Minimum sample size and optimal positioning of flanking markers in marker-assisted backcrossing for transfer of a target gene

In recurrent backcrossing designed for introgression of a target allele from a donor into the genetic background of a recurrent parent (RP), molecular markers can accelerate recovery of the recurrent parent genome (RPG). The objectives of this study were to determine in marker-assisted backcrossing (MAB) (i) the optimum distances (d₁, d₂) between the flanking markers and the target locus and (ii) the minimum number of individuals (n) required for obtaining with a certain probability a given number of individuals that carry the donor allele at the target locus and have a minimum proportion of donor genome on the carrier chromosome. Analytical solutions and tabulated results are given for relevant parameters (d₁, d₂, n) required to obtain, with a specified probability of success, at least one desired individual. They depend on the length of the carrier chromosome, the chromosomal position of the target locus, its distance to the flanking marker loci, and the number of individuals evaluated. Our approach can increase the efficiency of MAB by reducing the number of individuals and marker data points required.