Extreme Polygenicity of Complex Traits Is Explained by Negative Selection

Abstract

Complex traits and common diseases are extremely polygenic, their heritability spread across thousands of loci. One possible explanation is that thousands of genes and loci have similarly important biological effects when mutated. However, we hypothesize that for most complex traits, relatively few genes and loci are critical, and negative selection-purging large-effect mutations in these regions-leaves behind common-variant associations in thousands of less critical regions instead. We refer to this phenomenon as flattening. To quantify its effects, we introduce a mathematical definition of polygenicity, the effective number of independently associated SNPs (M e), which describes how evenly the heritability of a trait is spread across the genome. We developed a method, stratified LD fourth moments regression (S-LD4M), to estimate M e , validating that it produces robust estimates in simulations. Analyzing 33 complex traits (average N ¼ 361k), we determined that heritability is spread $43 more evenly among common SNPs than among low-frequency SNPs. This difference, together with evolutionary modeling of new mutations, suggests that complex traits would be orders of magnitude less polygenic if not for the influence of negative selection. We also determined that heritability is spread more evenly within functionally important regions in proportion to their heritability enrichment; functionally important regions do not harbor common SNPs with greatly increased causal effect sizes, due to selective constraint. Our results suggest that for most complex traits, the genes and loci with the most critical biological effects often differ from those with the strongest common-variant associations.

Functionally-informed fine-mapping and polygenic localization of complex trait heritability

“…Our results demonstrate that half of the common SNP heritability of complex traits is causally explained by typically thousands of SNPs (median % =3.4K), and the remaining heritability is spread across an extremely large number of extremely weak-effect SNPs (median % =4.3 million), consistent with extremely polygenic but heavy-tailed trait architectures 1,29,45,46,[50][51][52][53][54] .…”

“…where is the causal effect size of SNP in standardized units (the number of standard deviations increase in phenotype per 1 standard deviation increase in genotype), is the vector of functional annotations of SNP , and var[ | ] is the estimated per-SNP heritability of SNP from step 4 (see above). Equation 1 is derived by applying the law of total variance to var [ | ], assuming that SNP effect sizes are sampled from a mixture distribution and that functional enrichment is primarily due to differences in polygenicity rather than differences in effect-size magnitude, which is motivated by our recent work 29 (see Methods). We discuss the proportionality constant of Equation 1 in the Methods section.…”

“…where are the functional annotations of SNP , ( ≠ 0| ) is its prior causal probability, and var[ | ≠ 0] is its causal variance, which we assume is independent of . This assumption is motivated by our recent work showing that functional enrichment is primarily due to differences in polygenicity rather than differences in effect-size magnitude, which is constrained by negative selection 29 .…”

“…We verified that % estimates were strongly correlated with estimates of the effective number of independently associated SNPs (Me; ref. 29 ), with log-scale r=0.88 (P=6.2×10 -5 ) across 13 genetically uncorrelated traits with published Me estimates ( Supplementary Table 27); as noted above, PolyLoc provides the SNP sets underlying its estimates, unlike ref. 29 .…”

“…We thus propose polygenic localization, whose aim is to identify a minimal set of common SNPs causally explaining a specified proportion of common SNP heritability. A key difference between polygenic localization and previous studies of polygenicity 29,[44][45][46][47] is that polygenic localization aims to identify (not just characterize) such SNPs.…”