Detecting epistatic selection with partially observed genotype data by using copula graphical models

In cross-breeding experiments it can be of interest to see whether there are any synergistic effects of certain genes. This could be by being particularly useful or detrimental to the individual. This type of effect involving multiple genes is called epistasis. Epistatic interactions can affect growth, fertility traits or even cause complete lethality. However, detecting epistasis in genomewide studies is challenging as multiple-testing approaches are underpowered. We develop a method for reconstructing an underlying network of genomic signatures of high dimensional epistatic selection from multilocus genotype data. The network captures the conditionally dependent short- and long-range linkage disequilibrium structure and thus reveals 'aberrant' marker-marker associations that are due to epistatic selection rather than gametic linkage. The network estimation relies on penalized Gaussian copula graphical models, which can account for a large number of markers p and a small number of individuals n. We demonstrate the efficiency of the proposed method on simulated data sets as well as on genotyping data in Arabidopsis thaliana and maize.