Genet. Sel. Evol. 34 (2002) 171-192
DOI: 10.1051/gse:2002002

Optimal selection on two quantitative trait loci with linkage

Jack C.M. Dekkers^a, Reena Chakraborty^a and Laurence Moreau<sup>b

a</sup>  Department of Animal Science, 225 Kildee Hall, Iowa State University Ames, IA, 50011, USA
^b  Inra-UPS-Ina PG, Station de génétique végétale, Ferme du Moulon, 91190 Gif-sur-Yvette, France

(Received 5 February 2001; accepted 15 October 2001)

Abstract
A mathematical approach to optimize selection on multiple quantitative trait loci (QTL) and an estimate of residual polygenic effects was applied to selection on two linked or unlinked additive QTL. Strategies to maximize total or cumulative discounted response over ten generations were compared to standard QTL selection on the sum of breeding values for the QTL and an estimated breeding value for polygenes, and to phenotypic selection. Optimal selection resulted in greater response to selection than standard QTL or phenotypic selection. Tight linkage between the QTL (recombination rate 0.05) resulted in a slightly lower response for standard QTL and phenotypic selection but in a greater response for optimal selection. Optimal selection capitalized on linkage by emphasizing selection on favorable haplotypes. When the objective was to maximize total response after ten generations and QTL were unlinked, optimal selection increased QTL frequencies to fixation in a near linear manner. When starting frequencies were equal for the two QTL, equal emphasis was given to each QTL, regardless of the difference in effects of the QTL and regardless of the linkage, but the emphasis given to each of the two QTL was not additive. These results demonstrate the ability of optimal selection to capitalize on information on the complex genetic basis of quantitative traits that is forthcoming.

Key words: selection / marker-assisted selection / quantitative trait loci / optimization

Correspondence and reprints: Jack C.M. Dekkers
    e-mail: jdekkers@iastate.edu

© INRA, EDP Sciences 2002