"Polygenic dynamics underlying the response of quantitative traits to directional selection"Bürger, ReinhardThis talk is based on joint work with Hannah Götsch in which we studied the response of a quantitative trait to exponential directional selection in a finite haploid population, both at the genetic and the phenotypic level. An infinite sites model is assumed, in which the number of new mutations in the population per generation follows a Poisson distribution with mean $\Th$ and each mutation occurs at a new, previously monomorphic site. Mutation effects are beneficial and drawn from a distribution. Sites are unlinked and contribute additively to the trait. Assuming that selection is stronger than random genetic drift, we model the initial phase of the dynamics by a supercritical Galton-Watson process and combine it with deterministic growth in later phases. We show that the copy-number distribution of the mutant in generation n, conditioned on non-extinction until n, is described accurately by the deterministic increase from a geometric intial distribution . A suitable transformation yields the approximate mutant frequency distribution in a Wright-Fisher population of size $N$ as a function of time. It is highly accurate except when mutant frequencies are close to 1. On this basis, we derive explicitly the (approximate) time dependence of the expected mean and variance of the trait and of the expected number of segregating sites. We obtain highly accurate approximations for all times, even for the quasi-stationary phase when the expected per-generation response and the trait variance have equilibrated. The latter refine classical results. In addition, we find that $\Th$ is the main determinant of the pattern of adaptation at the genetic level, i.e., whether the initial allele-frequency dynamics are best described by sweep-like patterns at few loci or small allele-frequency shifts at many. The number of segregating sites is an appropriate indicator for these patterns. |
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