closedN: Closed population estimates

closedNR Documentation

Closed population estimates


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


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



capthist object


character; name of estimator (see Details)


confidence level (1 – alpha)


upper bound for population size


numeric, the maximum AIC difference for inclusion in confidence set


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 = \frac{\exp(-\Delta_i / 2)}{ \sum{\exp(-\Delta_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 \hat{N}-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


A dataframe with one row per estimator and columns


model in the sense of Otis et al. 1978


number of parameters estimated


maximized log likelihood


Akaike's information criterion


AIC with small-sample adjustment of Hurvich & Tsai (1989)


difference between AICc of this model and the one with smallest AICc


number of distinct individuals caught


estimate of population size


estimated standard error of Nhat


lower 100 x level % confidence limit


upper 100 x level % confidence limit


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.


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 (e.g., Chao et al. 2016).


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., Ma, K. H., Hsieh, T. C. and Chiu, Chun-Huo (2016) SpadeR: Species-Richness Prediction and Diversity Estimation with R. R package version 0.1.1.

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



secr documentation built on Oct. 18, 2023, 1:07 a.m.