A population genetic interpretation of GWAS findings for human quantitative traits
GWAS in humans are revealing the genetic architecture of biomedical and anthropomorphic 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 architecture is shaped by basic population genetics processes-notably, by mutation, natural selection and genetic drift. Because many quantitative 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 multi-dimensional trait space. We solve the model for the phenotypic distribution and allelic dynamics at steady state and derive robust, closed form solutions for summary statistics of the genetic architecture. Our results provide a simple interpretation for missing heritability and why it varies among traits. They also predict that the distribution of variances contributed by loci identified in GWAS is 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. We test this prediction against the results of GWAS for height and BMI and find that it fits the data 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 similarly-sized GWAS for BMI, and to predict the increase in explained heritability with study sample size. Considering the demographic history of European populations, in which these GWAS 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 $s=10^{-3}$.