The Evolution of Plasticity and Nonplastic Spatial and Temporal Adaptations in the Presence of Imperfect Environmental Cues

Abstract

A model for the evolution of plasticity is considered in which the phenotype, undergoing stabilizing selection, is modeled as a linear function of an environmental cue correlated with the phenotypic optimum, with the coefficients z0 and z1 evolving according to standard quantitative genetic theory. In contrast to previous theoretical models, as the rate of migration between demes or the rate of cyclic fluctuations in the optimum increases, the amount of plasticity $$\overline{z}_{1}$$ at equilibrium is shown to increase gradually, in part accounting for the effect of reduced nonplastic adaptation and reaching a maximum equal to the squared correlation between the environmental cue and the phenotypic optimum. Given that information available to the organism is limited, this bias of the expressed phenotype toward the global optimum is still optimal, however, in a certain decision‐theoretic sense. When genetic variation in the plastic component of the trait is small so that spatial or temporal differentiation in plasticity is small, the effect of plasticity on nonplastic adaptation is to reduce the effects of variation in the phenotypic optimum by a factor $$1-\overline{z}_{1}$$ only. Information acquisition costs and joint evolution of sensory systems are discussed.