The evolution of dispersal is investigated in a landscape of many patches w
ith fluctuating carrying capacities and spatial heterogeneity in temporal f
luctuations. Although asynchronous temporal fluctuations select for dispers
al, spatial heterogeneity in the distribution of fluctuating environmental
variables selects against it. We find evolutionary branching in dispersal r
ate leading to the evolutionarily stable coexistence of a high- and a low-d
ispersal phenotype. We study how the opposing forces of selection for and a
gainst dispersal change with the relative size and the environmental qualit
ies of the source and sink habitats. Our results suggest that the evolution
of dispersal dimorphism could be a first step towards speciation and local
adaptation.