Estimation of the joint distribution of effect size and minor allele frequency (MAF) for genetic variants is important for understanding the genetic basis of complex trait variation and can be used to detect signature of natural selection. We develop a Bayesian mixed linear model that simultaneously estimates SNP-based heritability, polygenicity (i.e. the proportion of SNPs with nonzero effects) and the relationship between effect size and MAF for complex traits in conventionally unrelated individuals using genome-wide SNP data. We apply the method to 28 complex traits in the UK Biobank data (N = 126,752), and show that on average across 28 traits, 6% of SNPs have nonzero effects, which in total explain 22% of phenotypic variance. We detect significant (p < 0.05/28 = 1.8×10-3) signatures of natural selection for 23 out of 28 traits including reproductive, cardiovascular, and anthropometric traits, as well as educational attainment. We further apply the method to 27,869 gene expression traits (N = 1,748), and identify 30 genes that show significant (p < 2.3×10-6) evidence of natural selection. All the significant estimates of the relationship between effect size and MAF in either complex traits or gene expression traits are consistent with a model of negative selection, as confirmed by forward simulation. We conclude that natural selection acts pervasively on human complex traits shaping genetic variation in the form of negative selection.

Widespread signatures of negative selection in the genetic architecture of human complex traits