Gaussian covariance graph models accounting for correlated marker effects in genome‐wide prediction

Several statistical models used in genome‐wide prediction assume uncorrelated marker allele substitution effects, but it is known that these effects may 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 data sets, 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 multi‐allelic loci case is straightforward.