simHDS {AHMbook} | R Documentation |

## Simulate data under hierarchical distance sampling protocol (line or point)

### Description

The function simulates hierarchical distance sampling (HDS) data under either a line or a point transect protocol. At each site, it works with a strip of width `B*2`

(for line transects) or a circle of radius `B`

inscribed in a square of side `B*2`

(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.lambda`

and `beta.lam`

to calculate the expected number of animals, lambda, in each strip or square.

For line transects, the distance from the line is drawn from a Uniform(0, B) distribution. For point transects, the animals are distributed randomly over the square before calculating the distance of each from the point. Observations of animals further than B from the point are discarded.

A detection covariate, "wind", for each site is drawn from a Uniform(-2, 2) distribution. This is used in a log-linear regression with arguments `mean.sigma`

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

```
simHDS(type=c("line", "point"), nsites = 100, mean.lambda = 2, beta.lam = 1,
mean.sigma = 1, beta.sig = -0.5, B = 3, discard0 = TRUE, show.plot = TRUE)
```

### Arguments

`type` |
type of transect, "line" or "point". |

`nsites` |
Number of sites (spatial replication) |

`mean.lambda` |
the expected value of lambda when the habitat covariate = 0; the intercept of the log-linear regression for lambda is log(mean.lambda). |

`beta.lam` |
the slope of the log-linear regression for lambda on a habitat covariate. |

`mean.sigma` |
the expected value of the scale parameter of the half-normal detection function when the wind speed = 0; the intercept of the log-linear regression for sigma is log(mean.sigma). |

`beta.sig` |
the slope of log-linear regression of scale parameter of the half-normal detection function on wind speed |

`B` |
the strip half-width or circle radius |

`discard0` |
If TRUE, subset to sites at which individuals were captured. You may or may not want to do this depending on how the model is formulated so be careful. |

`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 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 |

`habitat` |
simulated habitat covariate |

`wind` |
simulated detection covariate |

`N` |
simulated number of individuals at each site |

`N.true` |
for point counts, the simulated number of individuals within the circle sampled |

### Author(s)

Marc Kéry & Andy Royle

### References

Kéry, M. & Royle, J.A. (2016) *Applied Hierarchical Modeling in Ecology* AHM1 - 8.5.1.

### Examples

```
# Simulate a data set with the default arguments and look at the structure of the output
set.seed(123)
tmp <- simHDS()
str(tmp)
head(tmp$data)
tmp <- simHDS("point", discard0=FALSE)
str(tmp)
head(tmp$data, 10)
```

*AHMbook*version 0.2.9 Index]