A mathematical approach to multiple genetic relationships

A fundamental concept in the treatment of genetic relationships is that of gene identity which first was introduced by Cotterman (1940). Based on this notion several measures of relationship evolved such as the inbreeding coefficient, the coefficient of kinship, and the identity coefficients; by means of these quantities joint and conditional phenotype probabilities could be derived. This paper is an attempt at a general mathematical treatment of genetic relationships: Identity states are defined for any number of individuals, a method is given for the calculation of the corresponding identity coefficients by means of generalized coefficients of kinship, and applications are emphasized.