Toward a theory of marker-assisted gene pyramiding

We investigate the best way to combine into a single genotype a series of target genes identified in different parents (gene pyramiding). Assuming that individuals can be selected and mated according to their genotype, the best method corresponds to an optimal succession of crosses over several generations (pedigree). For each pedigree, we compute the probability of success from the known recombination fractions between the target loci, as well as the number of individuals (population sizes) that should be genotyped over successive generations until the desired genotype is obtained. We provide an algorithm that generates and compares pedigrees on the basis of the population sizes they require and on their total duration (in number of generations) and finds the best gene-pyramiding scheme. Examples are given for eight target genes and are compared to a reference genotype selection method with random mating. The best gene-pyramiding method combines the eight targets in three generations less than the reference method while requiring fewer genotypings.