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[…] We estimated the ancestral similarity matrix A for all unrelated individuals in a study using the local ancestry estimates for all autosomal loci. Let xij represent the local ancestry, i.e., 0, 1, or 2 chromosomes of African ancestry for the jth of M individuals at the ith of N loci. For the jth individual, the genome-wide average of local ancestry 12N∑i=1Nxij is known as global ancestry or the individual admixture proportion. For the HUFS data set, the mean global ancestry was 79.9% ± 11.6%. Similarly, for the ARIC data set, the mean global ancestry was 82.2% ± 10.3%. At the ith locus, let pi=12M∑j=1Mxij. As expected, the trace of ancestry by locus is nearly constant across the autosomes (Figure ), indicating robustness to natural selection acting at specific loci.We consider three estimators of pairwise ancestral similarity. First, at a causal locus i, we can estimate pairwise ancestral similarity between the jth and kth individuals based on identity in state:Second, we can estimate pair-wise ancestral similarity for use in **GCTA** (Yang et al., ) asFor both studies, the number of genotyped SNPs is more than sufficient to yield 100% coverage of switches in local ancestry in African Americans (Shriner et al., ), providing 100% coverage of chromosomal segments and all genetic variation therein. Therefore, corrections for linkage disequilibrium used for genotype data are unnecessary with local ancestry data.Third, we can estimate pair-wise ancestral similarity as Ajk=1N∑i=1N(xij-2pi)(xik-2pi). We then estimate the proportion of phenotypic variance explained by local ancestry using **GEMMA** (Zhou and Stephens, ). It is important to note that estimation of similarity in GCTA includes centering by 2pi and scaling by 2pi(1 − pi); this scaling induces an inverse relationship between pi and effect size (Speed et al., ). In contrast, our estimation of similarity using GEMMA includes centering but not scaling, which a priori is more appropriate given that mean local ancestry estimates do not follow an exponential distribution as do allele frequencies but are expected to follow a uniform distribution (Figure ). […]