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Prediction and evaluation of response to selection with overlapping generations

Published online by Cambridge University Press:  02 September 2010

William G. Hill
William G. Hill
Affiliation:
Institute of Animal Genetics, West Mains Road, Edinburgh EH9 3JN
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Summary

In a population in which generations overlap the improvement in performance in successive years resulting from a single year of selection is not constant, for the genes from a group of selected individuals may take many years to pass through the population. A formal method is developed for predicting responses and discounted returns from improvement in populations with overlapping generations including, if necessary, generations of multiplication of breeding stock.

The method is based on a matrix which specifies the passage of genes between the different age groups and sexes. Simple matrix operations can be used to compute the proportion of genes in animals of both sexes and each age in the population at any time which derive from a group of selected animals at an earlier time. The response produced by these selected animals equals the product of their genetic selection differential and the proportion of genes deriving from them. Comparisons are made between responses predicted using this theory and the classical theory of uniform rates of response, and a method is given for computing the time lag of genes passing through the population.

The results are extended to enable computation of discounted returns from improvement.

Type
Research Article
Information
Animal Production , Volume 18 , Issue 2 , April 1974 , pp. 117 - 139
Copyright
Copyright © British Society of Animal Science 1974

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References

REFERENCES

Bichard, M. 1971. Dissemination of genetic improvement through a livestock industry. Anim. Prod. 13: 401–411.Google Scholar
Bichard, M., Pease, A. H. R., Swales, P. H. and Ozkutuk, K. 1973. Selection in a population with overlapping generations. Anim. Prod. 17: 215–227.Google Scholar
Dickerson, G. E. and Hazel, L. N. 1944. Effectiveness of selection on progeny performance as a supplement to earlier culling in livestock. J. agr. Res. 69: 459–476.Google Scholar
Hill, W. G. 1971. Investment appraisal for national breeding programmes. Anim. Prod. 13: 37–50.Google Scholar
Hill, W. G. 1972. Effective size of populations with overlapping generations. Theor. Pop. Biol. 3: 278–289.CrossRefGoogle ScholarPubMed
Hinks, C. J. M. 1970. The selection of dairy bulls for A.I. Anim. Prod. 12: 569–576.Google Scholar
Hinks, C. J. M. 1971. The genetic and financial consequences of selection amongst dairy bulls in artificial insemination. Anim. Prod. 13: 209–218.Google Scholar
Hinks, C. J. M. 1972. The effects of continuous sire selection on the structure and age composition of dairy cattle populations. Anim. Prod. 15: 103–110.Google Scholar
Kemeny, J. G. and Snell, J. L. 1960. Finite Markov Chains, van Nostrand, Princeton, New Jersey.Google Scholar
Leslie, P. H. 1945. On the use of matrices in certain population mathematics. Biometrika 33: 183–212.CrossRefGoogle ScholarPubMed
Poutous, M. and Vissac, B. 1962. Recherche thtoretique des conditions de rentabilitS maximum de l'epreuve de descendance des tauraux d'insemination artiflcielle. Annls Zootech. 11: 233–256.CrossRefGoogle Scholar
Rendel, J. M. and Robertson, A. 1950. Estimation of genetic gain in milk yield by selection in a closed herd of dairy cattle. J. Genet. 50: 1–8.CrossRefGoogle Scholar
Searle, S. R. 1961. Estimating herd improvement from selection programmes. J. Dairy. Sci. 44: 1103–1112.CrossRefGoogle Scholar
Van Vleck, L. D. 1964. Sampling the young sire in artificial insemination. J. Dairy. Sci. 47: 441–446.CrossRefGoogle Scholar