Global dynamics in a reaction-diffusion competition model with edge behavior

TL;DR

This paper analyzes the competitive dynamics of two species across multiple patches, revealing conditions for invasion, coexistence, and elimination based on strategies relative to an ideal free distribution in reaction-diffusion models.

Contribution

It extends the understanding of edge behavior and strategy dynamics from two patches to multiple patches in reaction-diffusion competition models.

Findings

Mutant species cannot invade if resident follows IFD strategy.

Species strategies above or below IFD lead to competitive exclusion.

Opposite side strategies enable coexistence.

Abstract

In this paper, we investigate a two-species competition model in a landscape consisting of a finite number of adjacent patches. For the two-patch scenario, by treating edge behavior at the interface as a strategy, it has been shown that there exists an ideal free distribution (IFD) strategy, which is a globally evolutionarily stable strategy. Specifically, when the resident species follows the IFD strategy and the mutant species does not, the mutant species is unable to invade the resident population. Building on this foundation, our work focuses on exploring the dynamics of the system when neither species can adopt the IFD strategy. We demonstrate that if the strategies of both species either exceed or fall below the IFD strategy, the mutant species can outcompete and eliminate the resident species, provided that its strategy is closer to the IFD strategy and its diffusion rates are equal to or slower than those of the resident species. Furthermore, if the strategies of the two species lie on opposite sides of the IFD strategy, the two species can coexist. This result is further extended to the case of an arbitrary but finite number of patches.