Evolution of dispersal in a spatially heterogeneous population with finite patch sizes and catastrophes

Evolution of costly dispersal has been one of the main topics in evolutionary biology. Theoreticians have tried to study realistic models including properties such as 1) finite patch sizes, 2) heterogeneity in patch qualities, 3) conditional dispersal strategy based on the patch quality, and 4) catastrophes (i.e, local population extinctions in habitat patches). Finite patch sizes lead to kin competition within each patch, promoting dispersal. Heterogeneity is expected to promote conditional dispersal from low-quality patches. Catastrophes cause temporal heterogeneity, which often promotes dispersal. Furthermore, catastrophes will cause non-dispersing organisms to go extinct. Here we study a model including all the four properties listed above. In parallel with previous studies, we found that the introduction of catastrophes generally promotes dispersal. We found, however, unexpected interactions between catastrophes and other demographic factors. Without catastrophes, increasing the dispersal survival probability increases dispersal, as expected. In the presence of catastrophes, dispersal can be non-monotonic with respect to the dispersal survival probability. Furthermore, when the dispersal survival probability is very small, including catastrophes in the model will have an abrupt positive effect on dispersal. Our findings strongly suggest that even a tiny chance of catastrophic events happening can qualitatively alter the course of evolution of dispersal. Our results might be applicable when small patches are well-isolated and local natural disasters happen rarely but do occur.