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The computation of persistence times of populations has become a central focus in conservation biology. We describe a simple, direct method for finding the statistics of persistence times by assuming that there is a maximum population size. Thus, even though the population dynamics may be very complex for population sizes below the maximum, it is possible to write a finite set of equations from which the mean and second moment of the persistence time can be found by using simple, algebraic methods. We apply the method to compute the mean and coefficient of variation of persistence times of populations that suffer large decrements (catastrophes). Our results show that in the presence of catastrophes, the increase in mean persistence time with large populations is not nearly as rapid as other theories suggest and that catastrophes occurring at even modest rates can considerably increase the risk of extinction.

A simple direct method for finding persistence times of populations and application to conservation problems.