30
intervals(microtusRDCH)[intervals(microtusRDCH)>0] <- c(35,28,35,28,34) / 30
## Not run:
# The text file JLYEXMPL distributed with JOLLY is in the extdata folder of the R package
# The microtusCH object may be rebuilt as follows
datadir <- system.file('extdata', package = 'openCR')
JLYdf <- read.table(paste0(datadir,'/JLYEXMPL'), skip = 3,
colClasses = c('character','numeric'))
names(JLYdf) <- c('ch', 'freq')
JLYdf$freq[grepl('2', JLYdf$ch)] <- -JLYdf$freq[grepl('2', JLYdf$ch)]
JLYdf$ch <- gsub ('2','1', JLYdf$ch)
microtusCH <- unRMarkInput(JLYdf)
# Compare to combined-sex data from Williams et al. Table 17.5
JS.counts(microtusCH) - JS.counts(microtusFMCH)
## End(Not run)

miscellaneous

Description
Miscellaneous functions

Data Manipulation

24

moving.fit

Usage
primarysessions(intervals)
secondarysessions(intervals)

Arguments
intervals

numeric vector of intervals for time between secondary sessions a of robust design

Details
These functions are used internally.
Value
primarysessions –
Integer vector with the number of the primary session to which each secondary session belongs.
secondarysessions –
Integer vector with secondary sessions numbered sequentially within primary sessions.
Examples
int <- intervals(join(ovenCH))
primary <- primarysessions(int)
primary
# number of secondary sessions per primary
table(primary)
# secondary session numbers
secondarysessions(int)

moving.fit

Moving Window Functions

Description
Apply a function to successive multi-session windows from a capthist object. The default function
is openCR.fit, but any function may be used whose first argument accepts a capthist object.

25

moving.fit
Usage
moving.fit (..., width = 3, centres = NULL, filestem = NULL,
trace = FALSE, FUN = openCR.fit)
extractFocal (ocrlist, ...)

Arguments
...

named arguments passed to openCR.fit (see Details)

width

integer; moving window width (number of primary sessions)

centres

integer; central sessions of windows to consider

filestem

character or NULL; stem used to form filenames for optional intermediate output

trace

logical; if TRUE a status message is given at each call of FUN

FUN

function to be applied to successive capthist objects

ocrlist

openCRlist object returned by moving.fit when FUN = openCR.fit

Details
moving.fit applies FUN to successive multi-session subsets of the data in the capthist argument.
width should be an odd integer. centres may be used to restrict the range of windows considered;
the default is to use all complete windows (width%/%2 + 1)...).
If a filestem is specified then each result is output to a file that may be loaded with load. This is
useful if fitting takes a long time and analyses may be terminated before completion.
extractFocal returns the focal-session (central) estimates from a moving.fit with FUN = openCR.fit.
The . . . argument is passed to predict.openCR; it may be used, for example, to choose a different
alpha level for confidence intervals.
extractFocal is untested for complex models (e.g. finite mixtures).
Value
A list in which each component is the output from FUN applied to one subset. The window width
is saved as attribute ‘width’.
See Also
openCR.fit
Examples
## number of individuals detected
moving.fit(capthist = OVpossumCH, FUN = nrow)
## Not run:
moving.fit(capthist = OVpossumCH, FUN = ucare.cjs, width = 5, tests = "overall_CJS")
## using default FUN = openCR.fit

26

openCR.design

mf1 <- moving.fit(capthist = OVpossumCH, type = 'JSSAfCL',
model = list(p~t, phi~t))
lapply(mf1, predict)
extractFocal(mf1)
msk <- make.mask(traps(OVpossumCH[[1]]), nx = 32)
mf2 <- moving.fit(capthist = OVpossumCH, mask = msk, type = 'JSSAsecrfCL')
extractFocal(mf2)

## End(Not run)

openCR.design

Design Data for Open population Models

Description
Internal function used by openCR.fit.
Usage
openCR.design(capthist, models, type, naive = FALSE,
timecov = NULL, sessioncov = NULL, dframe = NULL,
contrasts = NULL, initialage = 0, maximumage = 1, ...)

Arguments
capthist

single-session capthist object

models

list of formulae for parameters of detection

type

character string for type of analysis "CJS", "JSSA" or "Pradel"

naive

logical if TRUE then modelled parameter is for a naive animal (not caught previously)

timecov

optional vector or dataframe of values of occasion-specific covariate(s).

sessioncov

optional dataframe of values of session-specific covariate(s)

dframe

optional data frame of design data for detection parameters

contrasts

contrast specification as for model.matrix

initialage

numeric or character (name of individual covariate containing initial ages)

maximumage

numeric; age at which to truncate

...

