Coexistence for a multitype contact process with seasons

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.Comment: Published in at http://dx.doi.org/10.1214/09-AAP599 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Coexistence in Periodic Environments

“…Researchers have cogently argued that temporal variations can promote species coexistence via fluctuation-dependent coexistence mechanisms (e.g., storage effect, relative nonlinearity, equalizing mechanisms) (Namba and Takahashi 1993;Chesson and Huntly 1997;Adler et al 2006;Li and Chesson 2016;Miller and Klausmeier 2017;Chesson 2018;Hastings 2022a, 2022b;Meyer et al 2022). With these mechanisms, temporal niche differentiation enables coexistence between species with different competitive advantages that would otherwise not be possible in static environments (Chesson 2000;Chan et al 2009;Mathias and Chesson 2013;Scranton and Vasseur 2016;Miller and Klausmeier 2017;Rossi et al 2017;Zielinski et al 2017).…”

“…Researchers have cogently argued that temporal variations can promote species coexistence via fluctuation-dependent coexistence mechanisms (e.g., storage effect, relative nonlinearity, equalizing mechanisms) (Namba and Takahashi 1993; Chesson and Huntly 1997; Adler et al 2006; Li and Chesson 2016; Miller and Klausmeier 2017; Chesson 2018; Johnson and Hastings 2022a, 2022b; Meyer et al 2022). With these mechanisms, temporal niche differentiation enables coexistence between species with different competitive advantages that would otherwise not be possible in static environments (Chesson 2000; Chan et al 2009; Mathias and Chesson 2013; Scranton and Vasseur 2016; Miller and Klausmeier 2017; Rossi et al 2017; Zielinski et al 2017). For example, temporally changing resource conditions, which fluctuate between periods of high productivity to periods of very little to no productivity (Fretwell 1972; Campbell et al 2008; Suski and Ridgway 2009; Huntly et al 2021), may favour different species at different times (Armstrong and McGehee 1980; Litchman and Klausmeier 2001; Hastings 2012; Huntly et al 2021).…”

A heterogeneous spatial model in which savanna and forest coexist in a stable equilibrium

“…We will let L → ∞ and scale space by L so that the particle system can be replaced by an integro-differential equation. This approach has been used to analyze a number of examples [2,5,8,10,14,20,25] that are not tractable if one assumes a fixed finite range. Before we can state our long-range limit theorem we have to explain what it means for a seqeunce of particle systems ξ L t : Z 2 /L → {0, 1} to converge to a function u(t, x).…”

The timing of life history events in the presence of soft disturbances

“…For the simplest among this models, the branching random walk, much has been done: for instance in [4,5,7,32,45,47] one finds characterization of the persistence/disappearance of genotypes (seen as locations for the model), on general space structures; the same can be found, for some random graphs, in [8,35]. Stochastic modelling and interacting particle systems have been successfully applied to biology and ecology (see [1,2,3,12,13,24,25,26,28,19,48] just to mention a few). Although stochastic modelling is very interesting and complex, here we will assume that over many generations, our populations have been sufficiently large to justify the use of a model where stochasticity appears only in the random time at which the disturbance strikes.…”