closedN {secr} | R Documentation

## Closed population estimates

### Description

Estimate N, the size of a closed population, by several conventional non-spatial capture–recapture methods.

### Usage

    closedN(object, estimator = NULL, level = 0.95, maxN = 1e+07,
        dmax = 10 )

### Arguments

`object` | `capthist` object
`estimator` | character; name of estimator (see Details)
`level` | confidence level (1 – alpha)
`maxN` | upper bound for population size
`dmax` | numeric, the maximum AIC difference for inclusion in confidence set

### Details

Data are provided as spatial capture histories, but the spatial information (trapping locations) is ignored.

AIC-based model selection is available for the maximum-likelihood estimators `null`, `zippin`, `darroch`, `h2`, and `betabinomial`.

Model weights are calculated as

w_i = exp(-dAICc_i / 2) / sum{ exp(-dAICc_i / 2) }

Models for which dAICc > `dmax` are given a weight of zero and are excluded from the summation, as are non-likelihood models.

Computation of `null`, `zippin` and `darroch` estimates differs slightly from Otis et al. (1978) in that the likelihood is maximized over real values of N between `Mt1` and `maxN`, whereas Otis et al. considered only integer values.

Asymmetric confidence intervals are obtained in the same way for all estimators, using a log transformation of Nhat-Mt1 following Burnham et al. (1987), Chao (1987) and Rexstad and Burnham (1991).

The available estimators are

Name | Model | Description | Reference
`null` | M0 | null | Otis et al. 1978 p.105
`zippin` | Mb | removal | Otis et al. 1978 p.108
`darroch` | Mt | Darroch | Otis et al. 1978 p.106-7
`h2` | Mh | 2-part finite mixture | Pledger 2000
`betabinomial` | Mh | Beta-binomial continuous mixture | Dorazio and Royle 2003
`jackknife` | Mh | jackknife | Burnham and Overton 1978
`chao` | Mh | Chao's Mh estimator | Chao 1987
`chaomod` | Mh | Chao's modified Mh estimator | Chao 1987
`chao.th1` | Mth | sample coverage estimator 1 | Lee and Chao 1994
`chao.th2` | Mth | sample coverage estimator 2 | Lee and Chao 1994

### Value

A dataframe with one row per estimator and columns

`model` | model in the sense of Otis et al. 1978
`npar` | number of parameters estimated
`loglik` | maximized log likelihood
`AIC` | Akaike's information criterion
`AICc` | AIC with small-sample adjustment of Hurvich & Tsai (1989)
`dAICc` | difference between AICc of this model and the one with smallest AICc
`Mt1` | number of distinct individuals caught
`Nhat` | estimate of population size
`seNhat` | estimated standard error of Nhat
`lclNhat` | lower 100 x level % confidence limit
`uclNhat` | upper 100 x level % confidence limit

### Warning

If your data are from spatial sampling (e.g. grid trapping) it is recommended that you do not use these methods to estimate population size (see Efford and Fewster 2013). Instead, fit a spatial model and estimate population size with `region.N`.

### Note

Prof. Anne Chao generously allowed me to adapt her code for the variance of the ‘chao.th1’ and ‘chao.th2’ estimators.

Chao's estimators have been subject to various improvements not included here; please see Chao and Shen (2010) for details.

### References

Burnham, K. P. and Overton, W. S. (1978) Estimating the size of a closed population when capture probabilities vary among animals. Biometrika 65, 625–633.

Chao, A. (1987) Estimating the population size for capture–recapture data with unequal catchability. Biometrics 43, 783–791.

Chao, A. and Shen, T.-J. (2010) Program SPADE (Species Prediction And Diversity Estimation). Program and User's Guide available online at http://chao.stat.nthu.edu.tw.

Dorazio, R. M. and Royle, J. A. (2003) Mixture models for estimating the size of a closed population when capture rates vary among individuals. Biometrics 59, 351–364.

Efford, M. G. and Fewster, R. M. (2013) Estimating population size by spatially explicit capture–recapture. Oikos 122, 918–928.

Hurvich, C. M. and Tsai, C. L. (1989) Regression and time series model selection in small samples. Biometrika 76, 297–307.

Lee, S.-M. and Chao, A. (1994) Estimating population size via sample coverage for closed capture-recapture models. Biometrics 50, 88–97.

Otis, D. L., Burnham, K. P., White, G. C. and Anderson, D. R. (1978) Statistical inference from capture data on closed animal populations. Wildlife Monographs 62, 1–135.

Pledger, S. (2000) Unified maximum likelihood estimates for closed capture-recapture models using mixtures. Biometrics 56, 434–442.

Rexstad, E. and Burnham, K. (1991) User's guide for interactive program CAPTURE. Colorado Cooperative Fish and Wildlife Research Unit, Fort Collins, Colorado, USA.

### See Also

`capthist`, `closure.test`, `region.N`

### Examples

    closedN(deermouse.ESG)

[Package secr version 3.2.1 Index]