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)
head(tmp\$data[][])

tmp <- simHDSopen("point")
str(tmp)
head(tmp\$data[][])

tmp <- simHDSopen(discard0=FALSE)
str(tmp)
head(tmp\$data[][])
```

[Package AHMbook version 0.2.3 Index]