Abstract
SUMMARY: A theoretical analysis of open nucleus breeding systems, in which there is some introduction of breeding females to the sire breeding nucleus, is presented. Numerical analysis of a discrete generation model shows that the rate of genetic gain may be increased by 10 to 15% by opening the nucleus when selection intensity in females is low. In sheep and beef cattle breeding the optimal structure would be to have about 10% of the population in the nucleus, to get half of the nucleus female replacements from the base population, and to use all nucleus-born females not needed as nucleus replacements for breeding in the base population. The genetic gain, however, is not very sensitive to variation in these parameters. The rate of inbreeding in such an open nucleus would be about half that in a closed nucleus of the same size.

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