TY - JOUR
T1 - Genome-wide association studies with a genomic relationship matrix
T2 - A case study with wheat and arabidopsis
AU - Gianda, Daniel
AU - Fariello, Maria I.
AU - Naya, Hugo
AU - Schön, Chris Carolin
N1 - Publisher Copyright:
© 2016 Gianola et al.
PY - 2016
Y1 - 2016
N2 - Standard genome-wide association studies (GWAS) scan for relationships between each of ρ 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.
AB - Standard genome-wide association studies (GWAS) scan for relationships between each of ρ 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.
KW - GWAS
KW - Genomic relationship
KW - Heritability
KW - Whole-genome regression
UR - http://www.scopus.com/inward/record.url?scp=84994579851&partnerID=8YFLogxK
U2 - 10.1534/g3.116.034256
DO - 10.1534/g3.116.034256
M3 - Article
C2 - 27520956
AN - SCOPUS:84994579851
SN - 2160-1836
VL - 6
SP - 3241
EP - 3256
JO - G3: Genes, Genomes, Genetics
JF - G3: Genes, Genomes, Genetics
IS - 10
ER -