Effects of population size change on the genetics of adaptation following an abrupt change in environment

Since the rediscovery of Mendelian genetics over a century ago, there has been much debate about the evolutionary importance of mutations with large phenotypic effects. While population genetic models predict that large-effect mutations will typically contribute to adaptation following an abrupt change in environment, the prediction applies to populations of stable size and overlooks the effects of population size change on adaptation (e.g., population decline following habitat loss; growth during range expansion). We evaluate the phenotypic and fitness effects of mutations contributing to adaptation immediately following an abrupt environmental shift that alters both selection and population size dynamics. We show that large-effect mutations are likely to contribute to adaptation in populations declining to a new carrying capacity, somewhat smaller-effect mutations contribute to evolutionary rescue, and small-effect mutations predominate in growing populations. We also show that the relative contributions of positively selected and overdominant mutations to adaptation depend on interactions between the phenotypic effect size distribution for new mutations and the specific form of population size change during adaptation (i.e., growth, decline, or evolutionary rescue). Our results illustrate how population size dynamics can shape the genetic basis of adaptation, which should motivate empirical comparisons of populations adapting in different demographic contexts.