% pubman genre = article
@article{item_3384238,
title = {{A geometric relationship of F2, F3 and F4-statistics with principal component analysis}},
author = {Peter, Benjamin M.},
language = {eng},
issn = {0962-8436; 1471-2970},
doi = {10.1098/rstb.2020.0413},
publisher = {The Royal Society Publishing},
year = {2022},
date = {2022-06-06},
abstract = {{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.{\textless}br{\textgreater}{\textless}br{\textgreater}This article is part of the theme issue {\textquoteleft}Celebrating 50 years since Lewontin{\textquotesingle}s apportionment of human diversity{\textquoteright}.}},
journal = {{Philosophical Transactions of the Royal Society B: Biological Sciences}},
volume = {377},
number = {1852},
eid = {20200413},
}