Human genome-wide association studies (GWASs) are revealing the genetic architecture of anthropomorphic and biomedical traits, i.e., the frequencies and effect sizes of variants that contribute to heritable variation in a trait. To interpret these findings, we need to understand how genetic architectures are shaped by basic population genetic processes—notably, by mutation, natural selection, and genetic drift. Because many complex traits are subject to stabilizing selection and genetic variation that affects one trait often affects many others, we model the genetic architecture of a focal trait that arises under stabilizing selection in a multidimensional trait space. We solve the model at steady state, to find that the distribution of variances contributed by loci identified in GWASs should be well approximated by a simple functional form that depends on a single parameter: the expected contribution to genetic variance of a strongly selected site affecting the trait. This prediction fits the findings of GWASs for height and body mass index (BMI) well, allowing us to make inferences about the degree of pleiotropy and mutational target size for these traits. Our findings help to explain why the GWAS for height explains more of the heritable variance than the similarly sized GWAS for BMI and to predict the increase in explained heritability with study size. Considering the demographic history of European populations, in which these GWASs were performed, we further find that most of the associations they identified likely involve mutations that arose during the Out-of-Africa bottleneck at sites with selection coefficients around s = 10−3.
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