## Abstract

Capture–recapture methods for both open and closed populations have developed extensively in recent years, especially with the development of sophisticated computer programs and packages. There are now many different methods to estimate the abundance of closed populations. These include standard maximum likelihood methods, jackknife methods, coverage models, martingale estimating equation models, log-linear models, logistic models, non-parametric models, and mixture models, which are all discussed in some detail. Because of the large amount of materials, Bayesian methods are considered in the next chapter for convenience, as those methods are being used more. Covariates such as environmental variables are being used more, and with improved monitoring devices, including DNA methods, we can expect covariate methods to increase.

The two-sample capture–recapture model has been extensively used with a focus on variable catchability, use of two observers, which can also help with detectability problems, epidemiological populations using two lists (or later more lists), and dual record systems. For three or more capture–recapture samples, the glue behind the model development has been the setting out of eight particular model categories, due to Pollock, providing for a time factor, a behavioral factor, a heterogeneity factor, and combinations of these. Several variations of these have also been developed by various researchers, including time-to-detection models. Heterogeneity has been the biggest challenge and, as well as various models, has also been considered using covariates or even stratification where possible underlying assumptions are tested. Finally, sampling one at a time and continuous models are considered in detail.

With this plethora of methods, the practitioner is left in a quandary. What methods are appropriate for what conditions and types of studies? What is needed here is a comparison of the various closed models with respect to both efficiency and robustness. Also, further research is needed on interval estimation, with intervals based on profile likelihoods becoming more popular, and on model diagnostics.