Competitive exclusion in a model with seasonality: three species cannot coexist in an ecosystem with two seasons

TL;DR

This paper proves that in a seasonal environment, three competing species cannot coexist in an ecosystem with two seasons, confirming the competitive exclusion principle through analysis of a generalized ODE model.

Contribution

It provides a rigorous proof that three species cannot coexist in a two-season model, refuting previous numerical suggestions of coexistence.

Findings

Three species cannot coexist in a two-season environment.

The generalized ODE model supports competitive exclusion.

Numerical simulations are contradicted by theoretical results.

Abstract

Chan, Durrett, and Lanchier introduced a multitype contact process with temporal heterogeneity involving two species competing for space on the d-dimensional integer lattice. Time is divided into two seasons. They proved that there is an open set of the parameters for which both species can coexist when their dispersal range is sufficiently large. Numerical simulations suggested that three species can coexist in the presence of two seasons. The main point of this paper is to prove that this conjecture is incorrect. To do this we prove results for a more general ODE model and contrast its behavior with other related systems that have been studied in order to understand the competitive exclusion principle.