Expected minimum population size as a measure of threat

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Abstract
Risks of population decline are studied extensively in conservation biology, but are difficult to estimate because they change abruptly over a relatively narrow range of parameters. We propose that risks of decline may be usefully summarized by the expected minimum population size. This is the smallest population size that is expected to occur within a particular time period. Analytical solutions for the expected minimum population size are obtained for a stochastic population model of exponential growth. In more complex models that are analyzed by Monte Carlo simulation, the expected minimum population size may be determined by recording the smallest population size obtained in each iteration and taking the average of these values. Whereas risks of decline change abruptly with changes in parameter values, the expected minimum population size changes more gradually. The results demonstrate that the expected minimum population size provides a better indication of the propensity for decline than the risk of extinction (or risk of decline to some other small population size), especially when the risk of extinction is small.