Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments

TL;DR

This paper analyzes how stochastic environmental variation influences the evolution and stability of habitat selection strategies in a population with two morphs, providing conditions for coexistence and characterizing evolutionarily stable strategies.

Contribution

It rigorously characterizes evolutionarily stable habitat selection strategies in stochastic environments, extending previous models with explicit formulas and conditions for coexistence and stability.

Findings

Protected polymorphisms can occur under positive invasion rates.

Environmental stochasticity influences habitat use, favoring bet-hedging strategies.

Explicit conditions for ESS existence and formulas for two habitat types.

Abstract

We consider a population living in a patchy environment that varies stochastically in space and time. The population is composed of two morphs (that is, individuals of the same species with different genotypes). In terms of survival and reproductive success, the associated phenotypes differ only in their habitat selection strategies. We compute invasion rates corresponding to the rates at which the abundance of an initially rare morph increases in the presence of the other morph established at equilibrium. If both morphs have positive invasion rates when rare, then there is an equilibrium distribution such that the two morphs coexist; that is, there is a protected polymorphism for habitat selection. Alternatively, if one morph has a negative invasion rate when rare, then it is asymptotically displaced by the other morph under all initial conditions where both morphs are present. We refine the characterization of an evolutionary stable strategy for habitat selection from [Schreiber, 2012] in a mathematically rigorous manner. We provide a necessary and sufficient condition for the existence of an ESS that uses all patches and determine when using a single patch is an ESS. We also provide an explicit formula for the ESS when there are two habitat types. We show that adding environmental stochasticity results in an ESS that, when compared to the ESS for the corresponding model without stochasticity, spends less time in patches with larger carrying capacities and possibly makes use of sink patches, thereby practicing a spatial form of bet hedging.