Three-tier open nucleus breeding schemes

Abstract

AbstractOptimum designs of three-tier open nucleus breeding schemes are evaluated deterministically by maximizing the equilibrium rate of genetic gain for two methods of selection. Methodology is developed for both restricted and unrestricted migration between tiers and incorporates the loss of variance due to selection. A formula is derived for calculating the asymptotic rate of inbreeding. In the extensive livestock industries, proportional improvements in the equilibrium rate of genetic gain of between 0·12 and 0·22 are possible over a closed nucleus if no restrictions are imposed on male and female migration between tiers. The value of the extra tier in an optimized three-tier open nucleus scheme is approximately 0-45 of the maximum proportional improvement of a two-tier open nucleus over a closed nucleus scheme. The optimum structure is to have approximately 1% and 10% of the population in the nucleus and multiplier respectively. With this optimum structure the asymptotic rate of inbreeding will be reduced to one-sixth of that in a closed nucleus. The effects of various factors on the optimum structure, genetic gain and inbreeding are examined. The advantage of a three-tier open nucleus scheme over a closed nucleus scheme can be reduced substantially if thesefactors are operating.