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virtualPollen
April 25, 2019
Type Package
Title Generation of virtual pollen curves
Version 0.1.0
Author Blas M. Benito
Maintainer Blas M. Benito 
Description Provides tools to simulate pollen curves of annual resolution based on virtual taxa with different traits (life-span, fecundity, growth-rate, niche position and niche breadth) by using a simple individual-based model. It also provides the mean to generate a virtual sediment accumulation rate to aggregate simulated pollen curves into centimetres, to represent taphonomical processes.
License GPL-2 (see LICENSE file)
Encoding UTF-8
LazyData true
RoxygenNote 6.1.1
Imports ggplot2, cowplot, viridis, mgcv, plyr, tidyr

R topics documented:
accumulationRate . .
acfToDf . . . . . . .
aggregateSimulation
compareSimulations
driverA . . . . . . .
driverB . . . . . . .
drivers . . . . . . . .
fixParametersTypes .
parameters . . . . . .
parametersCheck . .
parametersDataframe
plotAcf . . . . . . .
plotSimulation . . . .
rescaleVector . . . .

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2
3
4
6
8
9
9
10
11
12
13
15
16
18

2

accumulationRate
simulateAccumulationRate
simulateDriver . . . . . .
simulateDriverS . . . . . .
simulatePopulation . . . .
simulation . . . . . . . . .
toRegularTime . . . . . .

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Index

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19
21
22
24
27
28
30

accumulationRate

Accumulation rate

Description
Dataframe, output of simulateAccumulationRate

Usage
data(accumulationRate)

Format
dataframe with 10000 rows and the following columns: #’ @return A dataframe with the following
columns.
• time numeric, time or age of the given case.
• accumulation.rate numeric, in years per centimetre, simulated accumulation rate.
• grouping integer, grouping variable to aggregate together (with aggregateSimulation) samples deposited in the same centimetre according accumulation.rate.

Author(s)
Blas M. Benito 

See Also
simulateAccumulationRate, aggregateSimulation

acfToDf

3

Applies acf to a vector and returns a dataframe for pretty plotting in
ggplot2.

acfToDf

Description
It reads a vector representing a time series, applies acf for a given number of lags
Usage
acfToDf(
x = NULL,
lag.max = 100,
length.out = 10
)
Arguments
x

numeric vector.

lag.max

integer, number of lags over which to compute temporal autocorrelation.

length.out

integer, total number of lags to consider for plotting. Should be a subset of
lag.max.

Details
This function computes temporal autocorrelation in a given vector using acf, and returns a dataframe
ready for easy plotting in ggplot2.
Value
A dataframe with the columns: #’
• lag: numeric, lag in the time units of x with a maximum determined by lag.max, and a
number of unique values determined by length.out
• acf: Pearson correlation index returned by the acf for a given number of lags for the given
lag.
• ci.max: Maximum value of the confidence interval of acf.
• ci.min: Minimum value of the confidence interval of acf.
Author(s)
Blas M. Benito 
See Also
acf

4

aggregateSimulation

Examples
#simulating driver
x <- simulateDriver(
random.seed = 10,
time = 1:1000,
autocorrelation.length = 200,
output.min = -10,
output.max = 20,
rescale = TRUE
)
#computing temporal autocorrelations
x.df <- acfToDf(
x = x,
lag.max = 300,
length.out = 100
)
str(x.df)
#plotting output
plotAcf(x.df)

aggregateSimulation

Aggregates the output of simulatePopulation.

Description
Takes the output of simulatePopulation and aggregates it into centimetres
Usage
aggregateSimulation(
simulation.output=NULL,
accumulation.rate=NULL,
sampling.intervals=1
)
Arguments
simulation.output
list, output of simulatePopulation.
accumulation.rate
dataframe, output of simulateAccumulationRate.
sampling.intervals
numeric or numeric vector, in centimetres, depth interval or intervals between
consecutive samples. If 1, all samples are returned, if 2, returned samples are
separated by 1 cm.

aggregateSimulation

5

Details
The function uses the values in the grouping column of the simulateAccumulationRate output
to aggregate together (by computing the mean) as many samples as cases in grouping have the
same identificator. Output samples are identified by the average age of the samples within the given
centimetre.
Value
A list of dataframes with as many rows as virtual taxa were produced by simulatePopulation,
and several columns. First column is the original data. Second column is the data aggregated into
centimetres according to the result of simulateAccumulationRate. Each additional column is the
data of the second column resampled as given by the sampling.intervals argument. See example
below for more clarity.
Author(s)
Blas M. Benito 
See Also
simulateAccumulationRate, simulatePopulation
Examples
#generating driver
driver <- simulateDriver(
random.seed = 10,
time = 1:1000,
autocorrelation.length = 200,
output.min = 0,
output.max = 100,
rescale = TRUE
)
#preparing parameters
parameters <- parametersDataframe(rows = 2)
parameters[1,] <- c("Species 1", 50, 20, 2, 0.2, 0, 100, 1000, 1, 0, 50, 10, 0, 0, NA, NA)
parameters <- fixParametersTypes(x = parameters)
#simulating population dynamics
sim.output <- simulatePopulation(
parameters = parameters,
driver.A = driver,
driver.B = NULL
)
#generating accumulation rate
acc.rate <- simulateAccumulationRate(
seed = 50,
time = 1:1000,
output.min = 10,

