Invasion of open space by two competitors: spreading properties of monostable two-species competition--diffusion systems

TL;DR

This study investigates the spreading dynamics of two competing species in a reaction-diffusion system, revealing conditions under which the faster, weaker competitor can invade first and characterizing the possible invasion speeds based on initial conditions.

Contribution

The paper advances understanding of two-species competition by establishing new spreading speed results and resolving open questions about invasion scenarios with specific initial decay conditions.

Findings

Faster, weaker competitors can invade first if they are also the faster species.

The first invasion speed matches the KPP speed of the fastest species.

An exact formula describes non-local pulling effects in invasion speeds.

Abstract

This paper is concerned with some spreading properties of monostable Lotka--Volterra two-species competition--diffusion systems when the initial values are null or exponentially decaying in a right half-line. Thanks to a careful construction of super-solutions and sub-solutions, we improve previously known results and settle open questions. In particular, we show that if the weaker competitor is also the faster one, then it is able to evade the stronger and slower competitor by invading first into unoccupied territories. The pair of speeds depends on the initial values. If these are null in a right half-line, then the first speed is the KPP speed of the fastest competitor and the second speed is given by an exact formula describing the possibility of non-local pulling. Furthermore, the unbounded set of pairs of speeds achievable with exponentially decaying initial values is characterized, up to a negligible set.