Genet. Sel. Evol. 34 (2002) 145-170
DOI: 10.1051/gse:2002001

A method to optimize selection on multiple identified quantitative trait loci

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

a</sup>  Department of Animal Science, 225C 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 was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.

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

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

© INRA, EDP Sciences 2002