292W Poster - Population Genetics
Wednesday June 08, 8:30 PM - 9:15 PM
A geometric relationship of F2, F3 and F4-statistics with Principal Component Analysis
Author: Benjamin Peter
Affiliation: MPI Evolutionary Anthropology
Keywords: Theory & Method Development
Principal Component Analysis (PCA) and F-statistics sensu Patterson are two of the most widely used population genetic tools to study human genetic variation. Here, I derive explicit connections between the two approaches and show that these two methods are closely related. F-statistics have a simple geometrical interpretation in the context of PCA, and orthogonal projections are a key concept to establish this link. I show that negative F3 corresponds to a circle on a PCA plot, and that F4 is related to an angle measurement. I illustrate my results on two examples, one of Western Eurasian, and one of global human diversity. In both examples, I find that the first few PCs are sufficient to approximate most F-statistics, and that PCA-plots are effective at predicting F-statistics. My results extend F-statistics to more continuous population models, moving towards a more complete descriptions of human genetic variation.