3-TIER OPEN NUCLEUS BREEDING SCHEMES

Optimum designs of three-tier open nucleus breeding schemes are evalua ted deterministically by maximizing the equilibrium rate of genetic ga in for two methods of selection. Methodology is developed for both res tricted and unrestricted migration between tiers and incorporates the loss of variance due to selection. A formula is derived for calculatin g the asymptotic rate of inbreeding. In the extensive livestock indust ries, proportional improvements in the equilibrium rate of genetic gai n of between 0.12 and 0.22 are possible over a closed nucleus if no re strictions are imposed on male and female migration between tiers. The value of the extra tier in an optimized three-tier open nucleus schem e is approximately 0.45 of the maximum proportional improvement of a t wo-tier open nucleus over a closed nucleus scheme. The optimum structu re is to have approximately 1% and 10% of the population in the nucleu s and multiplier respectively. With this optimum structure the asympto tic rate of inbreeding will be reduced to one-sixth of that in a close d nucleus. The effects of various factors on the optimum structure, ge netic gain and inbreeding are examined. The advantage of a three-tier open nucleus scheme over a closed nucleus scheme can be reduced substa ntially if these factors are operating.