  Several statistical models used in genome-wide prediction assume independence
of marker allele substitution effects, but it is known that these effects might
be correlated. In statistics, graphical models have been identified as a useful
tool for covariance estimation in high dimensional problems and it is an area
that has recently experienced a great expansion. In Gaussian covariance graph
models (GCovGM), the joint distribution of a set of random variables is assumed
to be Gaussian and the pattern of zeros of the covariance matrix is encoded in
terms of an undirected graph G. In this study, methods adapting the theory of
GCovGM to genome-wide prediction were developed (Bayes GCov, Bayes GCov-KR and
Bayes GCov-H). In simulated and real datasets, improvements in correlation
between phenotypes and predicted breeding values and accuracies of predicted
breeding values were found. Our models account for correlation of marker
effects and permit to accommodate general structures as opposed to models
proposed in previous studies which consider spatial correlation only. In
addition, they allow incorporation of biological information in the prediction
process through its use when constructing graph G, and their extension to the
multiallelic loci case is straightforward.
