The approach used in this work is similar to that of Yang et al.10, but instead of using genotypes to estimate genetic similarity we use the number of copies of local ancestry in an admixed population. A crucial element of our approach is that the phenotypic variation described by variation in local ancestry ( hγ2) is a function of all causal variation, not just that tagged by SNPs on the genotyping platform. This is because local ancestry tags both common and rare variation. To illustrate this approach we simulated 4 million unrelated admixed individuals from ancestral populations with genetic distance FSTC= 0.08 and an equal proportion of ancestry from each ancestral population θ = 0.5 (see Online Methods). Applying Haseman-Elston regression to regress the product of normalized phenotypes against genetic similarity of local ancestry, we observe a regression coefficient 0.033±0.007 ≈ 2FSTCθ(1−θ)h2= 0.032, corresponding to h2 = 0.83 (s.e. = 0.18) (Figure 1c). The Haseman-Elston regression used in generating these figures is for illustrative purposes (as in Figure 3 of [10]). In practice, we use a mixed model approach due to its lower standard errors10.
