%0 Journal Article
%A Peter, Benjamin M.
%+ Genetic Diversity through Space and Time, Department of Evolutionary Genetics, Max Planck Institute for Evolutionary Anthropology, Max Planck Society
%T A geometric relationship of F2, F3 and F4-statistics with principal component analysis :
%G eng
%U https://hdl.handle.net/21.11116/0000-000A-7AD1-1
%R 10.1098/rstb.2020.0413
%7 2022-04-18
%D 2022
%8 06.06.2022
%* Review method: peer-reviewed
%X 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 for any pair of populations, any population that is admixed as determined by an F3-statistic will lie inside a circle on a PCA plot. Furthermore, the F4-statistic is closely related to an angle measurement, and will be zero if the differences between pairs of populations intersect at a right angle in PCA space. 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. Thus, while F-statistics are commonly understood in terms of discrete populations, the geometric perspective illustrates that they can be viewed in a framework of populations that vary in a more continuous manner.

This article is part of the theme issue â€˜Celebrating 50 years since Lewontin's apportionment of human diversityâ€™.
%J Philosophical Transactions of the Royal Society B: Biological Sciences
%V 377
%N 1852
%] 20200413
%I The Royal Society Publishing
%@ 0962-84361471-2970