other arguments passed to the R function model.matrix

27

openCR.design
Details

This is an internal openCR function that you are unlikely ever to use. . . . may be used to pass
contrasts.arg to model.matrix.
Each real parameter is notionally different for each unique combination of individual, occasion and
latent class, i.e., for n individuals, J occasions and m latent classes there are potentially n × J × m
different values. Actual models always predict a much reduced set of distinct values, and the number
of rows in the design matrix is reduced correspondingly; a parameter index array allows these to
retrieved for any combination of session, individual, occasion and detector.
openCR.fit is more tolerant than openCR.design regarding the inputs ‘capthist’ and ‘models’.
Model formulae are processed to a standard form (a named list of formulae) before they are passed
to openCR.design, and multi-session capthist objects are automatically ‘reduced’ and ‘joined’ for
open-population analysis.
If timecov is a single vector of values (one for each secondary session) then it is treated as a
covariate named ‘tcov’. If sessioncov is a single vector of values (one for each primary session)
then it is treated as a covariate named ‘scov’.
The initialage and maximumage arguments are usually passed via the openCR.fit ’details’ argument.
Value
A list with the components
designMatrices list of reduced design matrices, one for each real parameter
parameterTable index to row of the reduced design matrix for each real parameter; dim(parameterTable)
= c(uniquepar, np), where uniquepar is the number of unique combinations of
paramater values (uniquepar < nJM ) and np is the number of parameters in the
detection model.
PIA

Parameter Index Array - index to row of parameterTable for a given animal,
occasion and latent class; dim(PIA) = c(n,J,M)

validlevels

a logical matrix of np rows and J columns, mostly TRUE, but FALSE for impossible combinations e.g. CJS recapture probability in session 1 (validlevels["p",1]),
or CJS final survival probability (validlevels["phi",J]). Also, validlevels["b",1]
is FALSE with type = "JSSA" because of the constraint that entry parameters
sum to one.

Note
The component validlevels is TRUE in many cases for which a parameter is redundant or confounded (e.g. validlevels["phi",J-1]); these are sorted out ‘post hoc’ by examining the fitted values,
their asymptotic variances and the eigenvalues of the Hessian matrix.
See Also
openCR.fit
Examples
## this happens automatically in openCR.fit
ovenCH1 <- join(reduce(ovenCH, by = "all", newtraps=list(1:44)))

28

openCR.fit
openCR.design (ovenCH1, models = list(p = ~1, phi = ~session),
interval = c(1,1,1,1), type = "CJS")

openCR.fit

Fit Open Population Capture–Recapture Model

Description
Nonspatial or spatial open-population analyses are performed on data formatted for ‘secr’. Several
parameterisations are provided for the nonspatial Jolly-Seber Schwarz-Arnason model (‘JSSA’, also
known as ‘POPAN’). Corresponding spatial models are designated ‘JSSAsecr’. Cormack-JollySeber (CJS) models are also fitted.
Usage
openCR.fit (capthist, type = "CJS", model = list(p~1, phi~1, sigma~1),
distribution = c("poisson", "binomial"), mask = NULL,
detectfn = c("HHN","HHR","HEX","HAN","HCG","HVP"),
binomN = 0, movementmodel = c("static", "uncorrelated", "normal", "exponential"),
start = NULL, link = list(), fixed = list(), timecov = NULL,
sessioncov = NULL, dframe = NULL, details = list(),
method = "Newton-Raphson", trace = NULL, ncores = NULL, ...)
Arguments
capthist

capthist object from ‘secr’

type

character string for type of analysis (see Details)

model

list with optional components, each symbolically defining a linear predictor for
the relevant real parameter using formula notation. See Details for names of
real parameters.

distribution

character distribution of number of individuals detected

mask

single-session mask object; required for spatial (secr) models

detectfn

character code

binomN

integer code for distribution of counts (see secr.fit)

movementmodel

character; model for movement between primary sessions (see Details)

start

vector of initial values for beta parameters, or fitted model(s) from which they
may be derived

link

list with named components, each a character string in {"log", "logit", "loglog",
"identity", "sin", "mlogit"} for the link function of the relevant real parameter

fixed

list with optional components corresponding to each ‘real’ parameter, the scalar
value to which parameter is to be fixed

timecov

optional dataframe of values of occasion-specific covariate(s).

sessioncov

optional dataframe of values of session-specific covariate(s).

dframe

optional data frame of design data for detection parameters (seldom used)

details

list of additional settings (see Details)

29

openCR.fit
method

character string giving method for maximizing log likelihood

trace

logical or integer; output log likelihood at each evaluation, or at some lesser
frequency as given

ncores

integer number of cores for parallel processing (see Details)

...

other arguments passed to join()

