This is an issue for our TW techniques, but not for PCA as such. Indeed, on this dataset the correlation of our principal eigenvector with the estimated European ancestry for each individual recovered by the admixture analysis program ANCESTRYMAP [12] is a remarkable .995 (STRUCTURE produces similar results). ANCESTRYMAP has complex modeling of admixture LD, and was also provided with parental allele frequencies, but did no better than the simple PCA. (There is an issue of interpretation here: the leading eigenvector is almost perfectly correlated with ancestry, but to infer actual ancestry proportions an affine transform must be applied, translating and scaling the values. In practice, some parental allele frequencies will be needed to determine the appropriate transform. A similar issue arises with STRUCTURE if parental frequencies are unknown.)
