R: Fit the generalized distance sampling model of Chandler et...

gdistsamp {unmarked} | R Documentation

## Fit the generalized distance sampling model of Chandler et al. (2011).

### Description

Extends the distance sampling model of Royle et al. (2004) to estimate the probability of being available for detection. Also allows abundance to be modeled using the negative binomial distribution.

### Usage

    gdistsamp(lambdaformula, phiformula, pformula, data, keyfun =
    c("halfnorm", "exp", "hazard", "uniform"), output = c("abund",
    "density"), unitsOut = c("ha", "kmsq"), mixture = c("P", "NB"), K,
    starts, method = "BFGS", se = TRUE, engine=c("C","R"), rel.tol=1e-4, ...)

### Arguments

`lambdaformula` | A right-hand side formula describing the abundance covariates.
`phiformula` | A right-hand side formula describing the availability covariates.
`pformula` | A right-hand side formula describing the detection function covariates.
`data` | An object of class `unmarkedFrameGDS`
`keyfun` | One of the following detection functions: "halfnorm", "hazard", "exp", or "uniform." See details.
`output` | Model either "density" or "abund"
`unitsOut` | Units of density. Either "ha" or "kmsq" for hectares and square kilometers, respectively.
`mixture` | Either "P" or "NB" for the Poisson and negative binomial models of abundance.
`K` | An integer value specifying the upper bound used in the integration.
`starts` | A numeric vector of starting values for the model parameters.
`method` | Optimization method used by `optim`.
`se` | logical specifying whether or not to compute standard errors.
`engine` | Either "C" to use fast C++ code or "R" to use native R code during the optimization.
`rel.tol` | relative accuracy for the integration of the detection function. See integrate. You might try adjusting this if you get an error message related to the integral. Alternatively, try providing different starting values.
`...` | Additional arguments to optim, such as lower and upper bounds

### Details

This model extends the model of Royle et al. (2004) by estimating the probability of being available for detection phi. This effectively relaxes the assumption that g(0)=1. In other words, inividuals at a distance of 0 are not assumed to be detected with certainty. To estimate this additional parameter, replicate distance sampling data must be collected at each transect. Thus the data are collected at i = 1, 2, ..., R transects on t = 1, 2, ..., T occassions. As with the model of Royle et al. (2004), the detections must be binned into distance classes. These data must be formatted in a matrix with R rows, and JT columns where J is the number of distance classses. See `unmarkedFrameGDS` for more information.

### Value

An object of class unmarkedFitGDS.

### Note

If you aren't interested in estimating phi, but you want to use the negative binomial distribution, simply set numPrimary=1 when formatting the data.

### Note

You cannot use obsCovs, but you can use yearlySiteCovs (a confusing name since this model isn't for multi-year data. It's just a hold-over from the colext methods of formatting data upon which it is based.)

### Author(s)

Richard Chandler rbchan@uga.edu

### References

Royle, J. A., D. K. Dawson, and S. Bates. 2004. Modeling abundance effects in distance sampling. Ecology 85:1591-1597.

Chandler, R. B, J. A. Royle, and D. I. King. 2011. Inference about density and temporary emigration in unmarked populations. Ecology 92:1429–1435.

### See Also

`distsamp`

### Examples

    # Simulate some line-transect data

    set.seed(36837)

    R <- 50 # number of transects
    T <- 5  # number of replicates
    strip.width <- 50
    transect.length <- 100
    breaks <- seq(0, 50, by=10)

    lambda <- 5 # Abundance
    phi <- 0.6  # Availability
    sigma <- 30 # Half-normal shape parameter

    J <- length(breaks)-1
    y <- array(0, c(R, J, T))
    for(i in 1:R) {
        M <- rpois(1, lambda) # Individuals within the 1-ha strip
        for(t in 1:T) {
            # Distances from point
            d <- runif(M, 0, strip.width)
            # Detection process
            if(length(d)) {
                cp <- phi*exp(-d^2 / (2 * sigma^2)) # half-normal w/ g(0)<1
                d <- d[rbinom(length(d), 1, cp) == 1]
                y[i,,t] <- table(cut(d, breaks, include.lowest=TRUE))
                }
            }
        }
    y <- matrix(y, nrow=R) # convert array to matrix

    # Organize data
    umf <- unmarkedFrameGDS(y = y, survey="line", unitsIn="m",
        dist.breaks=breaks, tlength=rep(transect.length, R), numPrimary=T)
    summary(umf)

    # Fit the model
    m1 <- gdistsamp(~1, ~1, ~1, umf, output="density", K=50)

    summary(m1)

    backTransform(m1, type="lambda")
    backTransform(m1, type="phi")
    backTransform(m1, type="det")

    ## Not run:
    # Empirical Bayes estimates of abundance at each site
    re <- ranef(m1)
    plot(re, layout=c(10,5), xlim=c(-1, 20))

    ## End(Not run)

[Package unmarked version 1.0.0 Index]