Details
The permitted nonspatial models are CJS, Pradel, Pradelg, JSSAbCL, JSSAfCL, JSSAgCL, JSSAlCL, JSSAb, JSSAf, JSSAg, JSSAl, JSSAB and JSSAN. The permitted spatial models are
CJSsecr, JSSAsecrbCL, JSSAsecrfCL, JSSAsecrgCL, JSSAsecrlCL, JSSAsecrb, JSSAsecrf, JSSAsecrg, JSSAsecrl, JSSAsecrB and JSSAsecrN. See the openCR-vignette.pdf for a table of the
‘real’ parameters associated with each model type.
Parameterisations of the JSSA models differ in how they include recruitment: the core parameterisations express recruitment either as a per capita rate (‘f’), as a finite rate of increase for the population
(‘l’ for lambda) or as per-occasion entry probability (‘b’ for the classic JSSA beta parameter, aka
PENT in MARK). Each of these models may be fitted by maximising either the full likelihood, or
the likelihood conditional on capture in the Huggins (1989) sense, distinguished by the suffix ‘CL’.
Full-likelihood JSSA models may also be parameterized in terms of the time-specific absolute recruitment (BN, BD) or the time-specific population size(N) or density (D).
Data are provided as secr ‘capthist’ objects, with some restrictions. For nonspatial analyses,
‘capthist’ may be single-session or multi-session, with any of the main detector types. For spatial
analyses ‘capthist’ should be a single-session dataset of a point detector type (‘multi’, ‘proximity’ or
‘count’) (see also details$distribution below). In openCR the occasions of a single-session dataset
are treated as open-population temporal samples except that occasions separated by an interval of
zero (0) are from the same primary session (multi-session input is collapsed to single-session if
necessary).
model formulae may include the pre-defined terms ‘b’, ‘B’, ‘session’,‘Session’, ‘h2’, and ‘h3’ as in
secr. ‘session’ is the name given to primary sampling times in ‘secr’, so a fully time-specific CJS
model is list(p ~ session, phi ~ session). ‘b’ refers to a within-session (learned) response to
capture and ‘B’ to a transient (Markovian) response. ‘bsession’ is used for a multi-session learned
response.‘Session’ is for a trend over sessions. ‘h2’ and ‘h3’ allow finite mixture models. Formulae may also include named occasion-specific and session-specific covariates in the dataframe
arguments ‘timecov’ and ‘sessioncov’ (occasion = secondary session of robust design). Individual covariates present as an attribute of the ‘capthist’ input may be used in CJS and ..CL models.
Groups are not supported in this version, but may be implemented via a factor-level covariate in
..CL models.
distribution specifies the distribution of the number of individuals detected; this may be conditional on the population size (or number in the masked area) ("binomial") or unconditional ("poisson"). distribution affects the sampling variance of the estimated density. The default is "binomial". For variance comparable with secr estimates this should be changed to "poisson".
Movement models are described in the vignette.
The mlogit link function is used for the JSSA (POPAN) entry parameter ‘b’ (PENT in MARK) and
for mixture proportions, regardless of link.
Spatial models use one of the hazard-based detection functions (see detectfn) and require data
from independent point detectors (secr detector types ‘multi’, ‘proximity’ or ‘count’).
Code is executed in multiple threads unless the user specifies ncores = 1 or there is only one core
available. The default value for ncores is one less than the number of cores available.

30

openCR.fit
The . . . argument may be used to pass a vector of unequal intervals to join (interval), or to vary
the tolerance for merging detector sites (tol).
The start argument may be
- a vector of beta parameter values, one for each of the NP beta parameters in the model
- a named vector of beta parameter values in any order
- a named list of one or more real parameter values
- a single fitted secr or openCR model whose real parameters overlap with the current model
- a list of two fitted models
In the case of two fitted models, the values are melded. This is handy for initialising an open spatial
model from a closed spatial model and an open non-spatial model. If a beta parameter appears in
both models then the first is used.
details is used for various specialized settings –
details$autoini (default 1) is the number of the session used to determine initial values of D,
lambda0 and sigma (secr types only).
details$contrasts may be used to specify the coding of factor predictors. The value should be
suitable for the ’contrasts.arg’ argument of model.matrix.
details$control is a list that is passed to optim - useful for increasing maxit for method = Nelder-Mead
(see vignette).
details$fixedbeta may be a vector with one element for each coefficient (beta parameter) in
the model. Only ’NA’ coefficients will be estimated; others will be fixed at the value given (coefficients define a linear predictor on the link scale). The number and order of coefficients may
be determined by calling openCR.fit with trace = TRUE and interrupting execution after the first
likelihood evaluation.
details$hessian is a character string controlling the computation of the Hessian matrix from
which variances and covariances are obtained. Options are "none" (no variances), "auto" (the default) or "fdhess" (use the function fdHess in nlme). If "auto" then the Hessian from the optimisation
function is used.
details$ignoreusage may be used to override usage in traps object of capthist.
details$initialage is either numeric (the uniform age at first capture) or a character value naming an individual covariate with initial ages; see age.matrix.
details$LLonly = TRUE causes the function to returns a single evaluation of the log likelihood at
the initial values, followed by the initial values.
details$maximumage sets a maximum age; older animals are recycled into this age class; see
age.matrix.
details$multinom = TRUE includes the multinomial constant in the reported log-likelihood (default FALSE).
details$R == TRUE may be used to switch from the default C++ code to slower functions in native
R (useful mostly for debugging; not all model types implemented).
details$squeeze == TRUE (the default) compacts the input capthist with function squeeze before
analysis. The new capthist includes only unique rows. Non-spatial models will fit faster, because
non-spatial capture histories are often non-unique.
If method = "Newton-Raphson" then nlm is used to maximize the log likelihood (minimize the
negative log likelihood); otherwise optim is used with the chosen method ("BFGS", "Nelder-Mead",
etc.). If maximization fails a warning is given appropriate to the method. method = "none"

