Understanding the role of rare variants is important in elucidating the genetic basis of human diseases and complex traits. It is widely believed that 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 by maximizing its profile likelihood in a linear mixed model framework using 1 . CC-BY-NC-ND 4.0 International license It is made available under a (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.The copyright holder for this preprint . http://dx.doi.org/10.1101/188086 doi: bioRxiv preprint first posted online Sep. 13, 2017; imputed genotypes, including rare variants (MAF > 0.07%). We applied this method to 25 UK Biobank diseases and complex traits (N=113,851). All traits produced negative α estimates with 20 significantly negative, implying larger rare variant effect sizes. The inferred best-fit distribution of true α values across traits had mean −0.38 (s.e. 0.02) and standard deviation 0.08 (s.e. 0.03), with statistically significant heterogeneity across traits (P=0.0014). Despite larger rare variant effect sizes, we show that for most traits analyzed, rare variants (MAF < 1%) explain less than 10% of total SNP-heritability. Using evolutionary modeling and forward simulations, we validated the α model of MAFdependent trait effects and estimated the level of coupling between fitness effects and trait effects. Based on this analysis an average genome-wide negative selection coefficient on the order of 10 −4 or stronger is necessary to explain the α values that we inferred.