The evolution of dispersal is investigated in a landscape of many patches with fluctuating carrying capacities and spatial heterogeneity in temporal fluctuations. Although asynchronous temporal fluctuations select for dispersal, spatial heterogeneity in the distribution of fluctuating environmental variables selects against it. We find evolutionary branching in dispersal rate leading to the evolutionarily stable coexistence of a high- and a low-dispersal phenotype. We study how the opposing forces of selection for and against dispersal change with the relative size and the environmental qualities 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.