Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T04:46:18.050Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimum linear selection indexes for multiple generation objectives with non-linear profit functions

Published online by Cambridge University Press:  02 September 2010

J. C. M. Dekkers ,
P. V. Birke  and
J. P. Gibson
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
P. V. Birke
Affiliation:
Nonlinear Synergetics, Guelph, Ontario N1G 3P2, Canada
J. P. Gibson
Affiliation:
Centre for Genetic Improvement of Livestock, Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario N1G 2W1, Canada
Get access

Abstract

A method to obtain linear selection indexes that maximize objectives that involve average profit in one or more generations within a planning horizon based on non-linear profit functions, was derived through application of optimal control theory. The method involves simultaneous optimization of indexes for each generation in the planning horizon. Optimum linear indexes were found to be conform indexes derived from selection index theory, with economic values equal to a weighted sum of partial derivatives of the profit function at the trait means which result in each generation of the planning horizon. Numerical procedures to derive optimum indexes are presented. Methods and properties of alternative strategies for selection witli non-linear profit functions are illustrated for selection on egg weight and rate of lay in poultry. In the example, the additional benefit of selection indexes that maximize cumulative net present value of profit over a planning horizon of10 years was small relative to use of traditional selection procedures. Optimal indexes were also derived with a derivative-free non-linear programming optimizer, with identical results. The latter method also allows incorporation of additional constraints.

Possible extensions of the optimal control methodology to address other problems related to optimization of selection over multiple generations are discussed.

Keywords

animal breedingnon-linear profit maximizationoptimal control theoryselection index
Type
Research Article
Information
Animal Science , Volume 61 , Issue 1 , August 1995 , pp. 165 - 175
Copyright
Copyright © British Society of Animal Science 1995

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

Bryson, A. E. and Ho, Y-C. 1975. Applied optimal control: optimization, estimation and control. John Wiley, New York.Google Scholar
Bulmer, M. C. 1971. The effect of selection on genetic variability. American Naturalist 105:201–211.CrossRefGoogle Scholar
Cunningham, E.P. 1979. Quantitative genetic theory and livestock improvement. University of New England, Armidale, Australia.Google Scholar
Elsen, J. M., Bibe, B., Landais, E. and Ricordeau, G. 1986. Twenty remarks on economic evaluation of selection goals. Proceeding of the third ivorld congress on genetics applied to Livestock Production, vol. 12, pp.321–327.Google Scholar
Gibson J. P. and Jeyaruban, M. G. 1994. BLUP evaluations and the balance between response and inbreeding in egg-laying lines of poultry. Proceedings of the tenth international symposium on current problems in avian genetics (ed. Gavora, J. S.), Nitra, Slovakia, pp.185-192.Google Scholar
Gibson, J. P. and Kennedy, B. W. 1990. The use of constrained selection indexes in breeding for economic merit. Theoretical and Applied Genetics 80:801–805.CrossRefGoogle ScholarPubMed
Goddard, M. E. 1983. Selection indices for non-linear profit functions. Theoretical and Applied Genetics 64: 339–344.CrossRefGoogle ScholarPubMed
Groen, A. F., Meuwissen, T. H. E., Vollema, A. R. and Brascamp, E. W. 1994. A comparison of alternative index procedures for multiple generation selection on non-linear profit. Animal Production 59:1–9.Google Scholar
Hazel, L. N. 1943. The genetic basis for constructing selection indexes. Genetics, USA 28:476–490.CrossRefGoogle ScholarPubMed
Hill, W. G. 1974. Prediction and evaluation of response to selection with overlapping generations. Animal Production 18:117–139.Google Scholar
Itoh, Y. and Yamada, Y. 1988. Linear selection indices for non-linear profit functions. Theoretical and Applied Genetics 75:553–560.CrossRefGoogle Scholar
Kamien, M. I. and Schwartz, N. L. 1981. Dynamic optimization. The calculus of variations and optimal control in economics and management. North-Holland Publication Company, Amsterdam.Google Scholar
Lewis, F. L. 1986. Optimal control. Wiley, New York.Google Scholar
Moav, R. and Hill, W. G. 1966. Specialised sire and dam lines. IV. Selection within lines. Animal Production 8:375–390.Google Scholar
Pasternak, H. and Weller, J. I. 1993. Optimum linea r indices for non-linear profit functions. Animal Production 6:43–50.Google Scholar
Villanueva, B., Wray, N. R. and Thompson, R. 1993. Prediction of asymptotic rates of response from selection on multiple traits using univariate and multivariate best linear unbiased predictors. Animal Production 57:1–13.Google Scholar
Wilton, J. W., Evans, A. and Van Vleck, L. D. 1968. Selection indices for quadratic models of total merit. Biometrics 24:937–949.CrossRefGoogle Scholar
Wray, N. R. and Hill, W. G. 1989. Asymptotic rates of response from index selection. Animal Production 49:217–227.Google Scholar
Wright, S. J. 1993. Interior point methods for optimal control of discrete time systems, journal of Optimization Theory and Application 77:161–187.CrossRefGoogle Scholar
Zuo, Z-Q. 1991. Two new techniques for optimal control. IEEE Transactions on Automatic Control 236:1307–1310.CrossRefGoogle Scholar