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Understanding the role of rare variants is important in elucidating the genetic basis of human disease. Negative selection can cause rare variants to have larger per-allele effect sizes than common variants. Here, we develop a method to estimate the minor allele frequency (MAF) dependence of SNP effect sizes. We use a model in which per-allele effect sizes have variance proportional to [ p (1 −  p )]  α  , where  p  is the MAF and negative values of  α  imply larger effect sizes for rare variants. We estimate  α  for 25 UK Biobank diseases and complex traits. All traits produce negative  α  estimates, with best-fit mean of –0.38 (s.e. 0.02) across traits. Despite larger rare variant effect sizes, rare variants (MAF < 1%) explain less than 10% of total SNP-heritability for most traits analyzed. Using evolutionary modeling and forward simulations, we validate the  α  model of MAF-dependent trait effects and assess plausible values of relevant evolutionary parameters.

Quantification of frequency-dependent genetic architectures in 25 UK Biobank traits reveals action of negative selection