Coevolution of Patch Selection in Stochastic Environments

Species interact in landscapes where environmental conditions vary in time and space. This variability impacts how species select habitat patches. Under equilibrium conditions, evolution of this patch selection can result in ideal free distributions where per capita growth rates are zero in occupied patches and negative in unoccupied patches. These ideal free distributions, however, do not explain why species occupy sink patches, why competitors have overlapping spatial ranges, or why predators avoid highly productive patches. To understand these patterns, we solve for coevolutionarily stable strategies (coESSs) of patch selection for multispecies stochastic Lotka-Volterra models accounting for spatial and temporal heterogeneity. In occupied patches at the coESS, we show that the differences between the local contributions to the mean and the variance of the long-term population growth rate are equalized. Applying this characterization to models of antagonistic interactions reveals that environmental stochasticity can partially exorcize the ghost of competition past, select for new forms of enemy-free and victimless space, and generate hydra effects over evolutionary timescales. Viewing our results through the economic lens of modern portfolio theory highlights why the coESS for patch selection is often a bet-hedging strategy coupling stochastic sink populations. Our results highlight how environmental stochasticity can reverse or amplify evolutionary outcomes as a result of species interactions or spatial heterogeneity.