Local dispersal can facilitate coexistence in the presence of permanent spatial heterogeneity

In the presence of permanent spatial heterogeneity, local dispersal, especially short-range dispersal, can facilitate coexistence by concentrating low-density species in the areas where their rates of increase are higher. We present a framework for predicting the effects of local dispersal on coexistence for arbitrary forms of dispersal and arbitrary spatial patterns of environmental variation. Using the lottery model as an example, we find that local dispersal contributes to coexistence by enhancing the effects of environmental variation on scales longer than typical dispersal distances, which can be characterized solely by the variance of the dispersal kernel. Higher moments of the dispersal kernel are not important.