title: Genotype probabilities at intermediate generations in the construction of recombinant inbred lines.
abstract: The mouse Collaborative Cross (CC) is a panel of eight-way recombinant inbred lines: eight diverse parental strains are intermated, followed by repeated sibling mating, many times in parallel, to create a new set of inbred lines whose genomes are random mosaics of the genomes of the original eight strains. Many generations are required to reach inbreeding, and so a number of investigators have sought to make use of phenotype and genotype data on mice from intermediate generations during the formation of the CC lines (so-called pre-CC mice). The development of a hidden Markov model for genotype reconstruction in such pre-CC mice, on the basis of incompletely informative genetic markers (such as single-nucleotide polymorphisms), formally requires the two-locus genotype probabilities at an arbitrary generation along the path to inbreeding. In this article, I describe my efforts to calculate such probabilities. While closed-form solutions for the two-locus genotype probabilities could not be derived, I provide a prescription for calculating such probabilities numerically. In addition, I present a number of useful quantities, including single-locus genotype probabilities, two-locus haplotype probabilities, and the fixation probability and map expansion at each generation along the course to inbreeding.
authors.affiliation: Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, Wisconsin 53706, USA. kbroman@biostat.wisc.edu
authors.forename: Karl W
authors.initials: KW
authors.lastname: Broman
mesh_terms: D000818:Animals; D003433:Crosses, Genetic; D056426:Genetic Loci; D005838:Genotype; D007178:Inbreeding; D051379:Mice; D008815:Mice, Inbred Strains / Q000235:genetics*; D008962:Models, Theoretical; D011336:Probability; D014960:X Chromosome