6

compareSimulations
output.max = 40,
direction = 1,
plot = TRUE
)
#aggregating simulated data
sim.output.aggregated <- aggregateSimulation(
simulation.output = sim.output,
accumulation.rate = acc.rate,
sampling.intervals = 3)
#comparing simulations
par(mfrow = c(3,1))
#notice the subsetting of the given column of the input list
plot(sim.output.aggregated[[1,1]]$Time,
sim.output.aggregated[[1,1]]$Pollen,
type = "l",
xlim = c(0, 1000),
main = "Annual"
)
plot(sim.output.aggregated[[1,2]]$Time,
sim.output.aggregated[[1,2]]$Pollen,
type = "l",
xlim = c(0, 1000),
main = "1cm"
)
plot(sim.output.aggregated[[1,3]]$Time,
sim.output.aggregated[[1,3]]$Pollen,
type = "l",
xlim = c(0, 1000),
main = "3cm"
)
#check differences in nrow
nrow(sim.output.aggregated[[1,1]]) #original data
nrow(sim.output.aggregated[[1,2]]) #1cm
nrow(sim.output.aggregated[[1,3]]) #3cm intervals

compareSimulations

Compares different simulations produced by simulatePopulation.

Description
Plots together the results of different taxa produced by a single run of simulatePopulation.
Usage
compareSimulations(
simulation.output = NULL,

compareSimulations

7

species = "all",
filename = NULL,
columns = "Pollen",
time.zoom = NULL,
width = 12,
text.size = 20,
title.size = 25,
plot.title = ""
)

Arguments
simulation.output
output of simulatePopulation.
species

a number or vector or numbers representing rows in the parameters dataframe, or
a string or vector of strings referencing to the "label" column of the parameters
dataframe.

filename

character string, name of output pdf file. If NULL or empty, no pdf is produced.

columns

character string or vector of character strings with these possible values: "Pollen",
"Population.mature", "Population.immature", "Population.viable.seeds", "Suitability", "Biomass.total", "Biomass.mature", "Biomass.immature", "Mortality.mature",
"Mortality.immature", "Driver.A", "Driver.B".

time.zoom

vector of two numbers indicating the beginnign and end of the time interval to
be plotted (i.e. "c(5000, 10000)")

width

plot width in inches.

text.size

text size of the plot.

title.size

plot title size.

plot.title

character string to use as plot title.

Details
The user can decide what virtual taxa to plot (argument species), and what information to show
throught the columns argument. Output is plotted on screen by default, and printed to pdf if the
filename argument is filled.

Author(s)
Blas M. Benito 

See Also
simulatePopulation, plotSimulation

8

driverA

Examples
driver <- simulateDriver(
random.seed = 10,
time = 1:1000,
autocorrelation.length = 200,
output.min = 0,
output.max = 100,
rescale = TRUE
)
#preparing parameters
parameters <- parametersDataframe(rows = 2)
parameters[1,] <- c("Species 1", 50, 20, 2, 0.2, 0, 100, 1000, 1, 0, 50, 10, 0, 0, NA, NA)
parameters[2,] <- c("Species 1", 500, 100, 10, 0.02, 0, 100, 1000, 1, 0, 50, 10, 0, 0, NA, NA)
parameters <- fixParametersTypes(x = parameters)
#simulating population dynamics
sim.output <- simulatePopulation(
parameters = parameters,
driver.A = driver
)
#plot simulation
compareSimulations(simulation.output = sim.output)

driverA

Driver A

Description
A vector of 10000 values (years) between 0 and 100 generated by simulateDriver with a temporal
autocorrelation significant for 600 years. It is meant to be used as input for simulatePopulation
Usage
data(driverA)
Format
numeric vector of length 10000.
Author(s)
Blas M. Benito 
See Also
simulateDriver

driverB

9

driverB

Driver B

Description
A vector of 10000 values (years) between 0 and 100 generated by simulateDriver with a temporal
autocorrelation significant for 600 years. It is meant to be used as input for simulatePopulation
Usage
data(driverB)
Format
numeric vector of length 10000.
Author(s)
Blas M. Benito 
See Also
simulateDriver

drivers

Drivers with different temporal autocorrelations.

