simHDSopen {AHMbook} R Documentation

Simulate open hierarchical distance sampling data

Description

Simulates distance sampling data for multiple replicate surveys in a multi-season (or multi-year) model, incorporating habitat and detection covariates, temporary emigration, and a trend in abundance or density.

At each site, it works with a strip of width B*2 (for line transects) or a circle of radius B (for point transects).

The state process is simulated by first drawing a covariate value, "habitat", for each site from a Normal(0, 1) distribution. This is used in a log-linear regression with arguments mean.lam, beta.lam and beta.trend to calculate the expected number of animals, lambda, in each strip or circle for each year. Site- and year-specific abundances are drawn from a Poisson distribution with mean lambda. The number available for capture at each replicate survey is simulated as a binomial distribution with probability phi.

For line transects, the distance from the line is drawn from a Uniform(0, B) distribution. For point transects, the distance from the point is simulated from B*sqrt(Uniform(0,1)), which ensures a uniform distribution over the circle.

A detection covariate, "wind", for each survey is drawn from a Uniform(-2, 2) distribution. This is used in a log-linear regression with arguments mean.sig and beta.sig to calculate the scale parameter, sigma, of the half-normal detection function. Detections are simulated as Bernoulli trials with probability of success decreasing with distance from the line or point.

Usage

simHDSopen(type=c("line", "point"), nsites = 100,
mean.lam = 2, beta.lam = 0, mean.sig = 1, beta.sig = 0,
B = 3, discard0 = TRUE, nreps = 2, phi = 0.7, nyears = 5, beta.trend = 0)

Arguments

 type the transect protocol, either "line" or "point" . nsites Number of sites (spatial replication) mean.lam intercept of log-linear regression of expected lambda on a habitat covariate beta.lam slope of log-linear regression of expected lambda on a habitat covariate mean.sig intercept of log-linear regression of scale parameter of half-normal detection function on wind speed beta.sig slope of log-linear regression of scale parameter of half-normal detection function on wind speed B strip half width, or maximum distance from the observer for point counts discard0 Discard sites at which no individuals were captured. You may or may not want to do this depending on how the model is formulated so be careful. nreps the number of distance sampling surveys within a period of closure in a season (or year) phi the availability parameter nyears the number of seasons (typically years) beta.trend loglinear trend of annual population size or density

Value

A list with the values of the arguments entered and the following additional elements:

 data simulated distance sampling data: a list with a component for each year, each itself a list with a component for each replicate; this is a matrix with a row for each individual detected and 5 columns: site ID, status (1 if captured), x and y coordinates (NA for line transects), distance from the line or point; if discard0 = FALSE, sites with no detections will appear in the matrix with NAs in columns 2 to 5. habitat simulated habitat covariate, a vector of length nsites wind simulated detection covariate, a nsites x nreps x nyears array M.true simulated number of individuals, a nsites x nyears matrix K = nreps Na the number of individuals available for detection, a nsites x nreps x nyears array Na.real for point counts, the number of individuals available for detection within the circle sampled, a nsites x nreps x nyears array

Note

For "point" the realized density is [(area of circle) /(area of square)]*lambda

Author(s)

Marc Kéry & Andy Royle

References

Kéry, M. & Royle, J.A. (2016) Applied Hierarchical Modeling in Ecology AHM1 - 9.5.4.1.

Examples

set.seed(123)
tmp <- simHDSopen() # Generate data with default parameters
str(tmp)