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Both evolution and ecology have long been concerned with the impact ofvariable environmental conditions on observed levels of genetic diversitywithin and between species. We model the evolution of a quantitative traitunder selection that fluctuates in space and time, and derive an analyticalcondition for when these fluctuations promote genetic diversification. Asecological scenario we use a generalized island model with soft selectionwithin patches in which we incorporate generation overlap. We allow forarbitrary fluctuations in the environment including spatio-temporalcorrelations and any functional form of selection on the trait. Using theconcepts of invasion fitness and evolutionary branching, we derive a simple andtransparent condition for the adaptive evolution and maintenance of geneticdiversity. This condition relates the strength of selection within patches toexpectations and variances in the environmental conditions across space andtime. Our results unify, clarify, and extend a number of previous results onthe evolution and maintenance of genetic variation under fluctuating selection.Individual-based simulations show that our results are independent of thedetails of the genetic architecture and on whether reproduction is clonal orsexual. The onset of increased genetic variance is predicted accurately also insmall populations in which alleles can go extinct due to environmentalstochasticity.

A general condition for adaptive genetic polymorphism in temporally and spatially heterogeneous environments