In an admixed population, the expected allele frequency of an individual is a linear mix of the frequencies in the parental populations. Unless the admixture is ancient—in which case the PCA methods will fail as everyone will have the same ancestry proportion—then the mixing weights will vary by individual. Because of the linearity, admixture does not change the axes of variation, or, more exactly, the number of “large” eigenvalues of the covariance is unchanged by adding admixed individuals, if the parental populations are already sampled. Thus, for example, if there are two founding populations, admixed individuals will have coordinates along a line joining the centers of the founding populations.
