Dynamics of Polygenic Adaptation

Polygenic adaptation in response to natural selection on a quantitative trait has become an important topic in population genetics and evolution. We modeled a scenario in which a population was assumed to be in equilibrium between mutation, selection and genetic drift, when a sudden shift in the fitness optimum occurred. It is well known that after an environmental shift the trait mean may approach the new optimum very quickly at a rate proportional to the equilibrium genetic variance. Here, we analyze the dynamics of the allele frequencies at individual loci, using diffusion theory. We show that genetic drift slows down the speed of polygenic adaptation. We also found that, while the frequencies of rare and very common alleles decrease during the adaptive phase, alleles starting at intermediate equilibrium frequencies at the time of the optimum shift change most quickly and thus may substantially modify the shape of the allele frequency distribution. Finally, we explain how these properties of the allele frequency spectrum may be utilized in statistical tests of polygenic selection.