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Species live and interact in patchy landscapes where environmental conditions vary both in time and space. In the face of this spatial-temporal heterogeneity, species may co-evolve strategies of patch-selection which determine their spatial distributions. Under equilibrium conditions and no costs to dispersal, coevolution of patch-selction leads to an ideal-free distribution for each species: the per-capita growth rates are zero in the patches occupied by the species and negative in the unoccupied patches. These ideal-free distributions explain some observed empirical patterns including enemy-free space and complete spatial segregation of competing species i.e. the ghost of competition past. However, they do not explain why some species live in sink patches where their per-capita growth rate is negative, why competing species aren’t always fully spatially segregated, or why predators make use of prey-free patches. To understand how accounting for temporal fluctuations may explain these latter patterns, we analyze a system of n species, stochastic Lotka-Volterra models that account for patchy space implicitly. To identify potential coevolutionary endpoints, we introduce a definition of a stochastic coevolutionarily stable strategy (coESS): a collection of patch-selection strategies for each species that resist invasion attempts from mutant subpopulations of any species utilizing other patch-selection strategies. We show that the coESS can be characterized via a system of second-order equations of the parameters. This characterization shows, surprisingly, that the stochastic per-capita growth rates of species are negative in all occupied patches despite the species persisting. Applying this characterization to the coevolution of habitat-choice of competitors and predator-prey systems identifies under what environmental conditions, natural selection exorcizes the ghost of competition past and banishes some predators to prey-free patches. Collectively, our results highlight the importance of temporal fluctuations, spatial heterogeneity and species interactions on the evolution of species’ spatial distributions. This work is in collaboration with Alex Hening (College Station) and Dang Nguyen (Tuscaloosa).

Seminar hosted in hybrid format. Email organizer for Zoom link.