Global behavior of N competing species with strong diffusion: diffusion leads to exclusion

TL;DR

This paper demonstrates that in a spatially heterogeneous environment, fast diffusion leads to species exclusion consistent with the homogeneous model, extending the competitive exclusion principle.

Contribution

It introduces an aggregated model for multiple species competition in heterogeneous environments and proves its validity under fast diffusion conditions.

Findings

Fast diffusion causes the heterogeneous model to behave like the homogeneous one.

Competitive exclusion principle applies to the heterogeneous model when it holds for the aggregated model.

The aggregated model can be explicitly computed for analysis.

Abstract

It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an heterogeneous environment. We propose a spatially heterogeneous system modeling the competition of several species for a single resource. If spatial movements are fast enough, we show that our system can be well approximated by a spatially homogeneous system, called aggregated model, which can be explicitly computed. Moreover, we show that if the competitive exclusion principle holds for the aggregated model, it holds for the spatially heterogeneous model too.