simPOP {AHMbook} | R Documentation |

## Simulate data for a demographic state-space model

### Description

Simulate multiple time-series of counts under a pure Markov model (with exponential population model) or under an extended Markov model with exponential-plus-random-immigration population model; see Sollmann et al.(2015). Default is Markov model, setting `sd.rho`

to a value greater than 0 changes to extended Markov and sets the amount of random immigration.

### Usage

```
simPOP(M = 100, T = 10, mean.lam = 3, beta.lam = 0, sd.log.lam = 0,
mean.gamma = 1.0, beta.gamma = 0, sd.log.gamma.site = 0,
sd.log.gamma.time = 0, sd.log.gamma.survey = 0, sd.rho = 0,
mean.p = 0.6, beta.p = 0, sd.logit.p.site = 0, sd.logit.p.time = 0,
sd.logit.p.survey = 0, show.plot = TRUE)
```

### Arguments

`M` |
The number of sites. |

`T` |
The number of years. |

`mean.lam` |
The mean abundance for year 1. |

`beta.lam` |
The covariate coefficient for lambda. |

`sd.log.lam` |
The over-dispersion in lambda. |

`mean.gamma` |
The mean population growth rate. |

`beta.gamma` |
The covariate coefficient for gamma. |

`sd.log.gamma.site` |
SD of random site effects for gamma. |

`sd.log.gamma.time` |
SD of random time effects for gamma. |

`sd.log.gamma.survey` |
SD of random survey (site+time) effects for gamma. |

`sd.rho` |
The random immigration term. |

`mean.p` |
The mean detection probability. |

`beta.p` |
The covariate coefficient for p. |

`sd.logit.p.site` |
SD of random site effects for p on the logit scale. |

`sd.logit.p.time` |
SD of random time effects for p on the logit scale. |

`sd.logit.p.survey` |
SD of random survey (site+time) effects for p on the logit scale. |

`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:

`Xsite1` |
M vector, site covariate affecting initial abundance (lambda). |

`Xsiteyear1` |
M x T matrix, yearly site covariate affecting recruitment (gamma). |

`Xsiteyear2` |
M x T matrix, yearly site covariate affecting detection (p). |

`eps.N` |
M vector, site over-dispersion at t = 1. |

`lambda` |
M vector, abundance in year 1. |

`eps.gamma.site` |
M vector, random site effect for gamma. |

`eps.gamma.time` |
T vector, random time effect for gamma. |

`eps.gamma.survey` |
M x T matrix, random survey effect for gamma. |

`gamma` |
M x T matrix, population growth rate. |

`rho` |
(T-1) vector, immigration rate. |

`eps.p.site` |
M vector, random site effect for detection. |

`eps.p.time` |
T vector, random time effect for detection. |

`eps.p.survey` |
M x T matrix, random survey effect for detection. |

`p` |
M x T matrix, detection probability. |

`N` |
M x T matrix, true population. |

`C` |
M x T matrix, simulated counts. |

`zeroNyears` |
scalar, sum(N == 0). |

`Nextinct` |
scalar, number of sites where N == 0 at time T. |

`extrate` |
scalar, proportion of sites where N == 0 at time T. |

`sumN` |
T vector, total population in each year. |

`gammaX` |
(T-1) vector, realized population growth rate. |

### Author(s)

Marc Kéry & Andy Royle

### References

Sollmann, R. et al. (2015) An open-population hierarchical distance sampling model. *Ecology*, 96, 325-331.

Kéry, M. & Royle, J.A. (2021) *Applied Hierarchical Modeling in Ecology* AHM2 - 1.7.1.

### Examples

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

*AHMbook*version 0.2.9 Index]