CONSIDERATION OF STOCHASTIC DEMOGRAPHY IN THE DESIGN AND MANAGEMENT OF BIOLOGICAL RESERVES

Abstract

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 dependence, random differences in events experienced by different individuals, and random environmental variation experienced by all individuals in concert. This model seems to capture the important features of real population dynamics for purposes of computing the mean persistence time, even though the underlying mechanisms presumed in the mathematics of the model are decidedly unrealistic. The lack of isomorphism between birth and death rates, as they feature in the model, and vital rates of real biological populations can lead to extremely misleading results, if the classic formulation, rather than the reparametrization is applied without due circumspection. Using the reparametrized model, we find that environmental variation poses a greater problem for population persistence than does individual variation. In particular, 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 somewhat less than linearly with the size of the population ceiling. The birth–and–death process model can also be applied to calculating the persistence time of a population on an ensemble of reserves which are linked by natural migration or by deliberate reintroduction programs. Results of this model, for an idealized ensemble, show that multiple independent reserves with a sufficient recolonization rate (natural or otherwise) will confer a longer persistence time than a single reserve with the same total carrying capacity, but in the absence of recolonization, the system of smaller separate reserves confers a shorter persistence time than the single large reserve.