  In genome-wide prediction, independence of marker allele substitution effects
is typically assumed; however, since early stages of this technology it has
been known that nature points to correlated effects. In statistics, graphical
models have been identified as a useful and powerful tool for covariance
estimation in high dimensional problems and it is an area that has recently
experienced a great expansion. In particular, Gaussian concentration graph
models (GCGM) have been widely studied. These are models in which the
distribution of a set of random variables, the marker effects in this case, is
assumed to be Markov with respect to an undirected graph G. In this paper,
Bayesian (Bayes G and Bayes G-D) and frequentist (GML-BLUP) methods adapting
the theory of GCGM to genome-wide prediction were developed. Different
approaches to define the graph G based on domain-specific knowledge were
proposed, and two propositions and a corollary establishing conditions to find
decomposable graphs were proven. These methods were implemented in small
simulated and real datasets. In our simulations, scenarios where correlations
among allelic substitution effects were expected to arise due to various causes
were considered, and graphs were defined on the basis of physical marker
positions. Results showed improvements in correlation between phenotypes and
predicted breeding values and accuracies of predicted breeding values when
accounting for partially correlated allele substitution effects. Extensions to
the multiallelic loci case were described and some possible refinements
incorporating more flexible priors in the Bayesian setting were discussed. Our
models are promising because they allow incorporation of biological information
in the prediction process, and because they are more flexible and general than
other models accounting for correlated marker effects that have been proposed
previously.
