The role of density-dependent dispersal in source-sink dynamics

I investigate two aspects of source-sink theory that have hitherto received little attention: density-dependent dispersal and the cost of dispersal to sources. The cost arises because emigration reduces the per capita growth rate of sources, thus predisposing them to extinction. I show that source-sink persistence depends critically on the interplay between these two factors. When the emigration rate increases with abundance at an accelerating rate, dispersal costs to sources is the lowest and risk of source-sink extinction the least. When the emigration rate increases with abundance at a decelerating rate, dispersal costs to sources is the highest and the risk of source-sink extinction the greatest. Density-independent emigration has an intermediate effect. Thus, density-dependent dispersal per se does not increase or decrease source-sink persistence relative to density-independent dispersal. The exact mode of dispersal is crucial. A key point to appreciate is that these effects of dispersal on source-sink extinction arise from the temporal density-dependence that dispersal induces in the per capita growth rates of source and sink populations. Temporal density-dependence due to dispersal is beneficial at low abundances because it rescues sinks from extinction, and detrimental at high abundances because it drives otherwise viable sources to extinction. These results are robust to the nature of population dynamics in the sink, whether exponential or logistic. They provide a means of assessing the relative costs and benefits of preserving sink habitats given three biological parameters.