Heritability is the ratio of genetic variance to the sum of genetic and environmental variance h2=σg2σg2+σe2. In this case we are defining these elements with respect to an admixed population. For a given phenotype, both σg2 and σe2 can vary between the ancestral European and African populations. For example, σg2 will vary with ancestry if the minor allele frequency at causal variants is systematically larger in one of the two populations. It is also possible for ancestry to be associated with environmental factors. In this case, by conditioning on genome-wide ancestry, our method will remove the environmental variance that can be explained by ancestry and estimate the heritability of the component of phenotype that cannot be predicted by genome-wide ancestry, thereby increasing the heritability estimate.
