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A spectral theory for Wright’s inbreeding coefficients and related quantities
- Source :
- PLoS Genetics, PLoS Genetics, Public Library of Science, 2021, 17 (7), pp.e1009665. ⟨10.1371/journal.pgen.1009665⟩, PLoS Genetics, Vol 17, Iss 7, p e1009665 (2021)
- Publication Year :
- 2021
- Publisher :
- HAL CCSD, 2021.
-
Abstract
- 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.<br />Author summary Principal component analysis (PCA) is the most-frequently used approach to describe population genetic structure from large population genomic data sets. In this study, we show that PCA not only estimates ancestries of sampled individuals, but also computes the average value of Wright’s inbreeding coefficient over the loci included in the genotype matrix. Our result shows that inbreeding coefficients and PCA eigenvalues provide equivalent descriptions of population structure. As a consequence, PCA extends the definition of those coefficients beyond the framework of allelic frequencies. We give examples on how FST can be computed from ancient DNA samples for which genotypes are corrected for coverage, and in an ecological genomic example where a proportion of genetic variation is explained by environmental variables.
- Subjects :
- 0301 basic medicine
0106 biological sciences
Cancer Research
Heredity
Population genetics
QH426-470
01 natural sciences
Consanguinity
Matrix (mathematics)
Mathematical and Statistical Techniques
Statistics
Quantitative Biology::Populations and Evolution
Inbreeding
Genetics (clinical)
Statistic
Mathematics
Principal Component Analysis
0303 health sciences
education.field_of_study
Genome
Approximation Methods
Simulation and Modeling
Genomics
Quantitative Biology::Genomics
Population model
Physical Sciences
Principal component analysis
Research Article
Genotype
Population
Biology
Research and Analysis Methods
010603 evolutionary biology
03 medical and health sciences
Genetic variation
Genetics
Animals
Humans
Statistical Methods
education
Molecular Biology
Ecology, Evolution, Behavior and Systematics
Eigenvalues and eigenvectors
030304 developmental biology
Evolutionary Biology
[SDV.GEN.GPO]Life Sciences [q-bio]/Genetics/Populations and Evolution [q-bio.PE]
Population Biology
Models, Genetic
Biology and Life Sciences
Genetic Variation
Eigenvalues
Models, Theoretical
Algebra
Genetics, Population
030104 developmental biology
Linear Algebra
Genetic Loci
Multivariate Analysis
Genetic Polymorphism
Population Genetics
Subjects
Details
- Language :
- English
- ISSN :
- 15537390 and 15537404
- Database :
- OpenAIRE
- Journal :
- PLoS Genetics, PLoS Genetics, Public Library of Science, 2021, 17 (7), pp.e1009665. ⟨10.1371/journal.pgen.1009665⟩, PLoS Genetics, Vol 17, Iss 7, p e1009665 (2021)
- Accession number :
- edsair.doi.dedup.....3ee0c86f480edeaf071fbd6216f4eef6