Description
A dataframe with 60000 rows and 4 columns (years) containing two drivers (A and B) generated by
simulateDriver with different temporal autocorrelations (200, 600, and 1800). It is meant to be
used as input for simulatePopulation
Usage
data(drivers)
Format
numeric vector of length 10000.
Details
• time integer.
• driver character, values are A and B
• autocorrelation.length numeric, values are 200, 600, and 1800.
• value numeric, value of the driver for the given time.

10

fixParametersTypes

Author(s)
Blas M. Benito 
See Also
simulateDriver

fixParametersTypes

Fix data types in parameters dataframe.

Description
It converts all columns (but the label one) of a parameters dataframe created by parametersDataframe
into type numeric, and checks the coherence of the parameters for each taxon. It provides feedback
on the check results on screen for each taxon.
Usage
fixParametersTypes(x)
Arguments
x

dataframe resulting from parametersDataframe.

Value
Same dataframe provided in argument x but with fixed data types.
Author(s)
Blas M. Benito 
See Also
parametersDataframe
Examples
parameters <- parametersDataframe(rows=1)
parameters[1,] <- c("Species 1", 50, 20, 2, 0.2, 0, 100, 1000, 1, 0, 50, 10, 0, 0, NA, NA)
parameters <- fixParametersTypes(x=parameters)

parameters

parameters

11

Parameters of 16 virtual taxa.

Description
A dataframe with 16 rows and 16 columns with the parameters of two virtual taxa. It was generated by parametersDataframe and fixParametersTypes. It is meant to be used as input for
simulatePopulation. It’s columns are:
Usage
data(drivers)
Format
Dataframe with 16 columns and 16 rows.
Details
• label: to store names (character string) of the virtual taxa.
• maximum.age: integer, maximum possible age of the individuals in years.
• reproductive.age: integer, age of sexual maturity in years.
• fecundity: integer, number of maximum viable seeds produced by a mature individual under
fully suitable conditions.
• growth.rate: numeric, parameter of the logistic growth function.
• pollen.control: numeric in the interval [0, 1]. If 0, pollen productivity depends on environmental suitability only. The larger the number, biomass takes over environmental suitability
in determining pollen productivity.
• maximum.biomass: integer, maximum biomass of the individuals.
• carrying.capacity: integer, maximum sum of biomass of the individuals. Very large carrying
capacities plus a low maximum.biomass generates too many individuals for the simulation
to remain efficient. Try to set carrying.capacity and maximum.biomass to carrying.capacity
divided by biomass returns a number lower than 1000 (and even better if it is closer to 100).
• driver.A.weight: numeric in the interval [0, 1], represents the relative influence of the driver
on environmental suitability.
• driver.B.weight: numeric in the interval [0, 1], represents the relative influence of the driver
on environmental suitability. The sum of weights of drivers A and B should be 1.
• niche.A.mean: numeric, in the same units as driver A. It is the mean of the normal function
defining the response of the virtual taxa to driver A.
• niche.A.sd: numeric, in the same units as driver A. It is the standard deviation of the normal
function defining the response of the virtual taxa to driver A.
• niche.B.mean: as above, but for driver B.
• niche.B.sd: as above, but for driver B.

12

parametersCheck
• autocorrelation.length.A: numeric, only useful if several drivers generated with different autocorrelation lengths are available (and identified by the column autocorrelation.length)
in the drivers argument provided to the simulatePopulation function.
• autocorrelation.length.B: same as above.

Author(s)
Blas M. Benito 
See Also
parametersCheck, parametersDataframe, simulatePopulation

Plots main simulation parameters.

parametersCheck

Description
Plots the normal function/s, fecundity, growth curve, and maturity age, of each virtual taxa in
parameters.
Usage
parametersCheck(
parameters,
species = "all",
driver.A = NULL,
driver.B = NULL,
drivers = NULL,
filename = NULL
)
Arguments
parameters

the parameters dataframe.

species

if "all" or "ALL", all species in "parameters" are plotted. It also accepts a vector
of numbers representing the rows of the selected species, or a vector of names
of the selected species.

driver.A

numeric vector with driver values.

driver.B

numeric vector with driver values.

drivers

dataframe with drivers

filename

character string, filename of the output pdf.

