Identity coefficients and covariances between relatives in a parent-offspring inbreeding system

A one-locus "operator" for a younger parent-offspring inbreeding system is obtained by a generation matrix method in which 14 "classes" of matings are defined. The eigenvalues and a set of eigenvectors for the generation matrix and, also, the general solution for the frequencies of mating classes among descendants of an original mating of genotypes ab x cd are given. The operator gives the genotypic array of descendants of a given mating an arbitrary number of generations later. Using this operator, an algorithm is developed for calculating identity coefficients between any two relatives in a possibly branching younger parent-off spring mating system. Application to obtaining covariances between relatives for a one-locus model is illustrated.