unmarked (version 0.11-0)

gdistsamp: 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, 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.

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 s

...

Additional arguments to optim, such as lower and upper bounds

Value

• An object of class unmarkedFitGDS.

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.

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")

# Empirical Bayes estimates of abundance at each site
re <- ranef(m1)
plot(re, layout=c(10,5), xlim=c(-1, 20))