We assigned each individual to a specific geographic location by fitting independent linear models for latitude and longitude as predicted jointly by PC1 and PC2. We used the rotated PC1 and PC2 scores because these more strongly correlate with latitude and longitude (see main text). Specifically, we use the linear models: x=βx1u1+βx2u2+βx11u21+βx22u22+βx12u1u2+ε y=βy1u1+βy2u2+βy11u21+βy22u22+βy12u1u2+ε where x and y are vectors containing the longitude and latitude, respectively, of each individual, u1 and u2 are vectors containing the rotated PC1 and PC2 scores, respectively, for each individual (that is, u1 = g(θ, v1, v2), u2 = h(θ, v1, v2), where θ = −16 degrees), β coefficients are regression coefficients, and ε represents residual error.
