Hopefully by now the image to the left is familiar to you. It’s from a paper in Human Genetics, Self-reported ethnicity, genetic structure and the impact of population stratification in a multiethnic study. The paper is interesting in and of itself, as it combines a wide set of populations and puts the focus on the extent of disjunction between self-identified ethnic identity, and the population clusters which fall out of patterns of genetic variation. In particular, the authors note that the “Native Hawaiian” identification in Hawaii is characterized by a great deal of admixture, and within their sample only ~50% of the ancestral contribution within this population was Polynesian (the balance split between European and Asian). The figure suggests that subjective self assessment of ancestral quanta is generally accurate, though there are a non-trivial number of outliers. Dienekes points out that the same dynamic holds (less dramatically) for Europeans and Japanese populations within their data set.
All well and good. And I like these sorts of charts because they’re pithy summations of a lot of relationships in a comprehensible geometrical fashion. But they’re not reality, they’re a stylized representation of a slice of reality, abstractions which distill the shape and processes of reality. More precisely the x-axis is an independent dimension of correlations of variation across genes which can account for ~7% of the total population variance. This is the dimension with the largest magnitude. The y-axis is the second largest dimension, accounting for ~4%. The magnitudes decline precipitously as you descend down the rank orders of the principle components. The 5th component accounts for ~0.2% of the variance.
The first two components in these sorts of studies usually conform to our intuitions, and add a degree of precision to various population scale relations. Consider this supplement chart from a 2008 paper (I’ve rotated and reedited for clarity):