Abstract
An inbreedingmatrix (F) is defined for open nucleus breeding schemes, both with overlapping generations and with different selection differentials for male and female, for the nucleus and the base population and for the sex of progenies.Formula for inbreeding coefficient by year basis is derived using the inbreeding matrix.An approximate inbreeding coefficient is also expressed by adding a matrix P which specifies the passage of genes to the inbreeding matrix, and further a formula for annual rate of inbreeding is provided.In numerical example, inbreeding coefficients are presented for the population in which sires are all selected from progeny born in nucleus and the sires have three different selection differentials for those used in nucleus to produce male progenies, female progenies and for those used in the base population.
