Evolution of density- and patch-size-dependent dispersal rates.

Based on a marginal value approach, we derive a nonlinear expression for evolutionarily stable (ES) dispersal rates in a metapopulation with global dispersal. For the general case of density-dependent population growth, our analysis shows that individual dispersal rates should decrease with patch capacity and-beyond a certain threshold-increase with population density. We performed a number of spatially explicit, individual-based simulation experiments to test these predictions and to explore further the relevance of variation in the rate of population increase, density dependence, environmental fluctuations and dispersal mortality on the evolution of dispersal rates. They confirm the predictions of our analytical approach. In addition, they show that dispersal rates in metapopulations mostly depend on dispersal mortality and inter-patch variation in population density. The latter is dominantly driven by environmental fluctuations and the rate of population increase. These conclusions are not altered by the introduction of neighbourhood dispersal. With patch capacities in the order of 100 individuals, kin competition seems to be of negligible importance for ES dispersal rates except when overall dispersal rates are low.