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

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 { trunc(DA), 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

1. Determine the number of clusters (parents) as a random Poisson variate with lambda = DA/mu
2. Locate each parent by drawing uniform random x- and y-coordinates
3. Generate mu offspring for each parent and locate them by adding random normal error to each parent coordinate
4. 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.

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.

Note

Other buffertypes will be defined later. (e.g. convex hull, concave)

Author(s)

Murray Efford murray.efford@otago.ac.nz

See Also

popn, simulate

Examples

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'))