On the Probabilities of Identity States in Permutable
Populations
C. Cannings
School of Mathematics and Statistics, University of Sheffield, Sheffield, United
Kingdom
American Journal of Human Genetics,
62:698-702 (March 1998)
Abstract
Génin and Clerget-Darpoux recently discussed the derivation of
the probabilities of identity states for populations in which there was
some degree of kinship, primarily to allow the extension of the
classical affected-sib-pair method to such populations. It is argued
here that their derivation makes certain assumptions that are valid only
for some very restricted population models and that are not needed
for an appropriate treatment. Here the probabilities of the identity
states of two individuals with a given genealogical relationship are
specified in terms of the kinship parameters of the underlying
population, from which the founders of the individuals' genealogy
have been randomly selected. It is argued that an appropriate
representation for a permutable population, one in which gene identity
does not depend on the pattern of genes across individuals, requires
three parameters. This representation is related to that of Génin and
Clerget-Darpoux and to that of Weir.
Allele-sharing linkage analysis