Application of population genetic theory and simulation models to efficiently pyramid multiple genes via marker-assisted selection

Breeders face many complex choices in the design of efficient crossing and selection strategies aimed at combining desired alleles into a single target genotype. Both population genetic theory and a breeding simulation tool were used to study the effects of different strategies on population size and number of marker assays required to recover a target genotype in wheat (Triticum aestivum L.). Enriching the frequency of desirable alleles in the F of single-cross and in the F of backcross and topcross populations greatly reduced the minimum required population size, but the gain from another enrichment selection is minor. General equations were developed to determine appropriate crossing strategies, and sequential culling was proposed to minimize total marker screening costs. For a topcross of three adapted lines from an existing breeding program, simulation of changes in allele frequencies at nine target genes (seven unlinked) showed that population size was minimized with a three-stage selection strategy in the F generation of the topcross (TCF), the F generation of the topcross (TCF ), and doubled haploid lines (DHs). Enrichment of allelic frequencies in TCF reduced the total number of lines screened from >3500 to 0.97 after selection, while the tin reduced-tillering allele was only at 0.77 in the final selected population due to its strong repulsion-phase linkage to the grain quality gene Glu-A3 in this cross and the incomplete linkage of the tin marker. Therefore, the presence of the tin gene needs to be further confirmed by other methods