Dispersal can sharpen parapatric boundaries on a spatially varying environment

Parapatry describes a geographic pattern in which the ranges of two species have separate but contiguous distributions without any physical barriers between them. We present results from a study of ecological mechanisms to explain parapatry in closely related species. These include competition, spatially varying performances, and dispersal that depends on the densities of both species. We use a model consisting of two coupled nonlinear reaction-diffusion equations with density-dependent diffusion terms and space-dependent Lotka-Volterra-like competing interaction terms. The model is analyzed by using a mixture of phase-plane analysis and numerical simulations. Results show that competition and dispersal can lead to completely segregated species ranges. Spatial variation favored and provided stability to parapatric distribution. Parapatry occurred under several conditions, including when both species were identical in dispersal, intrinsic rate of growth, and competition but differed in their spatial performances. Results indicate that overlapping distributions and parapatry are equally expected for close species. Moreover, similar species in parapatry tend to exhibit equivalent range sizes. This model explains how species can coexist regionally while maintaining spatial exclusion. It also describes how a species that is rare in distribution can invade the range of a similar and widespread species. We discuss the limitations of using present species distributions for recognizing modes of speciation, and we suggest studying more extensively the relationship between density-dependent dispersal and interspecific competition. We show that density-dependent dispersal can favor segregation