Density dependence and unpredictable selection in a heterogeneous environment: Compromise and polymorphism in the ESS reaction norm

Abstract

In quantitative genetic models of the evolution of reaction norms, an individual is selected in the habitat in which it develops; as a consequence, selection leads to the optimum phenotype in each habitat. Here, individuals are assumed to experience unpredictable habitat change between development and selection, so that the environment in which an individual is selected may differ from the environment in which it developed. The model reveals that unpredictability of the selection an individual actually faces leads to the evolutionarily stable bet-hedging reaction norm constituting a compromise between the phenotypic optima in the different patches. We also examine the effect of local density regulation before selection, in the patches in which the individuals develop, and after selection, in the patches in which they are selected. Density regulation before selection has a much lower influence on the evolution of the reaction norm than density regulation after selection. The source-sink structure of the environment caused by differential productivity of patches strongly affects how the compromise bet-hedging strategy weighs the different phenotypic optima and might compromise the local evolutionary stability of the evolved reaction norm. If the strength and variability among patches of density regulation after selection is sufficiently large, no single reaction norm is evolutionary stable. Polymorphic reaction norms constitute the evolutionarily stable population. We also show that a polymorphic reaction norm is more likely to be observed in a less productive habitat. The relations between the present model and the Dempster and the Levene models are discussed.