31

openCR.fit

may be used to compute or re-compute the variance-covariance matrix at given starting values (i.e.
providing a previously fitted model as the value of start).
Parameter redundancies are common in open-population models. The output from openCR.fit
includes the singular values (eigenvalues) of the Hessian - a useful post-hoc indicator of redundancy
(e.g., Gimenez et al. 2004). Eigenvalues are scaled so the largest is 1.0. Very small scaled values
represent redundant parameters - in my experience with simple JSSA models a threshold of 0.00001
seems effective.
[There is an undocumented option to fix specific ‘beta’ parameters.]
Value
If details$LLonly == TRUE then a numeric vector is returned with logLik in position 1, followed
by the named coefficients.
Otherwise, an object of class ‘openCR’ with components
model = model, distribution = distribution, mask = mask, detectfn = detectfn, binomN = binomN,
movementmodel = movementmodel, usermodel = usermodel, moveargsi = moveargsi, start = start,
call

function call

capthist

saved input

type

saved input

model

saved input

distribution

saved input

mask

saved input

detectfn

saved input

binomN

saved input

movementmodel

saved input

usermodel

saved input

moveargsi

relative locations of move.a and move.b arguments

start

vector of starting values for beta parameters

link

saved input

fixed

saved input

timecov

saved input

sessioncov

saved input

dframe

saved input

details

saved input

method

saved input

ncores

saved input (NULL replaced with default)

design

reduced design matrices, parameter table and parameter index array for actual
animals (see openCR.design)

design0

reduced design matrices, parameter table and parameter index array for ‘naive’
animal (see openCR.design)

parindx

list with one component for each real parameter giving the indices of the ‘beta’
parameters associated with each real parameter

intervals

intervals between primary sessions

32

openCR.fit
vars

vector of unique variable names in model

betanames

names of beta parameters

realnames

names of fitted (real) parameters

sessionlabels

name of each primary session

fit

list describing the fit (output from nlm or optim)

beta.vcv

variance-covariance matrix of beta parameters

eigH

vector of eigenvalue corresponding to each beta parameter

posterior

posterior probabilities of class membership (mixture models), one row per individual.

version

openCR version number

starttime

character string of date and time at start of fit

proctime

processor time for model fit, in seconds

Note
Different parameterisations lead to different model fits when used with the default ‘model’ argument
in which each real parameter is constrained to be constant over time.
The JSSA implementation uses summation over feasible ’birth’ and ’death’ times for each capture
history, following Pledger et al. (2010). This enables finite mixture models for individual capture
probability (not fully tested), flexible handling of additions and losses on capture (aka removals)
(not yet programmed), and ultimately the extension to ‘unknown age’ as in Pledger et al. (2009).
openCR uses the generalized matrix inverse ‘ginv’ from the MASS package rather than ‘solve’ from
base R, as this seems more robust to singularities in the Hessian. Also, the default maximization
method is ‘BFGS’ rather than ‘Newton-Raphson’ as BFGS appears more robust in the presence of
redundant parameters.
References
Gimenez, O., Viallefont, A., Catchpole, E. A., Choquet, R. and Morgan, B. J. T. (2004) Methods
for investigating parameter redundancy. Animal Biodiversity and Conservation 27, 561–572.
Huggins, R. M. (1989) On the statistical analysis of capture experiments. Biometrika 76, 133–140.
Pledger, S., Efford, M., Pollock. K., Collazo, J. and Lyons, J. (2009) Stopover duration analysis
with departure probability dependent on unknown time since arrival. In: D. L. Thompson, E. G.
Cooch and M. J. Conroy (eds) Modeling Demographic Processes in Marked Populations. Springer.
Pp. 349–363.
Pledger, S., Pollock, K. H. and Norris, J. L. (2010) Open capture–recapture models with heterogeneity: II. Jolly-Seber model. Biometrics 66, 883–890.
Pradel, R. (1996) Utilization of capture-mark-recapture for the study of recruitment and population
growth rate. Biometrics 52, 703–709.
Schwarz, C. J. and Arnason, A. N. (1996) A general methodology for the analysis of capturerecapture experiments in open populations. Biometrics 52, 860–873.
See Also
openCR.design, derived.openCR, par.openCR.fit

33

openCR.make.newdata
Examples
## CJS default
openCR.fit(ovenCH)
## POPAN Jolly-Seber Schwarz-Arnason, lambda parameterisation
L1 <- openCR.fit(ovenCH, type = 'JSSAl')
predict(L1)
## Not run:
JSSA1 <- openCR.fit(ovenCH, type = 'JSSAf')
JSSA2 <- openCR.fit(ovenCH, type = 'JSSAf', model = list(phi~t))
JSSA3 <- openCR.fit(ovenCH, type = 'JSSAf', model = list(p~t,phi~t))
AIC (JSSA1, JSSA2, JSSA3)
predict(JSSA1)
RMdata <- RMarkInput (join(reduce(ovenCH, by = "all")))
if (require(RMark)) {
if (all (nchar(Sys.which(c('mark.exe', 'mark64.exe', 'mark32.exe'))) < 2))
stop ("MARK executable not found; set e.g. MarkPath = 'c:/Mark/'")
openCHtest <- process.data(RMdata, model='POPAN')
openCHPOPAN <- mark(data = openCHtest, model = 'POPAN',
model.parameters = list(p = list(formula = ~1),
pent = list(formula = ~1),
Phi = list(formula = ~1)))
popan.derived(openCHtest, openCHPOPAN)
cleanup(ask=F)
}
else message ("RMark not found")

