RT Journal Article
SR Electronic
T1 Genome-Wide Association Studies with a Genomic Relationship Matrix: A Case Study with Wheat and *Arabidopsis*
JF G3: Genes|Genomes|Genetics
FD Genetics Society of America
SP 3241
OP 3256
DO 10.1534/g3.116.034256
VO 6
IS 10
A1 Gianola, Daniel
A1 Fariello, Maria I.
A1 Naya, Hugo
A1 SchÃ¶n, Chris-Carolin
YR 2016
UL http://www.g3journal.org/content/6/10/3241.abstract
AB 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.