Details
The function prints the plot, can save it to a pdf file if filename is provided, and returns a ggplot2
object.

parametersDataframe

13

Value
A ggplot2 object.
Author(s)
Blas M. Benito 
See Also
parametersDataframe, fixParametersTypes
Examples
#generating driver
driver <- simulateDriver(
random.seed = 10,
time = 1:1000,
autocorrelation.length = 200,
output.min = 0,
output.max = 100,
rescale = TRUE
)
#preparing parameters
parameters <- parametersDataframe(rows = 2)
parameters[1,] <- c("Species 1", 50, 20, 2, 0.2, 0, 100, 1000, 1, 0, 50, 10, 0, 0, NA, NA)
parameters[2,] <- c("Species 1", 500, 100, 10, 0.02, 0, 100, 1000, 1, 0, 50, 10, 0, 0, NA, NA)
parameters <- fixParametersTypes(x = parameters)
#plotting parameters
parametersCheck(
parameters = parameters,
driver.A = driver,
filename = "Parameters.pdf"
)

parametersDataframe

Generates a template dataframe to contain simulation parameters.

Description
Generates the dataframe structure needed to contain the parameters used as input for the simulatePopulation
function.
Usage
parametersDataframe(rows=1)

14

parametersDataframe

Arguments
rows

integer, number of rows in the output dataframe.

Details
The resulting dataframe can either be filled manually through vectors, as shown in the example (but
this requires to use the function fixParametersTypes once the dataframe is completed), or can be
edited manually in Rstudio by installing the editData package.
Value
A dataframe filled with NA values and the columns:
• label: to store names (character string) of the virtual taxa.
• maximum.age: integer, maximum possible age of the individuals in years.
• reproductive.age: integer, age of sexual maturity in years.
• fecundity: integer, number of maximum viable seeds produced by a mature individual under
fully suitable conditions.
• growth.rate: numeric, parameter of the logistic growth function.
• pollen.control: numeric in the interval [0, 1]. If 0, pollen productivity depends on environmental suitability only. The larger the number, biomass takes over environmental suitability
in determining pollen productivity.
• maximum.biomass: integer, maximum biomass of the individuals.
• carrying.capacity: integer, maximum sum of biomass of the individuals. Very large carrying
capacities plus a low maximum.biomass generates too many individuals for the simulation
to remain efficient. Try to set carrying.capacity and maximum.biomass to carrying.capacity
divided by biomass returns a number lower than 1000 (and even better if it is closer to 100).
• driver.A.weight: numeric in the interval [0, 1], represents the relative influence of the driver
on environmental suitability.
• driver.B.weight: numeric in the interval [0, 1], represents the relative influence of the driver
on environmental suitability. The sum of weights of drivers A and B should be 1.
• niche.A.mean: numeric, in the same units as driver A. It is the mean of the normal function
defining the response of the virtual taxa to driver A.
• niche.A.sd: numeric, in the same units as driver A. It is the standard deviation of the normal
function defining the response of the virtual taxa to driver A.
• niche.B.mean: as above, but for driver B.
• niche.B.sd: as above, but for driver B.
• autocorrelation.length.A: numeric, only useful if several drivers generated with different autocorrelation lengths are available (and identified by the column autocorrelation.length)
in the drivers argument provided to the simulatePopulation function.
• autocorrelation.length.B: same as above.
Author(s)
Blas M. Benito 

plotAcf

15

See Also
simulatePopulation, fixParametersTypes
Examples
parameters <- parametersDataframe(rows=1)
parameters[1,] <- c("Species 1", 50, 20, 2, 0.2, 0, 100, 1000, 1, 0, 50, 10, 0, 0, NA, NA)

Plots results of acfToDf.

plotAcf

Description
Plots a dataframe resulting from acfToDf by using ggplot2 (and cowplot)
Usage
plotAcf(
x = NULL,
plot.title = ""
)
Arguments
x

dataframe, output of acfToDf

plot.title

string, title for the plot.

Value
A ggplot object
Author(s)
Blas M. Benito 
See Also
acfToDf

16

plotSimulation

Examples
#simulating driver
x <- simulateDriver(
random.seed = 10,
time = 1:1000,
autocorrelation.length = 200,
output.min = -10,
output.max = 20,
rescale = TRUE
)
#computing temporal autocorrelation
x.df <- acfToDf(
x = x,
lag.max = 300,
length.out = 100
)
#plotting output
plotAcf(x.df)

plotSimulation

Plots results of simulatePopulation.