## End(Not run)

openCR.make.newdata

Create Default Design Data

Description
Internal function used to generate a dataframe containing design data for the base levels of all
predictors in an openCR object.
Usage
openCR.make.newdata(object, all.levels = FALSE)

Arguments
object

fitted openCR model object

all.levels

logical; if TRUE then all covariate factor levels appear in the output

34

par.openCR.fit

Details
openCR.make.newdata is used by predict in lieu of user-specified ‘newdata’. There is seldom
any need to call openCR.make.newdata directly.
Value
A dataframe with one row for each session, and columns for the predictors used by object$model.
See Also
openCR.fit
Examples
## null example (no covariates)
ovenCJS <- openCR.fit(ovenCH)
openCR.make.newdata(ovenCJS)

Fit Multiple openCR Models

par.openCR.fit

Description
This function is a wrappers for openCR.fit.
Usage
par.openCR.fit (arglist, ncores = 1, seed = 123, trace = TRUE, logfile = "logfile.txt",
prefix = "")
openCRlist (...)

Arguments
arglist

list of argument lists for secr.fit or a character vector naming such lists

ncores

integer number of cores to be used for parallel processing

seed

integer pseudorandom number seed

trace

logical; if TRUE intermediate output may be logged

logfile

character name of file to log progress reports

prefix

character prefix for names of output

...

openCR objects

35

plot.openCR
Details
Any attempt in arglist to set ncores > 1 for a particular secr fit is ignored.

trace overrides any settings in arglist. Reporting of intermediate results is unreliable on Windows when ncores > 1.
It is convenient to provide the names of the capthist and mask arguments in each component of
arglist as character values (i.e. in quotes); objects thus named are exported from the workspace to
each worker process (see Examples).
openCRlist forms a special list (class openCRlist) of fitted model (openCR) objects.
Value
For par.openCR.fit - openCRlist of model fits (see openCR.fit). Names are created by prefixing
prefix to the names of argslist. If trace is TRUE then the total execution time and finish time
are displayed.
See Also
openCR.fit, Parallel, make.table
Examples
## Not run:
m1 <- list(capthist = ovenCH, model = list(p~1, phi~1))
m2 <- list(capthist = ovenCH, model = list(p~session, phi~1))
m3 <- list(capthist = ovenCH, model = list(p~session, phi~session) )
fits <- par.openCR.fit (c('m1','m2','m3'), ncores = 3)
AIC(fits)

## End(Not run)

plot.openCR

Plot Estimates

Description
Session-specific estimates of the chosen parameter are plotted.
Usage
## S3 method for class 'openCR'
plot(x, par = "phi", newdata = NULL, add = FALSE, xoffset = 0, ylim = NULL,
useintervals = TRUE, CI = TRUE, intermediate.x = TRUE, alpha = 0.05, ...)

36

plot.openCR

Arguments
x

openCR object from openCR.fit

par

character names of parameter to plot

newdata

dataframe of predictor values for predict (optional)

add

logical; if TRUE then points are added to an existing plot

xoffset

numeric offset to be added to all x values

ylim

numeric vector of limits on y-axis

useintervals

logical; if TRUE then x values are spaced according to the intervals attribute

CI

logical; if TRUE then 1-alpha confidence intervals are plotted

intermediate.x logical; if TRUE then turnover parameters are plotted at the mid point on the x
axis of the interval to which they relate
alpha

numeric confidence level default (alpha = 0.05) is 95% interval

...

other arguments passed to points

Details
If ylim is not provided it is set automatically.
Note that the . . . argument is passed only to points. If you wish to customize the base plot then do
that in advance and use add = TRUE.

Value
None

See Also
predict

Examples
## Not run:
fit <- openCR.fit(join(ovenCH), type='CJS', model = phi~session)
plot(fit,'phi', pch = 16, cex=1.3, yl=c(0,1))

## End(Not run)

37

plotKernel

plotKernel

Plot Movement Kernel

Description
Movement between primary sessions is modelled in openCR with a discretized kernel. Each cell
of the kernel contains the probability of movement from the central cell. Kernels are ‘normal’
(Gaussian), ‘exponential’ (negative exponential) or specified with a user-provided function. This
function allows you to preview a kernel specification.
Usage
plotKernel(movementmodel = c("normal", "exponential"), kernelradius = 10, spacing, pars,
clip = FALSE, plt = TRUE, contour = FALSE, levels = NULL, text = FALSE, ...)

