On Statistically Assessing Critical Population Size of an Endangered Species in a Random Environment

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Abstract
Factors that might influence critical population size in a random environment are considered. The female population is modelled as an age-dependent branching process, in which fertility and mortality depend on an autoregressive process that produces stochastic changes in the environment. Attention was also devoted to methods for utilizing sparse vital statistics in the computer implementation of the model as well as choosing those statistics that summarized a sample of Monte Carlo estimates of critical population size in an informative way. Two extreme values statistics, the Max and Min, and the sample means, computed as functions of time, were used to provide reductions of the data that were judged to be statistically informative. The experiments reported in this paper, using data on chimpanzees, along with those reported elsewhere for other species, indicated that, given two environmental processes with the same variance, the level of uncertainty surrounding mean estimates of critical population size is determined largely by the form of the autocorrelation function of the environmental process. In general, those autocorrelation functions that were strictly positive led to higher levels of uncertainty, as measured by the extreme value statistics, than did those that changed sign.

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