title: Genome-Wide Association Studies with a Genomic Relationship Matrix: A Case Study with Wheat and Arabidopsis.
abstract: Standard genome-wide association studies (GWAS) scan for relationships between each of p molecular markers and a continuously distributed target trait. Typically, a marker-based matrix of genomic similarities among individuals ( G: ) is constructed, to account more properly for the covariance structure in the linear regression model used. We show that the generalized least-squares estimator of the regression of phenotype on one or on m markers is invariant with respect to whether or not the marker(s) tested is(are) used for building G,: provided variance components are unaffected by exclusion of such marker(s) from G: The result is arrived at by using a matrix expression such that one can find many inverses of genomic relationship, or of phenotypic covariance matrices, stemming from removing markers tested as fixed, but carrying out a single inversion. When eigenvectors of the genomic relationship matrix are used as regressors with fixed regression coefficients, e.g., to account for population stratification, their removal from G: does matter. Removal of eigenvectors from G: can have a noticeable effect on estimates of genomic and residual variances, so caution is needed. Concepts were illustrated using genomic data on 599 wheat inbred lines, with grain yield as target trait, and on close to 200 Arabidopsis thaliana accessions.
authors: Department of Animal Sciences, University of Wisconsin-Madison, Wisconsin 53706 Department of Dairy Science, University of Wisconsin-Madison, Wisconsin 53706 Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Wisconsin 53706 Technical University of Munich School of Life Sciences Weihenstephan, Technical University of Munich, D-85354 Freising, Germany Institute for Advanced Study, Technical University of Munich, D-85748 Garching, Germany Bioinformatics Unit, Institut Pasteur de Montevideo, 11400, Uruguay gianola@ansci.wisc.edu.
authors: Daniel
authors: 0000-0001-8217-2348
authors: D
authors: Gianola
authors: Bioinformatics Unit, Institut Pasteur de Montevideo, 11400, Uruguay Instituto de Matemática y Estadística Rafael Laguardia, Facultad de Ingeniería, Universidad de la República, 11300 Montevideo, Uruguay.
authors: Maria I
authors: MI
authors: Fariello
authors: Bioinformatics Unit, Institut Pasteur de Montevideo, 11400, Uruguay.
authors: Hugo
authors: H
authors: Naya
authors: Technical University of Munich School of Life Sciences Weihenstephan, Technical University of Munich, D-85354 Freising, Germany Institute for Advanced Study, Technical University of Munich, D-85748 Garching, Germany.
authors: Chris-Carolin
authors: CC
authors: Schön
mesh_terms: D000465:Algorithms; D017360:Arabidopsis / Q000235:genetics*; D005819:Genetic Markers; D018745:Genome, Plant; D055106:Genome-Wide Association Study / Q000379:methods; D023281:Genomics / Q000379:methods; D040582:Inheritance Patterns; D008957:Models, Genetic; D015233:Models, Statistical; D010641:Phenotype; D040641:Quantitative Trait Loci; D014908:Triticum / Q000235:genetics*
chemical_list: D005819:Genetic Markers
keywords: GWAS; genomic relationship; heritability; whole-genome regression