Despite the reality that I've cautioned against taking PCA plots too literally as Truth, unvarnished and without any interpretive juice needed, papers which rely on them are almost magnetically attractive to me. They transform complex patterns of variation which you are not privy to via your gestalt psychology into a two or at most three dimensional representation which can you can grok immediately. That is why History and Geography of Genes was so engrossing. You recognize patterns which were otherwise unrecognizable. But how you interpret those patterns, that's a wholly different matter. And how those patterns arise is also not something one can ignore.
First, let's start with an easy case. To the left is a PCA plot with four populations. Nigerians, East Asians (Chinese + Japanese), Europeans (whites from Utah), and finally, African Americans. The x-axis is the first principal component of variation, and the y-axis the second. That ...