Predicting the prevalence of genetic trade-offs among adaptive substitutions

Genetic trade-offs-which occur when variants that are beneficial in some contexts of natural selection are harmful in others-can influence a wide range of evolutionary phenomena, from the maintenance of genetic variation to the evolution of aging and sex differences. An extensive body of evolutionary theory has focused on the consequences of such trade-offs, and recent analyses of Fisher's geometric model have further quantified the expected proportion of new mutations that exhibit trade-offs. However, the theory remains silent regarding the prevalence of trade-offs among the variants that contribute to adaptation. Here, we extend Fisher's geometric model to predict the prevalence of trade-offs among the adaptive mutations that become established or fixed in a population. We consider trade-offs between sexes, habitats, fitness components, and temporally fluctuating environments. In all 4 scenarios, trade-off alleles are consistently under-represented among established relative to new beneficial mutations-an effect that arises from the greater susceptibility of trade-off alleles to genetic drift. Adaptation during a population size decline exacerbates this deficit of trade-offs among established mutations, whereas population expansions dampen it. Consequently, threatened populations should primarily adapt using unconditionally beneficial alleles, while invasive populations are more prone to adaptation using variants that exhibit trade-offs.