Evolution of phenotypic plasticity and environmental tolerance of a labile quantitative character in a fluctuating environment

Quantitative genetic models of evolution of phenotypic plasticity are used to derive environmental tolerance curves for a population in a changing environment, providing a theoretical foundation for integrating physiological and community ecology with evolutionary genetics of plasticity and norms of reaction. Plasticity is modelled for a labile quantitative character undergoing continuous reversible development and selection in a fluctuating environment. If there is no cost of plasticity, a labile character evolves expected plasticity equalling the slope of the optimal phenotype as a function of the environment. This contrasts with previous theory for plasticity influenced by the environment at a critical stage of early development determining a constant adult phenotype on which selection acts, for which the expected plasticity is reduced by the environmental predictability over the discrete time lag between development and selection. With a cost of plasticity in a labile character, the expected plasticity depends on the cost and on the environmental variance and predictability averaged over the continuous developmental time lag. Environmental tolerance curves derived from this model confirm traditional assumptions in physiological ecology and provide new insights. Tolerance curve width increases with larger environmental variance, but can only evolve within a limited range. The strength of the trade-off between tolerance curve height and width depends on the cost of plasticity. Asymmetric tolerance curves caused by male sterility at high temperature are illustrated. A simple condition is given for a large transient increase in plasticity and tolerance curve width following a sudden change in average environment.