Diversification along environmental gradients in spatially structured populations. Evol Ecol Res

Questions: Does frequency-dependent and spatially localized competition in geographically structured populations generate phenotypic diversification in the form of multimodal phenotype distributions? Is such pattern formation an artifact of the boundary conditions assumed for numerical simulations? Do environmental gradients facilitate phenotypic diversification, and how does the slope of the environmental gradient influence this facilitation? Mathematical methods: We solve numerically partial differential equations models for the dynamics of density distributions of phenotypically varying populations that occupy a continuous geographical area. Key assumptions: We assume a linear spatial gradient in the optimal phenotype for the stabilizing component of selection (carrying capacity). To address the role of boundary conditions, we use two types of models. First, we use models in which the carrying capacity declines to 0 in both the phenotypic and the spatial dimensions as the corresponding coordin-ates become either large or small enough. Second, we use models with periodic boundary conditions in both the phenotypic and the geographical dimensions. For sexual populations, w