N. Camp et al., THE NUMBER OF GENOTYPIC ASSIGNMENTS ON A GENEALOGY .1. THE METHOD ANDSIMPLE EXAMPLES, IMA journal of mathematics applied in medicine and biology, 11(2), 1994, pp. 95-106
This paper demonstrates how the number of possible genotypic assignmen
ts consistent with the rules of Mendelian genetics and with any known
phenotypes can be calculated for an arbitrary genealogy. This is of in
terest both in the context of the uses of the Metropolis algorithm for
pedigree analysis and in its own right. Bounds on the number of state
s for certain regular and random genealogies are also obtained, and fu
rther results will be given in a later paper.