simHDSg {AHMbook}

Simulate data under HDS protocol with groups

Description

Simulates hierarchical distance sampling (HDS) data for groups under either a line or a point transect protocol and using a half-normal detection function (Buckland et al. 2001).

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 beta0 and beta1 to calculate the expected number of groups in each strip or circle. Group size is simulated by first drawing from a Poisson distribution with parameter lambda.group then adding 1.

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.

The group size is used in a log-linear regression with arguments alpha0 and alpha1 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

simHDSg(type = c("line", "point"), nsites = 100, lambda.group = 0.75,
  alpha0 = 0, alpha1 = 0.5,
  beta0 = 1, beta1 = 0.5, B = 4, discard0 = TRUE, show.plot = TRUE)

Arguments

type

The type of distance transect, either "line" or "point".

nsites

Number of sites (spatial replication)

lambda.group

Poisson mean of group size

alpha0

intercept of log-linear model relating sigma of the half-normal detection function to group size

alpha1

slope of log-linear model relating sigma of the half-normal detection function to group size

beta0

intercept of log-linear model relating the Poisson mean of the number of groups per unit area to habitat

beta1

slope of log-linear model relating the Poisson mean of the number of groups per unit area to habitat

B

strip half width or the radius of the circle

discard0

whether to discard or keep the data from sites with nobody detected

show.plot

choose whether to show plots or not. Set to FALSE when using function in simulations.

Value

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

data

simulated distance sampling data: a matrix with a row for each group detected and 6 columns: site ID, status (1 if captured), x and y coordinates (NA for line transects), distance from the line or point, group size; if discard0 = FALSE, sites with no detections will appear in the matrix with NAs in columns 2 to 6.

habitat

simulated habitat covariate

N

simulated number of groups at each site

N.true

for point counts, the simulated number of groups within the circle sampled

groupsize

group size for each of the groups observed

Author(s)

Marc Kéry & Andy Royle

References

Buckland, S.T., et al (2001) Introduction to distance sampling: estimating abundance of biological populations. Oxford University Press, Oxford, UK.

Kéry, M. & Royle, J.A. (2016) Applied Hierarchical Modeling in Ecology AHM1 - 9.2.1.

Examples

# Run with the default arguments and look at the structure of the output:
set.seed(123)
tmp <- simHDSg()
str(tmp)
head(tmp$data)

str(simHDSg(type = "line"))     # Defaults for line transect data
str(simHDSg(type = "point"))    # Defaults for point transect data
str(simHDSg(lambda.group = 5))  # Much larger groups
str(simHDSg(lambda.group = 5, alpha1 = 0)) # No effect of groups size on p