Graphical Model Selection to Infer the Partial Correlation Network of Allelic Effects in Genomic Prediction With an Application in Dairy Cattle

We addressed genomic prediction accounting for partial correlation of marker effects, which entails the estimation of the partial correlation network/graph (PCN) and the precision matrix of an unobservable m-dimensional random variable. To this end, we developed a set of statistical models and methods by extending the canonical model selection problem in Gaussian concentration, and directed acyclic graph models. Our frequentist formulations combined existing methods with the EM algorithm and were termed Glasso-EM, Concord-EM and CSCS-EM, whereas our Bayesian formulations corresponded to hierarchical models termed Bayes G-Sel and Bayes DAG-Sel. We implemented our methods in a real bull fertility dataset and then carried out gene annotation of seven markers having the highest degrees in the estimated PCN. Our findings brought biological evidence supporting the usefulness of identifying genomic regions that are highly connected in the inferred PCN. Moreover, a simulation study showed that some of our methods can accurately recover the PCN (accuracy up to 0.98 using Concord-EM), estimate the precision matrix (Concord-EM yielded the best results) and predict breeding values (the best reliability was 0.85 for a trait with heritability of 0.5 using Glasso-EM).