Dispersal in patchy environments: The effects of temporal and spatial structure

A model for the evolution of dispersal in fluctuating environments is extended to environments that are temporally correlated and spatially heterogeneous. The effects of dormancy also are examined. In some cases, evolutionarily stable strategies result, and are estimated through simulations and through analytical approximations. However, in other cases, e.g., in spatially heterogeneous environments, or in the homogeneous case with negative temporal correlation, there is no intermediate evolutionarily stable strategy; rather, in some situations the "best" type, termed an evolutionarily compatible strategy (ECS), is one that can invade any other single type, but also is open to invasion by any type. For these cases, it is conjectured that there is a stable coexisting band of types, not necessarily including the ECS. In general, positive (Markovian) temporal correlations decrease the optimal dispersal fraction by increasing the average yield of non-dispersing seeds; dormancy has a similar effect. Spatial heterogeneity has some features in common with positive temporal correlations, but the structure of the autocorrelation function is more complicated. Optimal dispersal is decreased; but as mentioned above, there is no ESS in general. Diffuse competitive effects may not be understood entirely in terms of pairwise interactions, and a variety of open problems exist in characterizing interactions among multiple types.