# Multi-season occupancy estimation

### Description

Functions to estimate occupancy from detection/non-detection data for multiple seasons. `occMS`

is the general purpose function; it allows for site-, season- and survey-level covariates, but it is slow. `occMScovSite`

excludes survey-level covariates, but is fast. `occMStime`

and `occMS0`

are simpler and faster.

### Usage

1 2 3 4 5 6 7 |

### Arguments

`DH` |
a 1/0/NA matrix (or data frame) of detection histories, sites x occasions. Rows with all NAs are silently removed. |

`occsPerSeason` |
the number of survey occasions per season; either a scalar if the number of surveys is constant, or a vector with one element for each season. |

`model` |
a list of formulae symbolically defining a linear predictor for each parameter in terms of covariates. The default corresponds to an intercept-only model. |

`data` |
a data frame containing the variables in the model: one row for each season or between-season period for |

`ci` |
the confidence interval to use. |

`verify` |
if TRUE, the data provided will be checked. |

### Details

`occMS0`

implements a simple multi-season model with one parameter each for initial occupancy, colonisation, local extinction, and probability of detection, ie. a `psi1(.) gamma(.) epsilon(.) p(.)`

model.

`occMStime`

allows for between-season differences in colonisation, local extinction, and probability of detection, either with covariates given in `data`

or the in-built covariates `.interval`

(for colonisation or extinction, or `.season`

(for detection).

`occMScovSite`

allows for between-season differences in colonisation, local extinction, and probability of detection with the in-built covariate `.season`

and for between-site differences with covariates defined in `data`

.

`occMS`

allows for survey-level covariates in addition to the above, and separate covariates for between-season colonisation and local extinction.

### Value

Returns an object of class `wiqid`

, which is a list with the following elements:

`call` |
The call used to produce the results |

`beta` |
Values of the coefficients of the terms in the linear predictors, with standard errors and confidence intervals. |

`beta.vcv ` |
The variance-covariance matrix for the beta estimates. |

`real` |
Estimates of occupancy and probability of detection on the real scale, with confidence intervals; |

`logLik` |
a vector with elements for log(likelihood), number of parameters, and effective sample size. If parameters |

There are `print`

, `logLik`

, and `nobs`

methods for class `wiqid`

.

### Benchmarks

Output has been checked against output from PRESENCE (Hines 2006) v.5.5 for the `GrandSkinks`

data set. Real values are mostly the same to 4 decimal places, though there is occasionally a discrepancy of 0.0001. AICs are the same.

### Author(s)

Mike Meredith

### References

MacKenzie, D I; J D Nichols; G B Lachman; S Droege; J A Royle; C A Langtimm. 2002. Estimating site occupancy rates when detection probabilities are less than one. *Ecology* 83:2248-2255.

MacKenzie, D I; J D Nichols; A J Royle; K H Pollock; L L Bailey; J E Hines 2006. *Occupancy estimation and modeling : inferring patterns and dynamics of species occurrence*. Elsevier Publishing.

Hines, J. E. (2006). PRESENCE - Software to estimate patch occupancy and related parameters. SGS-PWRC. http://www.mbr-pwrc.usgs.gov/software/presence.html.

MacKenzie, D I; J D Nichols; J E Hines; et al 2003. Estimating site occupancy, colonization, and local extinction when a species is imperfectly detected. *Ecology* 84, 2200-2207.

### Examples

1 2 3 4 5 6 7 8 9 | ```
data(GrandSkinks)
DH <- GrandSkinks[, 1:15]
occMS0(DH, 3)
occMStime(DH, 3, model=list(gamma ~ .interval, epsilon~1, p~.season))
occMScovSite(DH, 3,
model=list(psi1~habitat, gamma ~ .interval, epsilon~habitat, p~.season),
data=GrandSkinks)
``` |