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Principal components analysis, PCA, is a statistical method commonly used in population genetics to identify structure in the distribution of genetic variation across geographical location and ethnic background. However, while the method is often used to inform about historical demographic processes, little is known about the relationship between fundamental demographic parameters and the projection of samples onto the primary axes. Here I show that for SNP data the projection of samples onto the principal components can be obtained directly from considering the average coalescent times between pairs of haploid genomes. The result provides a framework for interpreting PCA projections in terms of underlying processes, including migration, geographical isolation, and admixture. I also demonstrate a link between PCA and Wright's f(st) and show that SNP ascertainment has a largely simple and predictable effect on the projection of samples. Using examples from human genetics, I discuss the application of these results to empirical data and the implications for inference.

Original publication

DOI

10.1371/journal.pgen.1000686

Type

Journal article

Journal

PLoS genetics

Publication Date

16/10/2009

Volume

5

Addresses

Department of Statistics, University of Oxford, Oxford, United Kingdom. mcvean@stats.ox.ac.uk

Keywords

Humans, Genetics, Population, Polymorphism, Single Nucleotide, Principal Component Analysis, Genealogy and Heraldry