Selection theory for marker-assisted backcrossing.

Marker-assisted backcrossing is routinely applied in breeding programs for gene introgression. While selection theory is the most important tool for the design of breeding programs for improvement of quantitative characters, no general selection theory is available for marker-assisted backcrossing. In this treatise, we develop a theory for marker-assisted selection for the proportion of the genome originating from the recurrent parent in a backcross program, carried out after preselection for the target gene(s). Our objectives were to (i) predict response to selection and (ii) give criteria for selecting the most promising backcross individuals for further backcrossing or selfing. Prediction of response to selection is based on the marker linkage map and the marker genotype of the parent(s) of the backcross population. In comparison to standard normal distribution selection theory, the main advantage of our approach is that it considers the reduction of the variance in the donor genome proportion due to selection. The developed selection criteria take into account the marker genotype of the candidates and consider whether these will be used for selfing or backcrossing. Prediction of response to selection is illustrated for model genomes of maize and sugar beet. Selection of promising individuals is illustrated with experimental data from sugar beet. The presented approach can assist geneticists and breeders in the efficient design of gene introgression programs.