Arguments
movementmodel

character or function

kernelradius

integer radius of kernel in grid cells

spacing

numeric spacing between cell centres

pars

numeric vector of 1 or 2 parameter values

clip

logical; if TRUE then corner cells are removed

plt

logical; if TRUE then a plot is produced

contour

logical; if TRUE then contour lines are overlaid on any plot

levels

numeric vector of contour levels

text

logical; if TRUE then cell probabilities are overprinted, roumnded to 3 d.p.

...

other arguments passed to plot.mask (e.g. breaks)

Details
Internally, a mask is generated with kernel probabilities in a covariate, and plotting is done with
plot.mask.
Value
A dataframe with columns x, y, and kernelp is returned invisibly.
Examples
plotKernel(spacing = 2, k = 10, pars = 10, contour = TRUE, clip = TRUE)

38

PPNpossums

PPNpossums

Orongorongo Valley Brushtail Possums

Description
A subset of brushtail possum (Trichosurus vulpecula) data from the Orongorongo Valley livetrapping study of Efford (1998) and Efford and Cowan (2005) that was used by Pledger, Pollock
and Norris (2003, 2010). The OVpossumCH dataset in secr is a different selection of data from the
same study. Consult ?OVpossumCH for more detail.
The data comprise captures in February of each year from 1980 to 1988.
Usage
FebpossumCH

Format
The format is a 9-session secr capthist object. Capture locations are not included.
Details
The data are captures of 448 animals (175 females and 273 males) over 9 trapping sessions comprising 4–10 occasions each. All were independent of their mothers, but age was not otherwise
distinguished. The individual covariate sex takes values ‘F’ or ‘M’.
Pledger, Pollock and Norris (2010) fitted 2-class finite mixture models for capture probability p
and apparent survival phi, with or without allowance for temporal (between year) variation, using
captures from only the first day of each trapping session. The first-day data relate to 270 individuals
(115 females and 155 males).
Source
M. Efford unpubl. See Efford and Cowan (2004) for acknowledgements.
References
Efford, M. G. (1998) Demographic consequences of sex-biased dispersal in a population of brushtail
possums. Journal of Animal Ecology 67, 503–517.
Efford, M. G. and Cowan, P. E. (2004) Long-term population trend of Trichosurus vulpecula in the
Orongorongo Valley, New Zealand. In: The Biology of Australian Possums and Gliders. Edited by
R. L. Goldingay and S. M. Jackson. Surrey Beatty & Sons, Chipping Norton. Pp. 471–483.
Pledger, S., Pollock, K. H. and Norris, J. L. (2010) Open capture–recapture models with heterogeneity: II. Jolly–Seber model. Biometrics 66, 883–890.

39

predict.openCR
Examples
summary(FebpossumCH)
m.array(FebpossumCH)
JS.counts(FebpossumCH)
FebD1CH <- subset(FebpossumCH, occasion = 1)
## Not run:
# reading the text file 'poss8088.data'
datadir <- system.file('extdata', package = 'openCR')
poss8088df <- read.table (paste0(datadir,'/poss8088.data'), header = TRUE)
capt <- poss8088df[,c('session','id','day','day','sex')]
# duplication of day is a trick to get a dummy trapID column in the right place
# this is needed because make.capthist does not have nonspatial option
capt$day.1[] <- 1
# keep only February samples
capt <- capt[capt$session %% 3 == 1,]
# build nonspatial secr capthist object using dummy trapping grid
FebpossumCH <- make.capthist(capt, make.grid(1,2,ID='numx'))
# discard dummy traps objects
for (i in 1:9) attr(FebpossumCH[[i]], 'traps') <- NULL
names(FebpossumCH) <- 1980:1988
sessionlabels(FebpossumCH) <- 1980:1988

## End(Not run)

predict.openCR

openCR Model Predictions

Description
Evaluate an openCR capture–recapture model. That is, compute the ‘real’ parameters corresponding
to the ‘beta’ parameters of a fitted model for arbitrary levels of any variables in the linear predictor.
Usage
## S3 method for
predict(object,
## S3 method for
predict(object,

class 'openCR'
newdata = NULL, se.fit = TRUE, alpha = 0.05, savenew = FALSE, ...)
class 'openCRlist'
newdata = NULL, se.fit = TRUE, alpha = 0.05, savenew = FALSE, ...)

40

print.derivedopenCR

Arguments
object

openCR object output from openCR.fit

newdata

optional dataframe of values at which to evaluate model

se.fit

logical for whether output should include SE and confidence intervals

alpha

alpha level

savenew

logical; if TRUE then newdata is saved as an attribute

...

other arguments passed to openCR.make.newdata

Details
Predictions are provided for each row in ‘newdata’. The default (constructed by openCR.make.newdata)
is to limit those rows to the first-used level of factor predictors; to include all levels pass all.levels = TRUE
to openCR.make.newdata in the . . . argument.
See Also
AIC.openCR, openCR.fit
Examples
c1 <- openCR.fit(ovenCH, type='CJS', model=phi~session)
predict(c1)

print.derivedopenCR

Print Method for Derived Estimates

Description
Formats output from derived.openCR.
Usage
## S3 method for class 'derivedopenCR'
print(x, Dscale = NULL, legend = FALSE, ...)

