Andres Legarra, Matias Bermann, Quanshun Mei, Ole F. Christensen
{"title":"Redefining and interpreting genomic relationships of metafounders","authors":"Andres Legarra, Matias Bermann, Quanshun Mei, Ole F. Christensen","doi":"10.1186/s12711-024-00891-w","DOIUrl":null,"url":null,"abstract":"Metafounders are a useful concept to characterize relationships within and across populations, and to help genetic evaluations because they help modelling the means and variances of unknown base population animals. Current definitions of metafounder relationships are sensitive to the choice of reference alleles and have not been compared to their counterparts in population genetics—namely, heterozygosities, FST coefficients, and genetic distances. We redefine the relationships across populations with an arbitrary base of a maximum heterozygosity population in Hardy–Weinberg equilibrium. Then, the relationship between or within populations is a cross-product of the form $${\\Gamma }_{\\left(b,{b}^{\\prime}\\right)}=\\left(\\frac{2}{n}\\right)\\left(2{\\mathbf{p}}_{b}-\\mathbf{1}\\right)\\left(2{\\mathbf{p}}_{{b}^{\\prime}}-\\mathbf{1}\\right)^{\\prime}$$ with $$\\mathbf{p}$$ being vectors of allele frequencies at $$n$$ markers in populations $$b$$ and $$b^{\\prime}$$ . This is simply the genomic relationship of two pseudo-individuals whose genotypes are equal to twice the allele frequencies. We also show that this coding is invariant to the choice of reference alleles. In addition, standard population genetics metrics (inbreeding coefficients of various forms; FST differentiation coefficients; segregation variance; and Nei’s genetic distance) can be obtained from elements of matrix $${\\varvec{\\Gamma}}$$ .","PeriodicalId":55120,"journal":{"name":"Genetics Selection Evolution","volume":null,"pages":null},"PeriodicalIF":3.6000,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Genetics Selection Evolution","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1186/s12711-024-00891-w","RegionNum":1,"RegionCategory":"农林科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AGRICULTURE, DAIRY & ANIMAL SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Metafounders are a useful concept to characterize relationships within and across populations, and to help genetic evaluations because they help modelling the means and variances of unknown base population animals. Current definitions of metafounder relationships are sensitive to the choice of reference alleles and have not been compared to their counterparts in population genetics—namely, heterozygosities, FST coefficients, and genetic distances. We redefine the relationships across populations with an arbitrary base of a maximum heterozygosity population in Hardy–Weinberg equilibrium. Then, the relationship between or within populations is a cross-product of the form $${\Gamma }_{\left(b,{b}^{\prime}\right)}=\left(\frac{2}{n}\right)\left(2{\mathbf{p}}_{b}-\mathbf{1}\right)\left(2{\mathbf{p}}_{{b}^{\prime}}-\mathbf{1}\right)^{\prime}$$ with $$\mathbf{p}$$ being vectors of allele frequencies at $$n$$ markers in populations $$b$$ and $$b^{\prime}$$ . This is simply the genomic relationship of two pseudo-individuals whose genotypes are equal to twice the allele frequencies. We also show that this coding is invariant to the choice of reference alleles. In addition, standard population genetics metrics (inbreeding coefficients of various forms; FST differentiation coefficients; segregation variance; and Nei’s genetic distance) can be obtained from elements of matrix $${\varvec{\Gamma}}$$ .
期刊介绍:
Genetics Selection Evolution invites basic, applied and methodological content that will aid the current understanding and the utilization of genetic variability in domestic animal species. Although the focus is on domestic animal species, research on other species is invited if it contributes to the understanding of the use of genetic variability in domestic animals. Genetics Selection Evolution publishes results from all levels of study, from the gene to the quantitative trait, from the individual to the population, the breed or the species. Contributions concerning both the biological approach, from molecular genetics to quantitative genetics, as well as the mathematical approach, from population genetics to statistics, are welcome. Specific areas of interest include but are not limited to: gene and QTL identification, mapping and characterization, analysis of new phenotypes, high-throughput SNP data analysis, functional genomics, cytogenetics, genetic diversity of populations and breeds, genetic evaluation, applied and experimental selection, genomic selection, selection efficiency, and statistical methodology for the genetic analysis of phenotypes with quantitative and mixed inheritance.