secr (version 2.5.0)

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", poly = NULL, covariates =
    list(sex = c(M = 0.5, F = 0.5)), number.from = 1,
    Ndist = "poisson", nsession = 1, details = NULL,
    seed = NULL, ...)

tile(popn, method = "reflect")

Arguments

D

density animals / hectare (10 000 m^2) (see Details for IHP case)

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", "coastal")

buffertype

character string for buffer type

poly

bounding polygon (see Details)

covariates

list of named covariates

number.from

integer ID for animal

Ndist

character string for distribution of number of individuals

nsession

number of sessions to simulate

details

optional list with additional parameters

seed

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

...

arguments passed to subset if poly is not NULL

popn

popn object

method

character string "reflect" or "copy"

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 random 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

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 Functiontilereplicates a popn pattern by either reflecting or copying and translating it to fill a 3 x 3 grid.

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 simulated. core should be a habitat mask and D should be either a vector of length equal to the number of cells (rows) in core or the name of a covariate in core that contains cell-specific densities (animals / hectare), or a constant. The number of individuals in each cell is Poisson-distributed with mean $DA$ where $A$ is the cell area (an attribute of the mask). buffertype and buffer are ignored, as the extent of the population is governed entirely by the mask in core. If model2D = "coastal" then a form of inhomogeneous Poisson distribution is simulated in which the x- and y-coordinates are drawn from independent Beta distributions. Default parameters generate the `coastal' distribution used by Fewster and Buckland (2004) for simulations of line-transect distance sampling (x ~ Beta(1, 1.5), y ~ Beta(5, 1), which places 50% of the population in the `northern' 13% of the rectangle). The four Beta parameters may be supplied in the vector component Beta of the `details' list (see Examples). The Beta parameters (1,1) give a uniform distribution. Coordinates are scaled to fit the limits of a sampled rectangle, so this method assumes buffertype = "rect". If model2D = "hills" then a form of inhomogeneous Poisson distribution is simulated in which intensity is a sine curve in the x- and y- directions (density varies symmetrically between 0 and 2 x D along each axis). The number of hills in each direction (default 1) is determined by the `hills' component of the `details' list (e.g. details = list(hills=c(2,3)) for 6 hills). If either number is negative then alternate rows will be offset by half a hill. Displacements of the entire pattern to the right and top are indicated by further elements of the `hills' component (e.g. details = list(hills=c(1,1,0.5,0.5)) for 1 hill shifted half a unit to the top right; coordinates are wrapped, so the effect is to split the hill into the four corners). Negative displacements are replaced by runif(1). Density is zero at the edge when the displacement vector is (0,0) and rows are not offset. If poly is specified, points outside poly are dropped. poly may be either

• a matrix or dataframe of two columns interpreted as x and y coordinates, or
• a SpatialPolygonsDataFrame object as defined in the package `sp', possibly from reading a shapefile with readShapePoly() from package `maptools'.

The subset method is called internally when poly is used; the ...argument may be used to pass values for keep.poly and poly.habitat. The random number seed is managed as in simulate.lm.

References

Fewster, R. M. and Buckland, S. T. 2004. Assessment of distance sampling estimators. In: S. T. Buckland, D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers and L. Thomas (eds) Advanced distance sampling. Oxford University Press, Oxford, U. K. Pp. 281--306.

See Also

popn, plot.popn, randomHabitat, 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
xy <- secrdemo.0$mask$x + secrdemo.0$mask$y - 900
tempD <- xy^2 / 1000
plot(sim.popn(tempD, secrdemo.0$mask, model2D = "IHP"))

## Coastal distribution in 1000-m square, homogeneous in
## x-direction
arena <- data.frame(x = c(0, 1000, 1000, 0),
    y = c(0, 0, 1000, 1000))
plot(sim.popn(D = 5, core = arena, buffer = 0, model2D =
    "coastal", details = list(Beta = c(1, 1, 5, 1))))

## Hills
plot(sim.popn(D = 100, core = arena, model2D = "hills",
    buffer = 0, details = list(hills = c(-2,3,0,0))), 
    cex = 0.4)

## tile demonstration
pop <- sim.popn(D = 100, core = make.grid(), model2D = "coastal")
par(mfrow = c(1,2), mar = c(2,2,2,2))
plot(tile(pop, "copy"))
polygon(cbind(-100,200,200,-100), c(-100,-100,200,200),
    col = "red", density = 0)
title("copy")
plot(tile(pop, "reflect"))
polygon(cbind(-100,200,200,-100), c(-100,-100,200,200),
    col = "red", density = 0)
title("reflect")


## simulate from inhomogeneous fitted density model
regionmask <- make.mask(traps(possumCH), type = 'polygon',
    spacing = 20, poly = possumremovalarea)
dsurf <- predictDsurface(possum.model.Dh2, regionmask)
possD <- covariates(dsurf)$D.0
posspop <- sim.popn(D = possD, core = dsurf, model = "IHP")
plot(regionmask, dots = FALSE, ppoly = FALSE)
plot(posspop, add = TRUE, frame = FALSE)
plot(traps(possumCH), add = TRUE)