We first construct a local ancestry based kinship matrix Kγ, which is constructed similarly to the genotype-based kinship matrix K in previous methods10, but with local ancestry substituted for genotypes at each SNP. We use a variance components approach to estimate the phenotypic variance explained by variation in local ancestry ( σγ2) and the residual phenotypic variance ( σε2)10,17. We included genome-wide ancestry proportion θ and the top five principal components as fixed effects when fitting the mixed model (see Online Methods). The heritability explained by local ancestry is given by hγ2=σγ2σγ2+σε2. Finally, to estimate h2, we use the formula hγ2 = 2FSTCθ(1−θ)h2, where FSTC is a specific measure of weighted allele frequency differences between ancestral populations at causal loci (see Online Methods). For dichotomous phenotypes we applied the same approach, but converted the observed scale estimates to a liability scale estimate of heritability using [18], and the published disease prevalence in African Americans. In our previous work11, this conversion was not possible because non-randomly ascertained individuals in multiple relatedness classes (e.g. siblings, first cousins, avuncular) were studied, and there
