Estimate N, the size of a closed population, by several conventional nonspatial capture–recapture methods.
1 2 
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 
Data are provided as spatial capture histories, but the spatial information (trapping locations) is ignored.
AICbased model selection is available for the maximumlikelihood
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 nonlikelihood 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 NhatMt1 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.1067 
h2  Mh  2part finite mixture  Pledger 2000 
betabinomial  Mh  Betabinomial 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 
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 smallsample 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 
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; please see Chao and Shen (2010) for details.
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 capturerecapture 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 capturerecapture 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.
capthist
,
closure.test
,
region.N
1 
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