{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T18:25:10Z","timestamp":1787595910875,"version":"build-2736575974"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2012,2,1]],"date-time":"2012-02-01T00:00:00Z","timestamp":1328054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,2,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>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.<\/jats:p>","DOI":"10.1534\/genetics.111.132647","type":"journal-article","created":{"date-parts":[[2012,2,16]],"date-time":"2012-02-16T12:16:05Z","timestamp":1329394565000},"page":"403-412","source":"Crossref","is-referenced-by-count":31,"title":["Genotype Probabilities at Intermediate Generations in the Construction of Recombinant Inbred Lines"],"prefix":"10.1093","volume":"190","author":[{"given":"Karl W","family":"Broman","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, Wisconsin 53706"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2012,2,1]]},"reference":[{"key":"2022011316233864300_bib1","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1101\/gr.111310.110","article-title":"Genetic analysis of complex traits in the emerging Collaborative Cross","volume":"21","author":"Aylor","year":"2011","journal-title":"Genome Res."},{"key":"2022011316233864300_bib2","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1534\/genetics.104.035212","article-title":"The genomes of recombinant inbred lines","volume":"169","author":"Broman","year":"2005","journal-title":"Genetics"},{"key":"2022011316233864300_bib3","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1093\/bioinformatics\/btg112","article-title":"R\/qtl: QTL mapping in experimental crosses","volume":"19","author":"Broman","year":"2003","journal-title":"Bioinformatics"},{"key":"2022011316233864300_bib4","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1214\/aoms\/1177706444","article-title":"A Markovian function of a Markov chain","volume":"29","author":"Burke","year":"1958","journal-title":"Ann. 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