Marker-assisted backcrossing for introgression of a recessive gene

Molecular markers are used to trace the presence of target genes (foreground selection) and accelerate recovery of the recurrent parent genome (background selection) in backcross programs. In this study, we present an approach for introgression of a recessive target gene from a donor into the genetic background of a recipient line by foreground selection combined with background selection for reducing the donor chromosome segment around the target gene. The goal of the proposed breeding plan is to generate with a given probability, q(2), up to the second backcross generation (BC2) at least k greater than or equal to 1 individuals, which carry the target gene and are homozygous for the recurrent parent alleles at flanking markers, by means of a minimum number of individuals. We provide formulas for calculation of (i) the population size required in generation BC1 and (ii) the probability of success q(2) of the breeding program in generation BC2. The latter depends on the number and genotype of the BC1 individuals selected for further backcrossing and the size of their BC2 families. The optimum allocation of individuals to generations BC1 and BC2 was determined by computer simulations for various map distances between the target gene and the flanking markers. Our approach is demonstrated by a numerical example and can assist breeders in the optimum design of breeding programs for marker-assisted introgression of a recessive gene.