Polygenic adaptation to an environmental shift: temporal dynamics of variation under Gaussian stabilizing selection and additive effects on a single trait

Predictions about the effect of natural selection on patterns of linked neutral variation are largely based on models involving the rapid fixation of unconditionally-beneficial mutations. However, polygenic traits are expected to evolve by small allele frequency changes at many loci. Here, I use explicit forward simulations of a single trait with additive-effect mutations adapting to an optimum shift. In this model, sweeps of large-effect mutations occur from a nearly equal number of new mutations and standing variants, except when the trait is highly polygenic and fixations from standing variation dominate. Large-effect mutations contribute to adaptation even when the trait is not mutation-limited. However, such mutations do not sweep to fixation on the time scale of adaptation for polygenic traits. The signature of hitch-hiking, measured using standard summaries of linked variation, are approximately identical for the two classes of sweeps, which is due to the equilibrium frequencies of standing variants at mutation-selection equilibrium at the time of the environmental shift. I also show that the mean times to adaptation and patterns of linked selection are robust to certain details of the distribution of effect sizes, and that the proportion of new mutations of large effect is a critical parameter affecting patterns of linked selection.