Reconstructing the history of polygenic scores using coalescent trees

1Genome-wide association studies (GWAS) have revealed that many traits are highly polygenic, in that their within-population variance is governed in part by small-effect variants at many genetic loci. Standard population-genetic methods for inferring evolutionary history are ill-suited for polygenic traits--when there are many variants of small effect, signatures of natural selection are spread across the genome and subtle at any one locus. In the last several years, several methods have emerged for detecting the action of natural selection on polygenic scores, sums of genotypes weighted by GWAS effect sizes. However, most existing methods do not reveal the timing or strength of selection. Here, we present a set of methods for estimating the historical time course of a population-mean polygenic score using local coalescent trees at GWAS loci. These time courses are estimated by using coalescent theory to relate the branch lengths of trees to allele-frequency change. The resulting time course can be tested for evidence of natural selection. We present theory and simulations supporting our procedures, as well as estimated time courses of polygenic scores for human height. Because of its grounding in coalescent theory, the framework presented here can be extended to a variety of demographic scenarios, and its usefulness will increase as both GWAS and ancestral recombination graph (ARG) inference continue to progress.