Under neutral drift, the difference (p 1−p 2) between observed allele frequencies of two populations at a given locus can be approximated as a normal distribution with mean 0 and variance p(1−p)(2F ST+1/N 1+1/N 2), where F ST is the genetic distance between the two populations, N 1 and N 2 are total allele counts in each population, and p is the ancestral allele frequency that can be approximated as the average of the two observed allele frequencies [37]. We note that this null model extends to the case of admixture, which simply scales F ST by the square of the admixture coefficient. It follows that (p 1−p 2)2/[p(1−p)(2F ST+1/N 1+1/N 2)] is χ2 distributed with 1 degree of freedom (d.o.f.). In fact, one can simply compute (p 1−p 2)2/[p(1−p)] divided by its mean across SNPs, avoiding complications involving the effective sample size in the case of related samples. In these computations we excluded SNPs with minor allele frequencies p<0.05 to minimize deviations from the normality assumption. An excess of large values of the χ2 statistic indicates deviations from the null model, suggesting the action of natural selection.
