unmarked (version 0.8-5)

distsamp: Fit the hierarchical distance sampling model of Royle et al. (2004)

Description

Fit the hierarchical distance sampling model of Royle et al. (2004) to line or point transect data recorded in discrete distance intervals.

Usage

distsamp(formula, data, keyfun=c("halfnorm", "exp",
    "hazard", "uniform"), output=c("density", "abund"),
    unitsOut=c("ha", "kmsq"), starts, method="BFGS",
    control=list(), se=TRUE)

Arguments

formula

Double right-hand formula describing detection covariates followed by abundance covariates. ~1 ~1 would be a null model.

data

object of class unmarkedFrameDS, containing response matrix, covariates, distance interval cut points, survey type ("line" or "point"), transect lengths (for survey = "line"), and units ("m" or "km") for cut points and transect lengths. Se

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.

starts

Vector of starting values for parameters.

method

Optimization method used by optim.

control

Other arguments passed to optim.

se

logical specifying whether or not to compute standard errors.

Value

• unmarkedFitDS object (child class of unmarkedFit-class) describing the model fit. Parameter estimates are displayed on the log-scale. Back-transformation can be achieved via the predict or backTransform methods.

Details

Unlike conventional distance sampling, which uses the 'conditional on detection' likelihood formulation, this model is based upon the unconditional likelihood and thus allows for modeling both abundance and detection function parameters.

The latent transect-level abundance distribution $f(N | \mathbf{\theta})$ is currently assumed to be Poisson with mean $\lambda$.

The detection process is modeled as multinomial: $y_{ij} \sim Multinomial(N_i, pi_{ij})$, where $pi_ij$ is the multinomial cell probability for transect i in distance class j. These are computed based upon a detection function $g(x | \mathbf{\sigma})$, such as the half-normal, negative exponential, or hazard rate.

Parameters $\lambda$ and $\sigma$ can be vectors affected by transect-specific covariates using the log link.

References

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

See Also

unmarkedFit-class fitList, formatDistData, parboot, calcAreas, sight2perpdist, detFuns,

Examples

## Line transect examples

data(linetran)

ltUMF <- with(linetran, {
	unmarkedFrameDS(y = cbind(dc1, dc2, dc3, dc4), 
	siteCovs = data.frame(Length, area, habitat), 
	dist.breaks = c(0, 5, 10, 15, 20),
	tlength = linetran$Length * 1000, survey = "line", unitsIn = "m")
	})

ltUMF
summary(ltUMF)
hist(ltUMF)

# Half-normal detection function. Density output (log scale). No covariates. 
(fm1 <- distsamp(~ 1 ~ 1, ltUMF))

# Some methods to use on fitted model
summary(fm1)
coef(fm1, type="det", altNames=TRUE)
backTransform(fm1, whichEstimate="det")
vcov(fm1, altNames=TRUE)
confint(fm1, type = "state")
predict(fm1, type = "state")
hist(fm1)	# This only works when there are no detection covariates

# Half-normal. Abundance output. No covariates. Note that transect length
# must be accounted for so abundance is animals per km of transect.
summary(fm2 <- distsamp(~ 1 ~ 1, ltUMF, output="abund", unitsOut="kmsq"))

# Halfnormal. Covariates affecting both density and and detection.  
(fm3 <- distsamp(~ poly(area, 2) + habitat ~ habitat, ltUMF))

# Negative exponential detection function.
(fm4 <- distsamp(~ 1 ~ 1, ltUMF, key="exp"))
hist(fm4, col="blue", ylim=c(0, 0.1), xlab="Distance (m)")

# Hazard-rate detection function. Density output in hectares.
summary(fmhz <- distsamp(~ 1 ~ 1, ltUMF, keyfun="hazard"))
hist(fmhz)


# Plot detection function.
fmhz.shape <- exp(coef(fmhz, type="det"))
fmhz.scale <- exp(coef(fmhz, type="scale"))
plot(function(x) gxhaz(x, shape=fmhz.shape, scale=fmhz.scale), 0, 25, 
	xlab="Distance (m)", ylab="Detection probability")

# Uniform detection function. Density output in hectars.
(fmu <- distsamp(~ 1 ~ 1, ltUMF, key="uniform"))

## Point transect example

data(pointtran)

ptUMF <- with(pointtran, {
	unmarkedFrameDS(y = cbind(dc1, dc2, dc3, dc4, dc5), 
	siteCovs = data.frame(area, habitat), 
	dist.breaks = seq(0, 25, by=5), survey = "point", unitsIn = "m")
	})

# Half-normal. Output is animals / ha on log-scale. No covariates.
summary(fmp1 <- distsamp(~ 1 ~ 1, ptUMF))
hist(fmp1, ylim=c(0, 0.07))