Global dynamics of a diffusive competition model with habitat degradation.

Abstract

In this paper, we propose a diffusive competition model with habitat degradation and homogeneous Neumann boundary conditions in a bounded domain that is partitioned into the healthy region (undisturbed habitat) and the degraded region (due to anthropogenic habitat disturbance). Species follow the Lotka-Volterra competition in the healthy region while in the degraded region species experience only exponential decay (not necessarily at the same rate). This setup is novel in that it requires no positivity assumption on the environmental heterogeneity, either absolute or on average, which would be far too restrictive for the study of the effects of habitat degradation. We rigorously show competitive exclusion and coexistence via global stability analysis. A remarkable finding is that the quality heterogeneity of landscapes can lead to the competitive exclusion of the slower species by the faster species. This result is robust as long as the degraded region has positive area, and moreover is at odds with classical results predicting the deterministic extinction of the stronger species. On the other hand, if the degraded region has intermediate negative effect on the faster competitor, species can coexist. Differing from comparable existing results, coexistence does not rely on a limit as the diffusion coefficients tend to zero or infinity. Together, these results imply that coexistence is always a possibility under this basic, yet general, configuration, providing insights into the varying impacts found through empirical study of habitat loss and fragmentation on species.