Arguments
x

object from derived.openCR

Dscale

numeric optional multiplier for densities (overrides saved Dscale)

legend

logical. if TRUE then a legend is provided to column headings

...

other arguments passed to print.data.frame

Details
By default (i.e. when not not specified in the in the . . . argument), row.names = FALSE and
digits = 4.

41

print.openCR
See Also
derived.openCR

Print openCR Object

print.openCR

Description
Print results from fitting a spatially explicit capture–recapture model.
Usage
## S3 method for class 'openCR'
print(x, newdata = NULL, alpha = 0.05, svtol = 1e-5,...)
Arguments
x

openCR object output from openCR.fit

newdata

optional dataframe of values at which to evaluate model

alpha

alpha level

svtol

threshold for non-null eigenvalues when computing numerical rank

...

other arguments (not used currently)

Details
Results are potentially complex and depend upon the analysis (see below). Optional newdata should
be a dataframe with a column for each of the variables in the model. If newdata is missing then a
dataframe is constructed automatically. Default newdata are for a naive animal on the first occasion; numeric covariates are set to zero and factor covariates to their base (first) level. Confidence
intervals are 100 (1 – alpha) % intervals.
call
time
N animals
N captures
N sessions
Model
Fixed
N parameters
Log likelihood
AIC
AICc
Beta parameters
Eigenvalues
Numerical rank
vcov
Real parameters

the function call
date and time fitting started
number of distinct animals detected
number of detections
number of sampling occasions
model formula for each ‘real’ parameter
fixed real parameters
number of parameters estimated
log likelihood
Akaike’s information criterion
AIC with small sample adjustment (Burnham and Anderson 2002)
coef of the fitted model, SE and confidence intervals
scaled eigenvalues of Hessian matrix (maximum 1.0)
number of eigenvalues exceeding svtol
variance-covariance matrix of beta parameters
fitted (real) parameters evaluated at base levels of covariates

42

read.inp

References
Burnham, K. P. and Anderson, D. R. (2002) Model selection and multimodel inference: a practical
information-theoretic approach. Second edition. New York: Springer-Verlag.
See Also
AIC.openCR, openCR.fit
Examples
c1 <- openCR.fit(ovenCH, type='CJS', model=phi~session)
c1

read.inp

Import Data from RMark Input Format

Description
read.inp forms a capthist object from a MARK input (.inp) file.
Usage
read.inp(filename, ngroups = 1, grouplabel = 'group', grouplevels = NULL,
covnames = NULL, skip = 0)

Arguments
filename

character file name including ‘.inp’.

ngroups

integer number of group columns in input

grouplabel

character

grouplevels

vector with length equal to number of groups

covnames

character vector of additional covariates names, one per covariate column

skip

integer number of lines to skip at start of file

Details
Comments bracketed with ‘/*‘ and ‘*/’ will be removed automatically.
If grouplevels is specified then ngroups is taken from the number of levels (ngroups is overridden). An individual covariate is output, named according to grouplabel. The order of levels
in grouplevels should match the order of the group frequency columns in the input. This also
determines the ordering of levels in the resulting covariate.
Value
A single-session capthist object with no traps attribute.

43

simulation
See Also
RMarkInput, unRMarkInput
Examples
datadir <- system.file('extdata', package = 'openCR')
dipperCH <- read.inp(paste0(datadir, '/ed.inp'), ngroups = 2)
summary(dipperCH)

simulation

Simulate Capture Histories

Description
Generate non-spatial or spatial open-population data and fit models.
Usage
sim.nonspatial (N, turnover = list(), p, nsessions, noccasions = 1, intervals = NULL,
recapfactor = 1, seed = NULL, savepopn = FALSE, ...)
runsim.nonspatial (nrepl = 100, seed = NULL, ncores = NULL, fitargs = list(),
extractfn = predict, ...)
runsim.spatial (nrepl = 100, seed = NULL, ncores = NULL, popargs = list(),
detargs = list(), fitargs = list(), extractfn = predict)
sumsims (sims, parm = 'phi', session = 1, dropifnoSE = TRUE, svtol = NULL, maxcode = 3)
runsim.RMark (nrepl = 100, model = "CJS", model.parameters = NULL, extractfn,
seed = NULL, ...)