Description
This function takes as input a list of dataframes or a single dataframe resulting from the execution of simulatePopulation, and plots the resulting time series of pollen abundance, number of
individuals, biomass, driver, and environmnetal suitability.
Usage
plotSimulation(
simulation.output=NULL,
species="all",
burnin=FALSE,
filename=NULL,
time.zoom=NULL,
panels=c("Driver A",
"Driver B",
"Suitability",
"Population",
"Mortality",
"Biomass",
"Pollen"
),

plotSimulation

17

plot.title=NULL,
width=12,
text.size=20,
title.size=25,
line.size=1
)
Arguments
simulation.output
output of simulatePopulation.
species

a number or vector or numbers representing rows in the parameters dataframe, or
a string or vector of strings referencing to the "label" column of the parameters
dataframe.

burnin

if FALSE, burn-in period is not considered in the model.

filename

character string, name of output pdf file. If NULL or empty, no pdf is produced.
It shouldn’t include the extension of the output file.

time.zoom

vector of two numbers indicating the beginnign and end of the time interval to
be plotted (i.e. "c(5000, 10000)")

panels

character string or vector of character strings with these possible values: "Driver
A", "Driver B","Suitability", "Population", "Mortality", "Biomass", "Pollen".

plot.title

character string to use as plot title.

width

plot width in inches.

text.size

text size of the plot.

title.size

plot title size.

line.size

size of lines in plots.

Details
The user can decide what virtual taxa to plot (argument species), and what information to show
throught the panels argument. Output is plotted on screen by default, and printed to pdf if the
filename argument is filled.
Author(s)
Blas M. Benito 
See Also
simulatePopulation, compareSimulations
Examples
driver <- simulateDriver(
random.seed = 10,
time = 1:1000,

18

rescaleVector
autocorrelation.length = 200,
output.min = 0,
output.max = 100,
rescale = TRUE
)
#preparing parameters
parameters <- parametersDataframe(rows = 2)
parameters[1,] <- c("Species 1", 50, 20, 2, 0.2, 0, 100, 1000, 1, 0, 50, 10, 0, 0, NA, NA)
parameters[2,] <- c("Species 1", 500, 100, 10, 0.02, 0, 100, 1000, 1, 0, 50, 10, 0, 0, NA, NA)
parameters <- fixParametersTypes(x = parameters)
#simulating population dynamics
sim.output <- simulatePopulation(
parameters = parameters,
driver.A = driver
)
#plot simulation
plotSimulation(simulation.output = sim.output)

Rescales a vector within given bounds.

rescaleVector

Description
Takes a numeric vector x and rescales it within the values given by new.min and new.max.
Usage
rescaleVector(
x = rnorm(100),
new.min = 0,
new.max = 100,
integer = FALSE
)
Arguments
x

numeric vector to be rescaled.

new.min

numeric, new minimum value for x. Default is 0.

new.max

numeric, new maximum value for x. Default is 100.

integer

boolean, if TRUE, output vector is returned as vector of integers. Default is
FALSE.

Value
A vector of the same length as x rescaled between output.min and output.max.

simulateAccumulationRate

19

Author(s)
Blas M. Benito 
Examples
#generating example data
x = rnorm(100)
#as float
x.float <- rescaleVector(
x = x,
new.min = 0,
new.max = 100,
integer = FALSE
)
#as integer
x.integer <- rescaleVector(
x = x,
new.min = 0,
new.max = 100,
integer = TRUE
)

simulateAccumulationRate
Simulates a virtual sediment accumulation rate.

Description
Generates a virtual sediment accumulation rate to be applied to the results of simulatePopulation
Usage
simulateAccumulationRate(
seed=50,
time=1:1000,
output.min=10,
output.max=40,
direction=1,
plot=TRUE
)
Arguments
seed

integer, seed to be used by set.seed to configure the state of the pseudo-random
number generator. It defines the shape of the curve.

20

simulateAccumulationRate
time

vector of time values (ideally the same used to generate the simulations).

output.min

numeric, in years per centimetre, minimum sediment accumulation rate (10 by
default).

output.max

numeric, in years per centimetre, maximum sediment accumulation rate (40 bu
default).

direction

integer, values 1 or -1, to invert the resulting accumulation rate.

plot

boolean, plots output accumulation rate if TRUE.

Details
The accumulation rate curve is generated through a random walk smoothed by a GAM model. The
value of the seed argument changes the shape of the curve, but the user has no more control than
trying different values to achieve a curve closer to the desired one. If plot is set to TRUE, the
accumulation rate curve is printed on screen, but not exported to pdf.
Value
A dataframe like accumulationRate, with the following columns:
• time numeric, time or age of the given case.
• accumulation.rate numeric, in years per centimetre, simulated accumulation rate.
• grouping integer, grouping variable to aggregate together (with aggregateSimulation) samples deposited in the same centimetre according accumulation.rate.
Author(s)
Blas M. Benito 
See Also
accumulationRate, aggregateSimulation
Examples
acc.rate <- simulateAccumulationRate(
seed = 50,
time = 1:1000,
output.min = 10,
output.max = 40,
direction = 1,
plot = TRUE
)
str(acc.rate)

simulateDriver

simulateDriver

21

Generates a random time series with temporal autocorrelation.

