Haplotype probabilities for multiple-strain recombinant inbred lines

Recombinant inbred lines (RIL) derived from multiple inbred strains can serve as a powerful resource for the genetic dissection of complex traits. The use of such multiple-strain RIL requires a detailed knowledge of the haplotype structure in such lines. Broman (2005) derived the two- and three-point haplotype probabilities for 2(n)-way RIL; the former required hefty computation to infer the symbolic results, and the latter were strictly numerical. We describe a simpler approach for the calculation of these probabilities, which allowed us to derive the symbolic form of the three-point haplotype probabilities. We also extend the two-point results for the case of additional generations of intermating, including the case of 2(n)-way intermated recombinant inbred populations (IRIP).