Interactions between local dynamics and dispersal: insights from single species models.

Population persistence in patchy environments is expected to result from an interaction between local density dependence, dispersal, and spatial heterogeneity. Using two-patch models of single species, I explore two aspects of this interaction that have hitherto received little attention. First, how is the interaction affected when local density dependence changes from negative (logistic) to positive (Allee)? Second, how does dispersal mortality influence persistence ? When local dynamics are logistic, dispersal changes the strength of negative density dependence within patches without much between-patch effect. For example, dispersal mortality reduces the population growth rate and counteracts the tendency towards complex dynamics. Density-dependent disperal amplifies the nonlinearity in the growth rate, thus opposing the stabilizing effects of dispersal mortality. Spatial heterogeneity has little or no effect on stability. In contrast to the logistic, dispersal under Allee dynamics creates between-patch effects that bring about a qualitative change. Patches that fall below the Allee threshold are rescued from extinction by immigrants from patches that are above the threshold. Density-dependent dispersal enhances this rescue effect. Persistence below the extinction threshold is contingent on spatial heterogeneity. Dispersal mortality is of little or no consequence.