Description
Generates a vector of the same legnth as the time argument, with a temporal autocorrelation
length close to the defined by autocorrelation.length, and a range within output.min and
output.max. The output of this function is intended to be used as an input to the function rescaleVector.
Note that the variable time runs from left to right, with lower values representing older samples.
Usage
simulateDriver(
random.seed = 50,
time = 1:10000,
autocorrelation.length = 100,
output.min = 0,
output.max = 100,
rescale = TRUE
)
Arguments
random.seed

integer, seed to be used by set.seed(). Default is 50.

integer, or numeric vector of integers with constant intervals. If a single integer
is provided, a time sequence is generated from 1 to the given integer as seq(1,
time, by = 1). Default is 1:10000.
autocorrelation.length
integer, represents the length of the convolution filter to be used to impose a
particular temporal structure on the time series. Default is 100, equivalent to a
filter composed by a hundred of ones.
time

output.min

numeric, minimum value of the output time series. Used as input for rescaleVector. Default is 0.

output.max

numeric, maximum value of the output time series. Used as input for rescaleVector. Default is 100.

rescale

boolean. If FALSE, output.min and output.max are ignored, and the original
data range provided by rnorm is preserved. Default is TRUE.

Details
It is recommended to use time vectors with a time step of 1 between consecutive values when the
output is to be used as input for simulatePopulation, which considers annual time-steps while
simulating virtual pollen curves. Initial random sequence is generated by rnorm. Desired temporal autocorrelation are approximate, but deviation becomes higher if autocorrelation.length is
larger than half the length of time. Consequently, the function limits autocorrelation.length to
length(time)/2.

22

simulateDriverS

Value
A vector of the same length as time. Datasets driverA and driverB are outputs of this function.
Author(s)
Blas M. Benito 
See Also
rescaleVector, driverA, driverB
Examples
x <- simulateDriver(
random.seed = 50,
time = 1:10000,
autocorrelation.length = 200,
output.min = -10,
output.max = 20,
rescale = TRUE
)
#plots output
plot(x, type = "l")
#checks temporal autocorrelation
acf(x, lag.max = 300)

simulateDriverS

Generates a long table with several drivers for simulatePopulation.

Description
Wrapper of simulateDriver to generate several drivers with different autocorrelation lengths, and
return a long format table to be used as input for simulatePopulation. Note that the variable time
runs from left to right, with lower values representing older samples.
Usage
simulateDriverS(
random.seeds=c(60, 120),
time=1:10000,
autocorrelation.lengths=c(200, 600, 1800),
output.min=c(0,0),
output.max=c(100, 100),
driver.names=c("A", "B"),
filename=NULL)

simulateDriverS

23

Arguments
random.seeds

vector of integers, seeds to be used by set.seed.

time

integer, or numeric vector of integers with constant intervals. If a single integer
is provided, a time sequence is generated from 0 to the given integer as seq(0,
time, by = 1). Default is 1:10000.

autocorrelation.lengths
vector of integers, represents the lengths of the convolution filters to be used to
impose a particular temporal structure on each driver. Default is 100, equivalent
to a filter composed by a hundred of ones.
output.min

numeric vector, minimum values of the output time series. Used as input for
rescaleVector. Default is 0.

output.max

numeric vector, maximum values of the output time series. Used as input for
rescaleVector. Default is 100.

driver.names

character vector, with labels to be used to identify the drivers.

filename

character string, name of output pdf file. If NULL or empty, no pdf is produced.

Details
It is recommended to use time vectors with a time step of 1 between consecutive values when the
output is to be used as input for simulatePopulation, which considers annual time-steps while
simulating virtual pollen curves. Initial random sequence is generated by rnorm. Desired temporal autocorrelation are approximate, but deviation becomes higher if autocorrelation.length is
larger than half the length of time. Consequently, the function limits autocorrelation.length to
length(time)/2.
Value
A long format dataframe (see dataset drivers) with the following columns:
• time integer.
• driver character, values are A and B
• autocorrelation.length numeric, values are 200, 600, and 1800.
• value numeric, value of the driver for the given time.
Author(s)
Blas M. Benito 
See Also
drivers, simulateDriver, simulatePopulation, drivers

24

simulatePopulation

Examples
drivers <- simulateDriverS(
random.seeds=c(60, 120),
time=1:10000,
autocorrelation.lengths=c(200, 600, 1800),
output.min=c(0,0),
output.max=c(100, 100),
driver.names=c("A", "B"),
filename=NULL)

simulatePopulation

Simulates population dynamics for virtual species with different traits.

