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Asymptotic response to selection on best linear unbiased predictors of breeding values

Published online by Cambridge University Press:  02 September 2010

J. C. M. Dekkers
J. C. M. Dekkers
Affiliation:
Centre for Genetic Improvement of Livestock, Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario N1G 2W1, Canada
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Abstract

Formulas were derived to predict asymptotic response to selection on best linear unbiased predictors (BLUP) of breeding values that account for selection-induced gametic phase disequilibrium, also known as the ‘Bulmer’ effect. Breeding programmes in populations of infinite size and with discrete generations were considered. For two-path breeding programmes with equal male and female accuracy of selection, relative reductions in response due to gametic phase disequilibrium were independent of heritability. Reductions in response depended only on intensities of selection and ranged from 0·22 to 0·27 when selected proportions were less than 04 for both males and females. With unequal accuracy of males and females, relative reductions in response depended on the ratio of accuracies, in addition to selection intensities. For given selection intensities, reductions were up to proportionately 0·08 larger with unequal accuracies than reductions obtained for equal accuracies. Relative reductions in response for breeding programmes with four paths of selection depended on intensity and accuracy of selection in each path, but were within a range similar to that observed for two-path programmes. Gametic phase disequilibrium will, therefore, not greatly affect ranking and relative differences among alternative breeding programmes.

Gametic phase disequilibrium had a larger effect on response with selection on BLUP than on phenotype, which is largely due to larger relative reductions in accuracy of selection with BLUP. Despite larger relative reductions, asymptotic response to selection on BLUP is expected to be larger than selection on phenotype.

Keywords

best linear unbiased predictionbreeding valuegenetic varianceselection responses
Type
Research Article
Information
Animal Production , Volume 54 , Issue 3 , June 1992 , pp. 351 - 360
Copyright
Copyright © British Society of Animal Science 1992

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References

Belonsky, G. M. and Kennedy, B. W. 1988. Selection on individual phenotype and best linear unbiased prediction of breeding value in a closed swine her. Journal of Animal Science. 66: 1124–1131.CrossRefGoogle Scholar
Bulmer, M. G. 1971. The effect of selection on genetic variabilit. American Naturalist. 105: 201–211.CrossRefGoogle Scholar
Bulmer, M. G. 1980. The mathematical theory of quantitative genetics. Clarendon Press, Oxford.Google Scholar
Cochran, W. G. 1951. Improvement by means of selection. Proceedings of the 2nd Berkeley symposium on mathematics, statistics and probability (ed. Neyman, J.), pp. 449–470. University of California Press, Berkeley.Google Scholar
Dekkers, J. C. M. 1990. Reduction of response to selection due to linkage disequilibrium with selection on best linear unbiase predictors. Proceedings 4th world congress of genetics applied to livestock production, vol. 13, pp. 277–280.Google Scholar
Dekkers, J. C. M. and Shook, G. E. 1990. A semi-stochastic model for simulation of genetic progress in a large dairy cattle population. Journal of Animal Breeding and Genetics. 107: 321–339.CrossRefGoogle Scholar
Falconer, D. S. 1989. Introduction to quantitative genetics. 3rd ed. Longman, London.Google Scholar
Fimland, E. 1979. The effect of selection on additive genetic parameter. Zeitschrift fur Tierzuchtung und Zuchtungsbiologie. 96: 120–134.CrossRefGoogle Scholar
Gomez-Raya, L. and Burnside, E. B. 1990. Linkage disequilibrium effects on genetic variance, heritability and response after repeated cycles of selectio. Theoretical and Applied Genetics. 79: 568–574.CrossRefGoogle Scholar
Henderson, C. R. 1973. Sire evaluation an d genetic trends. Proceedings of the animal breeding and genetics symposium in honor of Dr J. L. Lush, pp. 10–41. American Society of Animal Science and American Dairy Science Association, Champaign, II.Google Scholar
Henderson, C. R. 1975. Best linear unbiased estimation and prediction under a selection mode. Biometrics. 31: 423–447.CrossRefGoogle Scholar
Henderson, C. R. 1982. Best linear unbiase d prediction in populations that have undergone selection. Proceedings of the world congress of sheep and beef cattle breeding, New Zealand, vol. 1 (ed. Barton, R. A. and Smith, W. C.), pp. 191–201.Google Scholar
Henderson, C. R. 1988. Theoretical basis and computational methods for a number of different animal models. Journal of Dairy Science 71: suppl. 2, p. 1.CrossRefGoogle Scholar
Juga, J. and Maki-Tanila, A. 1987. Genetic change in nucleus breeding herds using embryo transfe. Acta Agriculturae Scandinavica. 37: 511–519.CrossRefGoogle Scholar
Kennedy, B. W. and SSrensen, D. A. 1987. Properties of mixed model methods for prediction of genetic merit. Proceedings of the 2nd international conference on quantitative genetics, Raleigh, NC, pp. 91–103.Google Scholar
Meyer, K. and Smith, C. 1990. Comparison of theoretical and simulated equilibrium genetic response rates with progeny testing in dairy cattl. Animal Production. 50: 207–212.Google Scholar
Nicholas, F. W. and Smith, C. 1983. Increased rates of genetic change in dairy cattle by embryo transfer and splittin. Animal Production. 36: 341–353.Google Scholar
Pearson, K. 1903. Mathematical contributions to the theory of evolution. XI. On the influence of natural selection on the variability and correlation of organs. Philosophical Transactions of the Royal Society London Series A. 200: 1–66.Google Scholar
Rendel, J. M. and Robertson, A. 1950. Estimation of genetic gain in milk yield by selection in a closed herd of dairy cattl. Journal of Genetics. 50: 1–9.CrossRefGoogle Scholar
Sorensen, D. A. 1988. Effect of selection index versus mixed model methods of prediction of breeding value on response o t selection in a simulated pig populatio. Livestock Production Science. 20: 135–148.CrossRefGoogle Scholar
Woolliams, J. A. 1990. Strategies to maximise selection progress in dairy cattle. Proceedings of the 4th world congress of genetics applied to livestock production, vol. 14, pp. 15–24.Google Scholar
Wray, N. R. and Hill, W. G. 1989. Asymptotic rates of response from index selectio. Animal Production. 49: 217–227.Google Scholar