Effects of local interactions and local migration on stability.

Mathematical models can help to resolve the longstanding question of whether more diverse communities are more stable. Here, I focus on how local dispersal and local interactions--hallmarks of spatial communities--affect stability in a spatially implicit model with demographic stochasticity. The results are based on a novel way to analyze moment equations. The main conclusion is that the type and strength of density-dependent factors, such as fecundity and competition, determine whether local dispersal and local interactions increase or decrease stability. Local dispersal has a stabilizing effect when fecundity is high, interspecific competition is either low or high, and the number of species is small. Effects of local migration on stability are amplified when space is explicit.