sim.popn {secr} | R Documentation

## 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

`D` | 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

### 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 `buffertype`s 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'))

[Package secr version 1.2.11 Index]