Coexistence for a multitype contact process with seasons

TL;DR

This paper introduces a multitype contact process with seasonal changes, demonstrating conditions for coexistence of two or three species on a lattice, contrasting with traditional models where the dominant species outcompetes others.

Contribution

It presents a novel model incorporating seasonal effects into multitype contact processes and proves coexistence is possible under certain parameters with large dispersal ranges.

Findings

Both species can coexist with large dispersal ranges.

Numerical simulations suggest three species can coexist with seasons.

Contrasts with time-homogeneous models where the dominant species outcompetes others.

Abstract

We introduce a multitype contact process with temporal heterogeneity involving two species competing for space on the $d$-dimensional integer lattice. Time is divided into seasons called alternately season 1 and season 2. We prove that there is an open set of the parameters for which both species can coexist when their dispersal range is large enough. Numerical simulations also suggest that three species can coexist in the presence of two seasons. This contrasts with the long-term behavior of the time-homogeneous multitype contact process for which the species with the higher birth rate outcompetes the other species when the death rates are equal.