The minimum viable population problem: 1. The demography of chance extinction

A generalized birth and death process serves as a simple, flexible model for computing the expected persistence time of a small population in a random world. We may reparametrize the model in ways that allow explicit incorporation of density depedendence, random differences between events experienced by individuals, and random environmental variation. We find that environmental variation poses a greater problem for population persistence than does individual variation, and that, comparatively, details of the form of the growth curve are not especially important, as long as the expected growth rate is positive. In particular, we find that with purely individual variation, the expected persistence time increases approximately with the power of the ceiling on population size; but with purely environmental variation, the expected persistence time increases approximately linearly with the size of the population ceiling. We discuss some aspects of reserve design and management in light of these results, noting in passing that an idealized system of separate reserves managed according to a reintroduction policy will confer a longer persistence time than a single reserve with the same total carrying capacity, but in the absence of the reintroduction policy the system of smaller separate reserves confers a shorter persistence time than the single large reserve. 1984 Contract no. 84-ABC-00173 NMFS (National Marine Fisheries Service) SWFSC (Southwest Fisheries Science Center) Library Public Domain 1930