A spectral theory for Wright's inbreeding coefficients and related quantities.

Wright's inbreeding coefficient, FST, is a fundamental measure in population genetics. Assuming a predefined population subdivision, this statistic is classically used to evaluate population structure at a given genomic locus. With large numbers of loci, unsupervised approaches such as principa...

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Autores principales:	Olivier François, Clément Gain
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Genetics QH426-470
Acceso en línea:	https://doaj.org/article/4948100822404aa2a62b0247776ba3f0
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spelling	oai:doaj.org-article:4948100822404aa2a62b0247776ba3f02021-12-02T20:02:56ZA spectral theory for Wright's inbreeding coefficients and related quantities.1553-73901553-740410.1371/journal.pgen.1009665https://doaj.org/article/4948100822404aa2a62b0247776ba3f02021-07-01T00:00:00Zhttps://doi.org/10.1371/journal.pgen.1009665https://doaj.org/toc/1553-7390https://doaj.org/toc/1553-7404Wright's inbreeding coefficient, FST, is a fundamental measure in population genetics. Assuming a predefined population subdivision, this statistic is classically used to evaluate population structure at a given genomic locus. With large numbers of loci, unsupervised approaches such as principal component analysis (PCA) have, however, become prominent in recent analyses of population structure. In this study, we describe the relationships between Wright's inbreeding coefficients and PCA for a model of K discrete populations. Our theory provides an equivalent definition of FST based on the decomposition of the genotype matrix into between and within-population matrices. The average value of Wright's FST over all loci included in the genotype matrix can be obtained from the PCA of the between-population matrix. Assuming that a separation condition is fulfilled and for reasonably large data sets, this value of FST approximates the proportion of genetic variation explained by the first (K - 1) principal components accurately. The new definition of FST is useful for computing inbreeding coefficients from surrogate genotypes, for example, obtained after correction of experimental artifacts or after removing adaptive genetic variation associated with environmental variables. The relationships between inbreeding coefficients and the spectrum of the genotype matrix not only allow interpretations of PCA results in terms of population genetic concepts but extend those concepts to population genetic analyses accounting for temporal, geographical and environmental contexts.Olivier FrançoisClément GainPublic Library of Science (PLoS)articleGeneticsQH426-470ENPLoS Genetics, Vol 17, Iss 7, p e1009665 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Genetics QH426-470
spellingShingle	Genetics QH426-470 Olivier François Clément Gain A spectral theory for Wright's inbreeding coefficients and related quantities.
description	Wright's inbreeding coefficient, FST, is a fundamental measure in population genetics. Assuming a predefined population subdivision, this statistic is classically used to evaluate population structure at a given genomic locus. With large numbers of loci, unsupervised approaches such as principal component analysis (PCA) have, however, become prominent in recent analyses of population structure. In this study, we describe the relationships between Wright's inbreeding coefficients and PCA for a model of K discrete populations. Our theory provides an equivalent definition of FST based on the decomposition of the genotype matrix into between and within-population matrices. The average value of Wright's FST over all loci included in the genotype matrix can be obtained from the PCA of the between-population matrix. Assuming that a separation condition is fulfilled and for reasonably large data sets, this value of FST approximates the proportion of genetic variation explained by the first (K - 1) principal components accurately. The new definition of FST is useful for computing inbreeding coefficients from surrogate genotypes, for example, obtained after correction of experimental artifacts or after removing adaptive genetic variation associated with environmental variables. The relationships between inbreeding coefficients and the spectrum of the genotype matrix not only allow interpretations of PCA results in terms of population genetic concepts but extend those concepts to population genetic analyses accounting for temporal, geographical and environmental contexts.
format	article
author	Olivier François Clément Gain
author_facet	Olivier François Clément Gain
author_sort	Olivier François
title	A spectral theory for Wright's inbreeding coefficients and related quantities.
title_short	A spectral theory for Wright's inbreeding coefficients and related quantities.
title_full	A spectral theory for Wright's inbreeding coefficients and related quantities.
title_fullStr	A spectral theory for Wright's inbreeding coefficients and related quantities.
title_full_unstemmed	A spectral theory for Wright's inbreeding coefficients and related quantities.
title_sort	spectral theory for wright's inbreeding coefficients and related quantities.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/4948100822404aa2a62b0247776ba3f0
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A spectral theory for Wright's inbreeding coefficients and related quantities.

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