Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-26T03:26:16.581Z Has data issue: false hasContentIssue false
  • English
  • Français

Prediction of asymptotic rates of response from selection on multiple traits using univariate and multivariate best linear unbiased predictors

Published online by Cambridge University Press:  02 September 2010

B. Villanueva ,
N. R. Wray  and
R. Thompson
B. Villanueva
Affiliation:
Scottish Agricultural College, West Mains Road, Edinburgh EH9 3JG
N. R. Wray
Affiliation:
Scottish Agricultural College, West Mains Road, Edinburgh EH9 3JG
R. Thompson
Affiliation:
AFRC Roslin Institute(Edinburgh), Research Station, Roslin, Midlothian EH25 9PS‡
Get access

Abstract

Predicted rate of genetic response for multiple trait breeding objectives from multivariate analyses is compared with that from univariate analyses for a range of breeding schemes, A selection index that approximates a multipl trait best linear unbiased prediction (BLUP) animal model is utilized. Changes in genetic parameters due to linkage disequilibrium generated by selection are accounted for. This study shows that asymptotic response in the aggregate breeding value, and its component traits, to selection on multivariate predictions, can easily be calculated from first generation responses, which use ancestral information. For two-path breeding schemes with equal accuracy for males and females, proportional reductions in responses depend only on selection intensity. In general, benefit from multivariate over univariate analyses is slightly smaller at the asymptote than in the first generation. Multivariate analyses give substantially more response than univariate analyses on untransformed data, when correlations between traits are high and when genetic and phenotypic correlations have opposite signs. The advantage of multivariate analyses decreases with increasing family size. When three random factors (additive genetic, common and individual environmental effects) are included in the model, the benefit of multivariate analysis is negligible if univariate analyses are performed on canonical traits. In this case, the advantage of multivariate analyses is never higher than 1% for all cases studied. These results are of particular relevance to the design of genetic evaluation programmes.

Keywords

best linear unbaised predictioncanonical analysislinkage disequilibriummultivariate analysisselection responses
Type
Research Article
Information
Animal Production , Volume 57 , Issue 1 , August 1993 , pp. 1 - 13
Copyright
Copyright © British Society of Animal Science 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, T. W. 1958. An introduction to multivariate statistical analysis. Wiley, New York.Google Scholar
Bulmer, M. G. 1971. The effect of selection on genetic variability. American Naturalist 105: 201–211.CrossRefGoogle Scholar
Bulmer, M. G. 1980. The mathematical theory of quantitative genetics. Clarendon Press, Oxford.Google Scholar
Crump, R. E. 1992. Quantitive genetic analysis of a commercial pig population undergoing selection. Ph.D. thesis, University of Edinburgh.Google Scholar
Dekkers, J. C. M. 1990. Reduction of response to selection due to linkage disequilibrium with selection on best linear unbiased predictors. Proceedings of the fourth world congress of genetics applied to livestock production, Edinburgh, vol. XIII, pp. 277–280.Google Scholar
Dekkers, J. C. M. 1992. Asymptotic response to selection on best linear unbiased predictors of breeding values. Animal Production 54: 351–360.Google Scholar
Fisher, R. A. 1918. The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edinburgh 52: 399–433.CrossRefGoogle Scholar
Gianola, D., Im, S. and Fernando, R. L. 1988. Prediction of breeding value under Henderson's selection model: a revisitation. Journal of Dairy Science 71: 2790–2798.CrossRefGoogle Scholar
Gjedrem, T. 1967. Selection indexes compared with single trait selection. I. The efficiency of including correlated traits. Ada Agriculturae Scandinavica 17: 263–268.CrossRefGoogle Scholar
Hayes, J. F. and Hill, W. G. 1980. A reparameterization of a genetic selection index to locate its sampling properties. Biometrics 36: 237–248.CrossRefGoogle ScholarPubMed
Henderson, C. R. 1975a. Best linear unbiased estimation and prediction under a selection model. Biometrics 31:423–447.CrossRefGoogle Scholar
Henderson, C. R. 1975b. Comparison of alternative sire evaluation methods, journal of Animal Science 41: 760–770.CrossRefGoogle Scholar
Henderson, C. R. 1984. Estimation of variances and covariances under multiple trait models, journal of Dairy Science 67:1581–1589.CrossRefGoogle Scholar
Henderson, C. R. and Quaas, R. L. 1976. Multiple trait evaluation using relatives' records. Journal of Animal Science 43:1188–1197.CrossRefGoogle Scholar
Lin, C. Y. and Smith, S. P. 1990. Transformation of multitrait to unitrait mixed model analysis of data with multiple random effects. Journal of Dairy Science 73:2494–2502.CrossRefGoogle ScholarPubMed
Meyer, K. 1983. Scope for evaluating dairy sires using first and second lactation records. Livestock Production Science 10: 531–553.CrossRefGoogle Scholar
Meyer, K. 1991. Estimating variances and covariances for multivariate animal models by restricted maximum likelihood. Genetique, Selection et Evolution 23: 67–83.CrossRefGoogle Scholar
Pollak, E. J., Werf, J. van der and Quaas, R. L. 1984. Selection bias and multiple trait evaluation. Journal of Dairy Science 67:1590–1595.CrossRefGoogle Scholar
Sales, J. and Hill, W. G. 1976. Effect of sampling error on efficiency of selection indices. 2. Use of information on associated traits for improvement of a single important trait. Animal Production 23:1–14.Google Scholar
Schaeffer, L. R. 1984. Sire and cow evaluation under multiple trait models. Journal of Dairy Science 67:1567–1580.CrossRefGoogle Scholar
Simm, G. and Dingwall, W. S. 1989. Selection indices for lean meat production in sheep. Livestock Production Science 21: 223–233.CrossRefGoogle Scholar
Thompson, R. 1977. Estimation of quantitative genetic parameters. Proceedings of the international conference on quantitative genetics (ed. Pollak, E., Kempthorne, O. and Bailey, T. B.), pp. 639–657. Iowa State University Press, Ames.Google Scholar
Thompson, R. and Meyer, K. 1986. A review of theoretical aspects in the estimation of breeding values for multi-trait selection. Livestock Production Science 15: 299–313.CrossRefGoogle Scholar
Villanueva, B. and Kennedy, B. W. 1991. Efficiency of indirect selection at selection equilibrium. Theoretical and Applied Genetics 81: 166–172.CrossRefGoogle ScholarPubMed
Villanueva, B. and Kennedy, B. W. 1993. Index versus tandem selection after repeated generations of selection. Theoretical and Applied Genetics 85: 706–712.CrossRefGoogle ScholarPubMed
Visscher, P. M., Hill, W. G. and Thompson, R. 1992. Univariate and multivariate parameter estimates for milk production using an animal model. II: Efficiency of selection when using simplified covariance structures. Genetique, Selection et Evolution 24: 431–447.CrossRefGoogle Scholar
Wray, N. R. and Hill, W. G. 1989. Asymptotic rates of response from index selection. Animal Production 49:217–227.Google Scholar