Ecological invasion in competition-diffusion systems when the exotic species is either very strong or very weak

TL;DR

This paper investigates competition-diffusion systems modeling ecological species interactions, providing criteria for invasion success or failure based on environmental favorability, especially when exotic species are very strong or very weak.

Contribution

It offers new criteria for non-coexistence in multi-species competition systems, focusing on invasion outcomes related to species strength and environmental conditions.

Findings

Invasive species always succeed when environment is highly favorable.

Invasion fails when environment is not sufficiently favorable.

Provides analytical criteria for invasion success or failure.

Abstract

Reaction-diffusion systems with a Lotka-Volterra-type reaction term, also known as competition-diffusion systems, have been used to investigate the dynamics of the competition among $m$ ecological species for a limited resource necessary to their survival and growth. Notwithstanding their rather simple mathematical structure, such systems may display quite interesting behaviours. In particular, while for $m=2$ no coexistence of the two species is usually possible, if $m \ge 3$ we may observe coexistence of all or a subset of the species, sensitively depending on the parameter values. Such coexistence can take the form of very complex spatio-temporal patterns and oscillations. Unfortunately, at the moment there are no known tools for a complete analytical study of such systems for $m \ge 3$. This means that establishing general criteria for the occurrence of coexistence appears to be very hard. In this paper we will instead give some criteria for the non-coexistence of species, motivated by the ecological problem of the invasion of an ecosystem by an exotic species. We will show that when the environment is very favourable to the invading species the invasion will always be successful and the native species will be driven to extinction. On the other hand, if the environment is not favourable enough, the invasion will always fail.