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Chan, Durrett, and Lanchier introduced a multitype contact process withtemporal heterogeneity involving two species competing for space on thed-dimensional integer lattice. Time is divided into two seasons. They provedthat there is an open set of the parameters for which both species can coexistwhen their dispersal range is sufficiently large. Numerical simulationssuggested that three species can coexist in the presence of two seasons. Themain point of this paper is to prove that this conjecture is incorrect. To dothis we prove results for a more general ODE model and contrast its behaviorwith other related systems that have been studied in order to understand thecompetitive exclusion principle.

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