Optimal Multiple Trait Selection for Multiple Linked Quantitative Trait Loci

A method was developed to optimize selection on multiple traits with multiple quantitative trait loci (QTLs) over multiple generations. The basis of the method was to replace in the objective function the genotypic value of a single trait with an aggregate genotypic value of multiple traits weighted by their corresponding economic weight, and to maximize the weighted sum of the selection response in the planning horizon. The optimization was formulated as a multiple stage optimal control problem and solved by a forward and backward iteration cycle. The practical utility of this method was illustrated in an example of pig breeding population, in which the number born alive (NBA) and days to 100 kg (D100) were used as parameters. The selection response of this method was compared with standard QTL selection and regular best linear unbiased prediction (BLUP) selection. Results showed that optimal selection achieved greater selection response than either standard QTL or regular BLUP selections. The influence of economic weight to optimal selection was significant, and the optimization was better as the economic weight of D100 increased. Optimal selection increased the total selection response by two ways: 1) it sacrificed some QTL responses during early generations and 2) it put more emphasis on D100. Optimal cumulative discounted selection gave more weight to D100 than optimal terminal selection in the longer generations.