Fig 1.
Relationships between allele frequency, selection differential, effect size, and variance explained.
(A) The blue curve shows how the percent of variance explained varies as a function of minor allele frequency, p, namely %Variance Explained = 2p(1-p)a2. The curve assumes 1,000 alleles, each with an additive contribution, a, of 0.015 sdu’s (about 1 mm of human height). (B) Simons et al [2] demonstrate that for relatively strongly selected alleles, the variance explained per site, vs, is a function of the contribution to fitness in a population size N with degree of pleiotropy n. Specifically, vs = 2w2/nN, and because the selection coefficient s = a2/w2, then vs = 2a2/snN. The magenta curve approximates the expected selection coefficient consistent with a = 0.015 in a population with an effective size of 10,000 alleles affecting 10 traits, and vs 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 s = 10−4 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 a = 0.023, and s = 10−4 and p ~ 0.1; with a = 0.05, and s = 5 × 10−4, p ~ 0.02, and so forth. sdu, standard deviation unit.