The effects of small dispersal rates on extinction times in structured metapopulation models

Habitat destruction is a critical factor that affects persistence in several taxa, including Pacific salmon. Salmon are noted for their ability to home to their natal streams for reproduction. Since straying (i.e., spawners reproducing in nonnatal streams) is typically low in salmon, its effects have not been appreciated. In this article, we develop both a general analytical model and a simple simulation model describing structured metapopulations to study how weak connections between subpopulations affect the ability of a species to tolerate habitat destruction and/or declines in habitat quality. Our goals are to develop general principles and to relate these principles to salmon population dynamics. The analytical model describes the dynamics of two density-dependent subpopulations, connected by dispersal, whose growth rates fluctuate in response to environmental and demographic stochasticity. We find that, for moderate levels of environmental variability, small dispersal rates can significantly increase mean extinction times. This effect declines with increasing habitat quality, increasing temporal correlation, and increasing spatial correlation, but it is still significant for realistic parameter values. The simulation model shows there is a threshold rate of dispersal that minimizes extinction probabilities. These results cannot be seen in classical metapopulation models and provide new insights into the rescue effect.