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

In unmarked: Models for Data from Unmarked Animals

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 and zero-inflated Poisson distributions.

Usage

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

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", "NB", or "ZIP" for the Poisson, negative binomial, or zero-inflated Poisson 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.
threads	Set the number of threads to use for optimization in C++, if OpenMP is available on your system. Increasing the number of threads may speed up optimization in some cases by running the likelihood calculation in parallel. If threads=1 (the default), OpenMP is disabled.
...	Additional arguments to optim, such as lower and upper bounds

Details

Extends the model of Royle et al. (2004) by estimating the probability of being available for detection \phi. 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 about data formatting.

The definition of availability depends on the context. The model is

M_i \sim \text{Pois}(\lambda)

N_{i,t} \sim \text{Bin}(M_i, \phi)

y_{i,1,t}, \dots, y_{i,J,t} \sim \text{Multinomial}(N_{i,t}, \pi_{i,1,t}, \dots, \pi_{i,J,t})

If there is no movement, then M_i is local abundance, and N_{i,t} is the number of individuals that are available to be detected. In this case, \phi=g_0. Animals might be missed on the transect line because they are difficult to see or detected. This relaxes the assumption of conventional distance sampling that g_0=1.

However, when there is movement in the form of temporary emigration, local abundance is N_{i,t}; it's the fraction of M_i that are on the plot at time t. In this case, \phi is the temporary emigration parameter, and we need to assume that g_0=1 in order to interpret N_{i,t} as local abundance. See Chandler et al. (2011) for an analysis of the model under this form of temporary emigration.

If there is movement and g_0<1 then it isn't possible to estimate local abundance at time t. In this case, M_i would be the total number of individuals that ever use plot i (the super-population), and N_{i,t} would be the number available to be detected at time t. Since a fraction of the unavailable individuals could be off the plot, and another fraction could be on the plot, it isn't possible to infer local abundance and density during occasion t.

Value

An object of class unmarkedFitGDS.

Note

If you aren't interested in estimating \phi, but you want to use the negative binomial or ZIP distributions, 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 [e-mail]

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)

unmarked documentation built on Sept. 11, 2024, 8:28 p.m.