The Evolution of Phenotypic Plasticity when Environments Fluctuate in Time and Space

Most studies have explored the evolution of plasticity when the environment, and there-fore the optimal trait, varies in time or space. When the environment varies in time and space we show that genetic adaptation to temporal fluctuations depends on the between-generation autocorrelation in the environment in exactly the same way that genetic adaptation to spatial fluctuations depends on the probability of philopatry. This is because both measure the correlation in parent-offspring environments and therefore the effectiveness of a genetic response to selection. If the capacity to genetically respond to selection is stronger in one dimension (e.g. space) then plasticity mainly evolves in response to fluctuations in the other dimension (e.g. time). If the relationship between the environments of development and selection are the same in time and space then the evolved plastic response to temporal fluctuations is useful in a spatial context and genetic differentiation in space is reduced. However, if the relationship between the environments of development and selection are different then the optimal level of plasticity is different in the two dimensions. In this case the plastic response that evolves to cope with temporal fluctuations may actually be maladaptive in space. This can result in the evolution of hyperplasticity or negative plasticity, the effects of which are mitigated by spatial genetic differentiation. However, genetic differentiation acts in opposition to plasticity resulting in counter-gradient variation. These results highlight the difficulty of making space-for-time substitutions in empirical work but identify the key parameters which need to be measured in order to test whether space-for-time substitutions are likely to be valid.