Description
This function takes as input a dataframe of parameters defining virtual taxa produced by parametersDataframe
and fixParametersTypes, a driver or drivers generated with simulateDriver, and simulates population dynamics at yearly resolution for the time-length defined by the driver or drivers. The model
relies on the following set of assumptions. Note that the variable time runs from left to right, with
lower values representing older samples.
• The spatial structure of the population is not important to explain its pollen productivity. This
is an operative assumption, to speed-up model execution.
• The environmental niche of the species follows a Gaussian distribution, characterized by a
mean (niche optimum, also niche position) and a standard deviation (niche breadth or tolerance).
• Different drivers can have a different influence on the species dynamics, and that influence
can be defined by the user by tuning the weights of each driver.
• Environmental suitability, expressed in the range [0, 1], is the result of an additive function of
the species niches (normal function defined by the species’ mean and standard deviation for
each driver), the drivers’ values, and the relative influence of each driver (driver weights).
• Pollen productivity is a function of the individual’s biomass and environmental suitability, so
under a hypothetical constant individual’s biomass, its pollen production depends linearly on
environmental suitability values.
• Effective fecundity is limited by environmental suitability. Low environmental suitability values limit recruitment, acting as an environmental filter. Therefore, even though the fecundity
of the individuals is fixed by the fecundity parameter, the overall population fecundity is limited by environmental suitability.
Usage
simulatePopulation(
parameters=NULL,
species="all",

simulatePopulation

25

driver.A=NULL,
driver.B=NULL,
drivers=NULL,
burnin=TRUE
)
Arguments
parameters

dataframe with parameters.

species

if "all" or "ALL", all species in "parameters" are simulated It also accepts a
vector of numbers representing the rows of the selected species, or a vector of
names of the selected species.

driver.A

numeric vector with driver values. Typically produced by simulateDriver.

driver.B

numeric vector with driver values. Typically produced by simulateDriver.
Must have same length as driver.A.

drivers

dataframe with drivers produced by simulateDriverS. It should have the columns:
•
•
•
•

burnin

time integer.
driver character, values are A and B
autocorrelation.length numeric, values are 200, 600, and 1800.
value numeric, value of the driver for the given time.

boolean, generates a warming-up period for the population model of a length of
five times the maximum age of the virtual taxa.

Details
The model starts with a population of 100 individuals with random ages, in the range [1, maximum age], taken from a uniform distribution (all ages are equiprobable). For each environmental
suitability value, including the burn-in period, the model performs the following operations:
• Aging: adds one year to the age of the individuals.
• Mortality due to senescence: individuals reaching the maximum age are removed from the
simulation.
• Local extinction and immigration If the number of individuals drops to zero, the population
is replaced by a "seed bank" of #’ 100 individuals with age zero, and the simulation jumps to
step 7.. This is intended to simulate the arrival of seeds from nearby regions, and will only
lead to population growth if environmental suitability is higher than zero.
• Plant growth: Applies a plant growth equation to compute the biomass of every individual.
• Carrying capacity: If maximum population biomass is reached, individuals are iteratively
selected for removal according to a mortality risk curve computed by the equation Pm =
1 − sqrt(a/A), were Pm is the probability of mortality, a is the age of the given individual,
and A is the maximum age reached by the virtual taxa. This curve gives removal preference to
younger individuals, matching observed patterns in natural populations.
• Pollen productivity: In each time step the model computes
the pollen productivity (in relative
P
values) of the population using the equation Pt =
xit × max(St , B), where t is time (a
given simulation time step), P is the pollen productivity of the population at a given time,

26

simulatePopulation
x_i represents the biomass of every adult individual, S is the environmental suitability at the
given time, B is the contribution of biomass to pollen productivity regardless of environmental
suitability (pollen.control parameter in the simulation, 0 by default). If B equals 1, P is equal
to the total biomass sum of the adult population, regardless of the environmental suitability. If
B equals 0, pollen productivity depends entirely on environmental suitability values.
• Reproduction: Generates as many seeds as reproductive individuals are available multiplied
by the maximum fecundity and the environmental suitability of the given time.
The model returns a table with climatic suitability, pollen production, and population size (reproductive individuals only) per simulation year. Figure 10 shows the results of the population model
when applied to the example virtual species.

Value
A list of dataframes, each one of them with the results of one simulation. The dataset simulation
exemplifies the output of this function. Each dataframe in the output list has the columns:
• Time integer, ages in years. Negative ages indicate the burn-in period.
• Pollen numeric, pollen counts
• Population.mature numeric, number of mature individuals.
• Population.immatre numeric, number of immature individuals.
• Population.viable.seeds numeric, number of viable seeds generated each year.
• Suitability numeric, environmental suitability computed from the driver by the normal function/s defining the taxon niche.
• Biomass.total numeric, overall biomass of the population.
• Biomass.mature numeric, sum of biomass of mature individuals.
• Biomass.immature numeric, sum of biomass of immature individuals.
• Mortality.mature numeric, number of mature individuals dead each year.
• Mortality.immature numeric, same as above for immature individuals.
• Driver.A numeric, values of driver A.
• Driver.B numeric, values of driver B, if available, and NA otherwise.
• Period qualitative, with value "Burn-in" for burn-in period, and "Simulation" otherwise.
Author(s)
Blas M. Benito 
See Also
parametersDataframe, fixParametersTypes, plotSimulation

