In addition to heritability and polygenicity, another important aspect of the genetic architecture of complex traits and diseases is the relationship between effect sizes at causal variants (hereafter denoted by β) and their minor alleles frequencies (hereafter denoted by p). This relationship has been modelled in many studies24–28 using a parameter S such that β2 is assumed to be proportional to [2p(1−p)]s. Values of S determine the relative contributions of common versus rare variants to the genetic variance in the population and thus have been used as an indirect measure of the strength of natural selection29. Our model assumes that the variance explained by each causal SNP is constant regardless of allele frequencies. This assumption is consistent with a strong negative selection on causal variants shared between populations and corresponds to a value of S = −1. Although previous studies24,26,30 have reported pervasive negative selection on complex traits and diseases, these studies often report estimates of S with less extreme magnitudes than that assumed in our model. Moreover, given that little is known on the strength of negative selection in non-European populations, we next investigated through additional simulations the impact of violations of this assumption.
