A novel selection algorithm for maximising genetic response while constraining the rate of inbreeding is presented. This method uses an augmented numerator relationship matrix and represents an improvement on previous procedures where the constraint is applied to an increase in the inbreeding coefficient. It is shown that the proposed method controls inbreeding by maintaining the squared genetic contributions at a constant value. The regression of the long-term contributions on the assigned mating proportions was close to one and the ratio of the sum of squared contributions to the sum of squared mating proportions was greater than one, even when the heritability was one. It was concluded that the known ideal solution to maximise genetic gain under constrained inbreeding is in general unattainable, at least from using this approach.

B. Grundy, Beatriz Villanueva, John A Woolliams

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume 25: Lactation; growth and efficiency; meat quality; role of exotic breeds in the tropics; design of village breeding programmes;, , 355–358, 1998
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