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 = c("poisson", "cluster",
  "IHP", "coastal", "hills", "linear", "even"), buffertype = c("rect",
  "concave", "convex"), poly = NULL, covariates = list(sex = c(M = 0.5,
  F = 0.5)), number.from = 1, Ndist = c("poisson", "fixed",
  "specified"), nsessions = 1, details = NULL, seed = NULL, keep.mask =
  model2D %in% c("IHP", "linear"), Nbuffer = NULL, ...)
tile(popn, method = "reflect")

Arguments

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

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

nsessions

number of sessions to simulate

details

optional list with additional parameters

seed

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

keep.mask

logical; if TRUE and model2D %in% c('IHP','linear') then core is saved as the attribute "mask"

Nbuffer

integer number of individuals to simulate

...

arguments passed to subset if poly is not NULL

popn

popn object

method

character string "reflect" or "copy"

Value

An object of class c("popn", "data.frame") 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.

If model2D = "linear" the output is of class c("linearpopn", "popn", "data.frame").

If model2D = "IHP" or model2D = "linear" the value of core is stored in the `mask' 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 $A$. If model2D = 'poisson' the buffer type may also be `convex' (points within a buffered convex polygon) or `concave' (corresponding to a mask of type `trapbuffer'); these buffer types use buffer.contour.

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 should usually 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. The option `specified' is undocumented; it is used in some open-population simulations.

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

Function tile replicates 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 either (i) Poisson-distributed with mean $DA$ where $A$ is the cell area (an attribute of the mask) (Ndist = "poisson") or (ii) multinomial with size $DA$ and relative cell probabilities given by D (Ndist = "fixed"). buffertype and buffer are ignored, as the extent of the population is governed entirely by the mask in core.

If model2D = "linear" then a linear population is simulated as for model2D = "IHP", except that core should be a linearmask object from package secrlinear, and density (D) is expressed in animals per km. The documentation of secrlinear should be consulted for further detail (e.g. the wrapper function sim.linearpopn).

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 model2D = "even" then the buffered area is divided into square cells with side sqrt(10000/D) and one animal is located at a random uniform location within each cell. If the height or width is not an exact multiple of the cell side then one whole extra row or column of cells is added; animals located at random in these cells are discarded if they fall outside the original area.

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 readOGR() from package `rgdal'.

The subset method is called internally when poly is used; the … argument may be used to pass values for keep.poly and poly.habitat.

Multi-session populations may be generated with nsessions > 1. Multi-session populations may be independent or generated by per capita turnover from a starting population. In the `independent' case (details$lambda not specified) D or Nbuffer may be a vector of length equal to nsessions. Turnover is controlled by survival and growth rate parameters provided as components of details and described in turnover.

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.

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
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(xpd = FALSE, mfrow=c(1,1))   ## defaults

## 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")


## Not run: ------------------------------------
# ## simulate from inhomogeneous fitted density model
# 
# regionmask <- make.mask(traps(possumCH), type = "polygon",
#     spacing = 20, poly = possumremovalarea)
# dts <- distancetotrap(regionmask, possumarea)
# covariates(regionmask) <- data.frame(d.to.shore = dts)
# dsurf <- predictDsurface(possum.model.Ds, 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)
## ---------------------------------------------

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