One key debate on genomic control is whether Xgc2 follows a central or non-central chi-square distribution (Gorroochurn et al., 2006). For a truly admixed population with a positive Wright’s FST value, the variance of the allele frequency is Varp = p(1 − p)(FST − FST /N + 1/(2N)) (the inbreeding coefficient is assumed to be zero) (Weir, 1996), which is inflated by a factor (FST−FST /N+1/(2N)). This admixture-induced variance inflation cannot be accounted for by a simple sample size reduction, because even of the infinite sample limit the residual variance is still nonzero. At the infinite sample size limit, the variance inflation factor is equal to FST, which is why FST is also called the standardized measure of variance, or Wahlund’s variance (Cavalli-Sforza and Bodmer, 1971). The only way to reconcile the variance inflation and sample size reduction here is to set α = 1/(1+2(N−1)FST), i.e., the sample size reduction itself depends on sample size. All these issues in correcting admixed subpopulations are not problematic for our relative samples because we assume the allele frequency does not change from pedigree to pedigree.
