  Recombinant Inbred Lines derived from divergent parental lines can display
extensive segregation distortion and long-range linkage disequilibrium (LD)
between distant loci. These genomic signatures are consistent with epistatic
selection during inbreeding. Epistatic interactions affect growth and fertility
traits or even cause complete lethality. Detecting epistasis is challenging as
multiple testing approaches are under-powered and true long-range LD is
difficult to distinguish from drift.
  Here we develop a method for reconstructing an underlying network of genomic
signatures of high-dimensional epistatic selection from multi-locus genotype
data. The network captures the conditionally dependent short- and long-range LD
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 accounts for a
large number of markers p and a small number of individuals n.
  A multi-core implementation of our algorithm makes it feasible to estimate
the graph in high-dimensions also in the presence of significant portions of
missing data. We demonstrate the efficiency of the proposed method on simulated
datasets as well as on genotyping data in A.thaliana and maize. In addition, we
implemented the method in the R package netgwas which is freely available at
https://CRAN.R-project.org/package=netgwas.
