Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES
Volume 377, Issue 1852, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rstb.2020.0413
Keywords
population structure; principal component analysis; F-statistics
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This article explores the relationship between principal component analysis (PCA) and F-statistics in studying human genetic variation. The author derives explicit connections between the two approaches and demonstrates that F-statistics can be interpreted geometrically in the context of PCA. The results show that PCA plots are effective at predicting F-statistics, providing a new perspective for understanding human genetic variation.
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 F-3-statistic will lie inside a circle on a PCA plot. Furthermore, the F-4-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 'Celebrating 50 years since Lewontin's apportionment of human diversity'.
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