Quantifying precision of mark-recapture estimates using the bootstrap and related methods

Bootstrap techniques yield variance estimates under any model for which parameter estimates can be calculated, and are useful in cases where analytic variances are not available in closed form, or are available only if more restrictive assumptions are made. Here the application of bootstrap techniques to mark-recapture models is discussed. The approach also allows generation of robust confidence intervals, which extend beyond the permissible parameter range only if the mark-recapture model itself allows out-of-range parameter estimates. If an animal population is assumed to be closed (i.e., no death, birth, or migration), two further methods of obtaining confidence limits for population size are suggested. The first is based on a Robbins-Monro search for each limit, and the second applies the concept of a randomisation or permutation test. In the absence of nuisance parameters, both methods are exact apart from Monte Carlo variation and the limitations imposed by a discrete distribution. For the second, if all possible permutations are enumerated, Monte Carlo variation is eliminated.