title: The number of genotypic assignments on a genealogy. I. The method and simple examples.
abstract: This paper demonstrates how the number of possible genotypic assignments consistent with the rules of Mendelian genetics and with any known phenotypes can be calculated for an arbitrary genealogy. This is of interest both in the contest of the uses of the Metropolis algorithm for pedigree analysis and in its own right. Bounds on the number of states for certain regular and random genealogies are also obtained, and further results will be given in a later paper.
authors.affiliation: School of Mathematics and Statistics, University of Sheffield, UK.
authors.forename: N
authors.initials: N
authors.lastname: Camp
authors.forename: C
authors.initials: C
authors.lastname: Cannings
authors.forename: N
authors.initials: N
authors.lastname: Sheehan
mesh_terms: D000465:Algorithms; D005260:Female; D005821:Genetic Techniques; D005838:Genotype; D006801:Humans; D008297:Male; D008957:Models, Genetic; D009010:Monte Carlo Method; D010375:Pedigree