Arguments
N

integer population size

turnover

list as described for turnover

p

numeric detection probability

nsessions

number of primary sessions

noccasions

number of secondary sessions per primary session

intervals

intervals between secondary sessions (see Details)

recapfactor

numeric multiplier for capture probability after first capture

seed

random number seed see random numbers

44

simulation
savepopn

logical; if TRUE the generated population is saved as an attribute of the capthist
object

...

other arguments passed to sim.popn (sim.nonspatial) or sim.nonspatial (runsims)

nrepl

number of replicates

ncores

integer number of cores to be used for parallel processing (see Details)

popargs

list of arguments for sim.popn

detargs

list of arguments for sim.capthist

fitargs

list of arguments for openCR.fit

extractfn

function applied to each fitted openCR model

sims

list output from runsim.nonspatial or runsim.spatial

parm

character name of parameter to summarise

session

integer vector of session numbers to summarise

dropifnoSE

logical; if TRUE then replicates are omitted when SE missing for parm

svtol

numeric; minimum singular value (eigenvalue) considered non-zero

maxcode

integer; maximum accepted value of convergence code

model
character; RMark model type
model.parameters
list with RMark model specification (see ?mark)
Details
For sim.nonspatial – If intervals is specified then the number of primary and secondary sessions is inferred from intervals and nsessions and noccasions are ignored. If N and p are
vectors of length 2 then subpopulations of the given initial size are sampled with the differing capture probabilities and the resulting capture histories are combined.
runsim.spatial is a relatively simple wrapper for sim.popn, sim.capthist, and openCR.fit.
Some arguments are set automatically: the sim.capthist argument ’renumber’ is always FALSE;
argument ’seed’ is ignored within ’popargs’ and ’detargs’; if no ’traps’ argument is provided in
’detargs’ then ’core’ from ’popargs’ will be used; detargs$popn and fitargs$capthist are derived
from the preceding step. The ’type’ specified in fitargs may refer to a non-spatial or spatial openpopulation model (’CJS’, ’JSSAsecrfCL’ etc.).
In runsim.nonspatial and runsim.spatial, if ncores is NULL (the default) then the available
cores (minus one) are used for multithreading by openCR.fit. Otherwise, (ncores specified) then
replicates are split across multiple cores; ’ncores’ is set to 1 for each replicate.
sumsims assumes output from runsim.nonspatial and runsim.spatial with ’extractfn = predict’. Missing SE usually reflects non-identifiability of a parameter or failure of maximisation, so
these replicates are dropped by default. If svtol is specified then the rank of the Hessian is determined by counting eigenvalues that exceed svtol, and replicates are dropped if the rank is less than
the number of beta parameters. A value of 1e-5 is suggested for svtol in AIC.openCR, but smaller
values may be appropriate for larger models (MARK has its own algorithm for this threshold).
Replicates are also dropped by sumsims if the convergence code exceeds ’maxcode’. The maximisation functions nlm (used for method = ’Newton-Raphson’, the default), and optim (all other
methods) return different convergence codes; their help pages should be consulted. The default is
to accept code = 3 from nlm, although the status of such maximisations is ambiguous.

45

simulation
Value
sim.nonspatial –
A capthist object representing an open-population sample
runsim.nonspatial and runsim.spatial –

List with one component (output from extractfn) for each replicate. Each component also has attributes ’eigH’ and ’fit’ taken from the output of openCR.fit. See Examples to extract convergence
codes from ’fit’ attribute.
See Also
sim.popn, sim.capthist
Examples
ch <- sim.nonspatial(100, list(phi = 0.7, lambda = 1.1), p = 0.3, nsessions = 8, noccasions=2)
openCR.fit(ch, type = 'CJS')

## Not run:
turnover <- list(phi = 0.85, lambda = 1.0, recrmodel = 'constantN')
## using type = 'JSSAlCL' and extractfn = predict
fitarg <- list(type = 'JSSAlCL', model = list(p~t, phi~t, lambda~t))
out <- runsim.nonspatial(nrepl = 100, N = 100, ncores = 6, turnover = turnover,
p = 0.2, recapfactor = 4, nsessions = 10, noccasions = 1, fitargs = fitarg)
sumsims(out, 'lambda', 1:10)
## using type = 'Pradelg' and extractfn = derived
## homogeneous p
fitarg <- list(type = 'Pradelg', model = list(p~t, phi~t, gamma~t))
outg <- runsim.nonspatial(nrepl = 100, N = 100, ncores = 6, turnover = turnover,
p = 0.2, recapfactor = 4, nsessions = 10, noccasions = 1,
fitargs = fitarg, extractfn = derived)
apply(sapply(outg, function(x) x$estimates$lambda),1,mean)
turnover <- list(phi = 0.85, lambda = 1.0, recrmodel = 'discrete')
## 2-class mixture for p
outg2 <- runsim.nonspatial(nrepl = 100, N = c(50,50), ncores = 6,
p = c(0.3,0.9), recapfactor = 1, nsessions = 10, noccasions =
fitargs = fitarg, extractfn = derived)
outg3 <- runsim.nonspatial(nrepl = 100, N = c(50,50), ncores = 6,
p = c(0.3,0.3), recapfactor = 1, nsessions = 10, noccasions =
fitargs = fitarg, extractfn = derived)
apply(sapply(outg2, function(x) x$estimates$lambda),1,mean)

turnover = turnover,
1,
turnover = turnover,
1,

plot(2:10, apply(sapply(outg2, function(x) x$estimates$lambda),1,mean)[-1],
type='o', xlim = c(1,10), ylim = c(0.9,1.1))
## RMark

46

squeeze
extfn 
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