Since the AA population is admixed, standardization of the genotype matrix based on Equation (2) does not consider the different admixed proportions of different individuals. Recently, an estimator of genetic relationship matrix named REAP was proposed to adjust the allele frequency in the admixed population [27]. Specifically, instead of using a single allele frequency for all individuals, an individual-specific allele frequency is used to standardize the genotype matrix (4)wim=(gim−pim)2pim(1−pim),where pim is the expected allele frequency of individual i at the m-th marker. Let qm=[qm1,…,qmK]T denote the vector of K ancestral population-specific allele frequencies of the m-th marker, and ai=[ai1,…,aiK]T denote the proportion of ancestry for individual i. The expect allele frequency for individual i at the m-th marker is given by pim=aiTqm. For our data analysis, qm and ai were inferred using the ADMIXTURE software [2], with YRI and CEU data from HapMap used as the reference panel.
