simHDSg {AHMbook} R Documentation

## 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
```

[Package AHMbook version 0.2.3 Index]