sim.popn: Simulate 2-D Population

Description

Simulate a Poisson process representing the locations of individual animals.

Usage

sim.popn (D, core, buffer = 100, model2D = 'poisson',
    buffertype = 'rect', covariates = list(sex = c(M=0.5, F=0.5)),
    Ndist = 'poisson', details = NULL, seed = NULL)

Arguments

density animals / hectare (10 000 m^2)

core

data frame of points defining the core area

buffer

buffer radius about core area

model2D

character string for 2-D distribution ('poisson', 'cluster', 'IHP')

buffertype

character string for buffer type

covariates

list of named covariates

Ndist

character string for distribution of number of individuals

details

optional list with additional parameters

seed

value for setting .Random.seed - either NULL or an integer

Value

An object of class 'popn', a data frame with columns 'x' and 'y'. Rows correspond to individuals. Individual covariates (optional) are stored as a data frame attribute. The initial state of the R random number generator is stored in the 'seed' attribute.

Details

core must contain columns 'x' and 'y'; a traps object is suitable. For buffertype = 'rect', animals are simulated in the rectangular area obtained by extending the bounding box of core by buffer metres to top and bottom, left and right. This box has area $A$. A notional covariate 'sex' is generated by default. Each element of covariates defines a categorical (factor) covariate with the given probabilities of membership in each class. No mechanism is provided for generating continuous covariates, but these may be added later (see Examples). Ndist may be 'poisson' or 'fixed'. The number of individuals $N$ has expected value $DA$. If $DA$ is non-integer then Ndist = 'fixed' results in $N \in { \mathrm{trunc}(DA), \mathrm{trunc}(DA)+1 }$, with probabilities set to yield $DA$ individuals on average. If model2D = 'cluster' then the simulated population approximates a Neyman-Scott clustered Poisson distribution. Ancillary parameters are passed as components of details: details$mu is the fixed number of individuals per cluster and details$hsigma is the spatial scale ($\sigma$) of a 2-D kernel for location within each cluster. The algorithm is

Determine the number of clusters (parents) as a random Poisson variate with$\lambda = DA/\mu$
Locate each parent by drawing uniform random x- and y-coordinates
Generate mu offspring for each parent and locate them by adding random normal error to each parent coordinate
Apply toroidal wrapping to ensure all offspring locations are inside the buffered area

Toroidal wrapping is a compromise. The result is more faithful to the Neyman-Scott distribution if the buffer is large enough that only a small proportion of the points are wrapped. If model2D = 'IHP' then an inhomogeneous Poisson distribution is fitted. core should be a habitat mask and D should be a vector of length equal to the number of cells (rows) in core. The number of individuals in each cell is Poisson-distributed with mean $DA$ where $A$ is the cell area (an attribute of the mask). The random number seed is managed as in simulate.lm.

Examples

Run this code

temppop <- sim.popn (D = 10, expand.grid(x = c(0,100), y = 
    c(0,100)), buffer = 50)

## plot, distinguishing 'M' and 'F'
plot(temppop, pch = 1, cex= 1.5,
    col = c('green','red')[covariates(temppop)$sex])

## add a continuous covariate
## assumes covariates(temppop) is non-null
covariates(temppop)$size <- rnorm (nrow(temppop), mean = 15, sd = 3)
summary(covariates(temppop))

## Neyman-Scott cluster distribution
oldpar <- par(xpd = TRUE, mfrow=c(2,3))
for (h in c(5,15))
for (m in c(1,4,16)) {
    temppop <- sim.popn (D = 10, expand.grid(x = c(0,100),
        y = c(0,100)), model2D = 'cluster', buffer = 100,
        details = list(mu = m, hsigma = h))
    plot(temppop)
    text (50,230,paste(' mu =',m, 'hsigma =',h))
}
par(oldpar)

## Inhomogeneous Poisson distribution
data(secrdemo)
xy <- secrdemo.0$mask$x + secrdemo.0$mask$y - 900
tempD <- xy^2 / 1000
plot(sim.popn(tempD, secrdemo.0$mask, model2D = 'IHP'))