The author has declared that no competing interests exist.

This primer provides some background to help non-specialists understand a new theoretical evolutionary genetics study that helps explain why thousands of variants of small effect contribute to complex traits.

If population genetics is the study of allele frequencies and quantitative genetics the study of allelic effects, then evolutionary genetics aims to understand how they interact over time. Matching of models to data has traditionally been constrained by the bias of observation toward common alleles that have large effects, limiting our ability to address questions such as “what maintains variation in natural populations,” “how many genes influence a trait,” or “to what extent do drift and selection influence allele frequencies” [

Two findings differentiate GWAS from much of 20th century genetics: the extraordinarily high polygenicity of traits and the dearth of evidence for interaction effects, whether among genes or with the environment [

Despite this complexity, there are also signs that what is called the “genetic architecture” does differ among traits, namely that different numbers of genes with different spectra of allele frequencies (and perhaps propensity to interact) associate with each trait [

Very soon after the first GWAS studies appeared 10 years ago, it was recognized that considerably less genetic variation was being discovered than expected, given well-validated heritability estimates [

Contrasting these interpretations requires accurate estimation of the distribution of allelic effects. Three general approaches have been used to do so, broadly extrapolation, interpolation, and simulation. Extrapolation studies [

The reason why allele frequencies matter is that the amount of variance a biallelic polymorphism contributes is equal to 2^{2}, where

(A) The blue curve shows how the percent of variance explained varies as a function of minor allele frequency, ^{2}. The curve assumes 1,000 alleles, each with an additive contribution, _{s}, is a function of the contribution to fitness in a population size _{s} = 2^{2}/^{2}/w^{2}, then _{s} = 2^{2}/s_{s} expected for 1,000 alleles to produce the indicated %Variance Explained: as selection increases, less variance is explained because the allele frequencies drop. Alternatively, the solid green curve assumes a constant ^{−4} and shows the effect sizes consistent with variation explained, while the dashed green curve shows how increasing the selection pressure 5-fold reduces the amount of variance that can be maintained. Alleles explaining on average 0.01% of the variance under these scenarios could be consistent with substitution effects of 0.015 sdu, intermediate selection coefficients approximately 5×10^{−5} leading to minor allele frequencies about 0.33; or with ^{−4} and ^{−4}, p ~ 0.02, and so forth. sdu, standard deviation unit.

The latter finding is parsimoniously attributed to purifying selection: larger effect alleles are more likely to be deleterious and less likely to rise in frequency in the gene pool. It is easy to think about purifying selection as selection against deleterious variants that promote disease, but it turns out that for a substantial proportion of GWAS hits, the “risk” allele is either the more common one and/or the ancestral one. Both properties belie the simple interpretation that selection against disease is the major factor shaping the genetic architecture of traits. Rather, many consider stabilizing selection to be more prominent [

Nevertheless, a convenient framework for accommodating pleiotropy and purifying selection, first introduced by R.A. Fisher almost a century ago, is the geometric model [

A corollary of the geometric model is that under pleiotropy, the distribution of allelic effects influencing a trait of interest can be very different from that expected if selection acted only on that trait. Previous research has explored these distributions under various assumptions, but the new paper derives mathematical expectations from first principles and then checks the conclusions against the most recent GWAS conclusions for height [

It should be emphasized that strong selection is a relative term: scaled by the effective population size, selection differentials need only be greater than about 10^{−3} in a population of 10,000 individuals, which is thought to represent most of human history. Such a differential is much smaller, for example, than de novo mutations that are causal in schizophrenia [

Simons et al [

genome-wide association study

quantitative trait loci

standard deviation unit