From statistical point of view it is just an application of Karl Broman's R/qtl package. From biological point of view it is "mystery of mysteries", the term used by Darwin to refer to the mechanism by which two groups of animals become genetically incompatible.
A house mouse is a nice model of that phenomenon because its subspecies diverged relatively recently and you can still force them to breed if you want to. However, as described in the paper, male offspring of certain combination of parents are then unable to reproduce. Our long-term goal is to describe what is behind this sterility.
Two "ingredients" are already known: Prdm9 gene on Chr17 and "something" hidden in 4.5Mb region on ChrX. If any these two are not present in the required combination of alleles, then the mouse is fertile (or at least has normal testes weight and sperm count). However, as we know, Chr17 and ChrX are not the full story. There is some "secret ingredient(s)" needed to reach the full sterility and we have been unsuccessful in mapping it. Maybe there are just too many genes involved, i.e. our tests are underpowered.
The second possible explanation (submitted to CTC Meeting in Paris) is that the "secret ingredient(s)" might not to be a gene or anything you can assign to specific genomic location. Prdm9 (Chr17) is famous for playing role in a genetic recombination, shuffling of genetic information during sperm/eggs production. And recently, we verified that 4.5Mb ChrX region is also taking part in this process. Specifically, Prdm9 determines the location of recombination events and ChrX region influences the recombination frequency. So, is the "secret ingredient" mobile elements, repetitive sequences, heterochromatin or Bigfoot? One day we hope to know.
- Prdm9 as the speciation (=sterility) gene - Mihola et al.: A Mouse Speciation Gene Encodes a Meiotic Histone H3 Methyltransferase, Science (2008).
- Prdm9 and its role in recombination - Baudat et al.: PRDM9 Is a Major Determinant of Meiotic Recombination Hotspots in Humans and Mice, Science (2010).
- Sterility QTL on ChrX - Storchova et al.: Genetic analysis of X-linked hybrid sterility in the house mouse, Mammalian Genome (2004).
- Major recombination QTL on ChrX - Dumont and Payseur: Genetic Analysis of Genome-Scale Recombination Rate Evolution in House Mice, PLOS Genetics (2012).