simulation

27

Examples
data(parameters)
data(driverA)
#simulating population dynamics
# of first taxon in parameters
# for first 500 values of driverA
sim.output <- simulatePopulation(
parameters=parameters[1,],
driver.A=driverA[1:500]
)
#checking output for Species 1
str(sim.output)

simulation

List with simulation outputs for all virtual taxa in parameters.

Description
A list of dataframes with 16 slots, output of simulatePopulation, taking parameters and drivers
as input. Each dataframe has the following columns:
Usage
data(simulation)
Format
List with 16 dataframes with outputs of simulatePopulation.
Details
• Time integer, ages in years. Negative ages indicate the burn-in period.
• Pollen numeric, pollen counts
• Population.mature numeric, number of mature individuals.
• Population.immatre numeric, number of immature individuals.
• Population.viable.seeds numeric, number of viable seeds generated each year.
• Suitability numeric, environmental suitability computed from the driver by the normal function/s defining the taxon niche.
• Biomass.total numeric, overall biomass of the population.
• Biomass.mature numeric, sum of biomass of mature individuals.
• Biomass.immature numeric, sum of biomass of immature individuals.

28

toRegularTime
• Mortality.mature numeric, number of mature individuals dead each year.
• Mortality.immature numeric, same as above for immature individuals.
• Driver.A numeric, values of driver A.
• Driver.B numeric, values of driver B, if available, and NA otherwise.
• Period qualitative, with value "Burn-in" for burn-in period, and "Simulation" otherwise.

Author(s)
Blas M. Benito 
See Also
simulatePopulation, plotSimulation

toRegularTime

Reinterpolates aggregated simulations into regular time.

Description
Takes the output of aggregateSimulation, and interpolates it into a regular time grid.
Usage
toRegularTime(
x,
time.column="Time",
interpolation.interval,
columns.to.interpolate=c("Suitability", "Driver.A", "Pollen")
)
Arguments
x

list of dataframes (generally the output of aggregateSimulation) or single
dataframe with irregular time series.

time.column
character string, default value is "Time".
interpolation.interval
integer, in years, time length encompassed by each sample.
columns.to.interpolate
character string or character vector, columns of simulation output to be interpolated. Any subset of: "Pollen", "Population.mature", "Population.immature",
"Population.viable.seeds", "Suitability", "Biomass.total", "Biomass.mature", "Biomass.immature",
"Mortality.mature", "Mortality.immature", "Driver.A", "Driver.B".

toRegularTime

29

Details
This function fits a loess model of the form y ~ x, where y is any column given by columns.to.interpolate
and x is the column given by the time.column argument. The model is used to interpolate column y
on a regular time series of intervals equal to interpolation.interval. If x is a matrix-like list returned by aggregateSimulation (on results of simulateAccumulationRate and simulatePopulation),
the first column of the matrix will already have a regular time column, and therefore nothing will
be done with this column of the list.
Value
If x is a list of dataframes, the function returns a list with the same structure as the input list. If x
is a dataframe, the function returns a dataframe. In any case, output dataframes have the columns
"Time" (now regular), and any column listed in columns.to.interpolate.
Author(s)
Blas M. Benito 
See Also
simulateAccumulationRate, aggregateSimulation

Index
∗Topic datasets
accumulationRate, 2
driverA, 8
driverB, 9
drivers, 9
parameters, 11
simulation, 27
accumulationRate, 2, 20
acf, 3
acfToDf, 3, 15
aggregateSimulation, 2, 4, 20, 28, 29
compareSimulations, 6, 17
cowplot, 15
driverA, 8, 22
driverB, 9, 22
drivers, 9, 23, 27
fixParametersTypes, 10, 11, 13–15, 24, 26
ggplot2, 3, 12, 13, 15
loess, 29
parameters, 11, 27
parametersCheck, 12, 12
parametersDataframe, 10–13, 13, 24, 26
plotAcf, 15
plotSimulation, 7, 16, 26, 28
rescaleVector, 18, 21, 22
set.seed, 19
simulateAccumulationRate, 2, 4, 5, 19, 29
simulateDriver, 8–10, 21, 23–25
simulateDriverS, 22, 25
simulatePopulation, 4–9, 11–17, 19, 21–23,
24, 27–29
simulation, 26, 27
toRegularTime, 28
30



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