Patchy Populations in Stochastic Environments: Critical Number of Patches for Persistence

Abstract

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be ≥1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the per- sistence of the population. As the magnitude of environmental fluc- tuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested de- creases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environ- mental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily dis- tributed organisms that are restricted to a small number of habitat patches.

Keywords

Affiliated Institutions

• University of California, Santa Barbara US
• National Center for Ecological Analysis and Synthesis US
• The University of Queensland AU
• Stanford University US

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