data.fn {AHMbook} | R Documentation |

## Simulate count data under a binomial N-mixture model

### Description

Function to simulate point counts replicated at M sites during J occasions. Population closure is assumed for each site. Expected abundance may be affected by elevation (elev), forest cover (forest) and their interaction. Expected detection probability may be affected by elevation, wind speed (wind) and their interaction. Used in AHM1 to illustrate how a data set under some specific model of interest can be simulated.

### Usage

```
data.fn(M = 267, J = 3, mean.lambda = 2, beta1 = -2, beta2 = 2, beta3 = 1,
mean.detection = 0.3, alpha1 = 1, alpha2 = -3, alpha3 = 0, show.plot = TRUE)
```

### Arguments

`M` |
Number of spatial replicates (sites) |

`J` |
Number of temporal replicates (occasions) |

`mean.lambda` |
Mean abundance at value 0 of abundance covariates |

`beta1` |
Main effect of elevation on abundance |

`beta2` |
Main effect of forest cover on abundance |

`beta3` |
Interaction effect on abundance of elevation and forest cover |

`mean.detection` |
Mean detection prob. at value 0 of detection covariates |

`alpha1` |
Main effect of elevation on detection probability |

`alpha2` |
Main effect of wind speed on detection probability |

`alpha3` |
Interaction effect on detection of elevation and wind speed |

`show.plot` |
if TRUE, plots of the data will be displayed; set to FALSE if you are running simulations |

### Value

A list with the input arguments and the following additional elements:

`elev` |
Scaled elevation (a vector of length M) |

`forest` |
Scaled forest cover (a vector of length M) |

`wind` |
Scaled wind speed (an M x J matrix) |

`lambda` |
Expected number of individuals at each site (a vector of length M) |

`N` |
Realized number of individuals at each site (a vector of length M) |

`p` |
Probability of detection for each survey (an M x J matrix) |

`C` |
The number of detections for each survey (an M x J matrix) |

`Ntotal` |
Total abundance, |

`psi.true` |
True occupancy in sample |

`summaxC` |
Sum of max counts (all sites) |

`psi.obs` |
Observed occupancy in sample |

### Note

The colors used for points in some of the plots indicate different temporal replicates.

### Author(s)

Marc Kéry & Andy Royle

### References

Kéry, M. & Royle, J.A. (2016) *Applied Hierarchical Modeling in Ecology* AHM1 - 4.3.

### Examples

```
# Generate a simulated data set with default arguments and look at the structure:
tmp <- data.fn()
str(tmp)
str(data.fn(J = 2)) # Only 2 surveys
str(data.fn(J = 1)) # No temporal replicate
str(data.fn(M = 1, J = 100)) # No spatial replicates, but 100 counts
str(data.fn(beta3 = 1)) # With interaction elev-wind on p
str(data.fn(M = 267, J = 3, mean.lambda = 2, beta1 = -2, beta2 = 2, beta3 = 1,
mean.detection = 1)) # No obs. process (i.e., p = 1, perfect detection)
str(data.fn(mean.lambda = 50)) # Really common species
str(data.fn(mean.lambda = 0.05)) # Really rare species
```

*AHMbook*version 0.2.9 Index]