Applications of Graphical Models in Quantitative Genetics and Genomics

In this chapter, we provide a brief introduction about graphical models, with an emphasis on Bayesian networks, and discuss some of their applications in genetics and genomics studies with agricultural and livestock species. First, some key definitions regarding stochastic graphical models are provided, as well as basic principles of inference related to graphical structure and model parameters. Next is a discussion of some examples of applications, which include prediction of complex traits using genomic information or other correlated traits as well as the investigation of the flow of information from DNA polymorphisms to endpoint phenotypes, including intermediate phenotypes such as gene expression. A first example with prediction refers to the forecasting of total egg production in quails using early expressed traits (such as weekly body weight, partial egg production, and egg quality traits) as explanatory variables to support decision making (e.g., earlier culling decisions) in production/breeding systems. An additional example uses genomic information for the estimation of genetic merit of selection candidates for genetic improvement of economically important traits. An example with causal inference deals with the network underlying carcass fat deposition and muscularity in pigs by jointly modeling phenotypic, genotypic, and transcriptomic data. Some additional applications of Bayesian networks and other graphical model techniques are highlighted as well, including multitrait quantitative trait loci (QTL) analysis and structural equation models with latent variables. It is shown that graphical models such as Bayesian networks offer a powerful and insightful approach both for prediction and for causal inference, with a myriad of applications in the areas of genetics and genomics, and the study of complex phenotypic traits in agriculture.