In the construction of recombinant inbred lines (RILs) from two divergent inbred parents certain genotype (or epigenotype) combinations may be functionally "incompatible" when brought together in the genomes of the progeny, thus resulting in sterility or lower fertility. Natural selection against these epistatic combinations during inbreeding can change haplotype frequencies and distort linkage disequilibrium (LD) relations between loci on the same or on different chromosomes. These LD distortions have received increased experimental attention, because they point to genomic regions that may drive a Dobzhansky-Muller type of reproductive isolation and, ultimately, speciation in the wild. Here we study the selection signatures of two-locus epistatic incompatibility models and quantify their impact on the genetic composition of the genomes of two-way RILs obtained by selfing. We also consider the biases introduced by breeders when trying to counteract the loss of lines by selectively propagating only viable seeds. Building on our theoretical results, we develop model-based maximum-likelihood (ML) tests that can be applied to multilocus RIL genotype data to infer the precise mode of incompatibility as well as the relative fitness of incompatible loci. We illustrate this ML approach in the context of two published Arabidopsis thaliana RIL panels. Our work lays the theoretical foundation for studying more complex systems such as RILs obtained by sibling mating and/or from multiparental crosses.