The length of the intact donor chromosome segment around a target gene in marker-assisted backcrossing

Recurrent backcrossing is an established procedure to transfer target genes from a donor into the genetic background of a recipient genotype. By assessing the parental origin of alleles at markers flanking the target locus one can select individuals with a short intact donor chromosome segment around the target gene and thus reduce the linkage drag. We investigated the probability distribution of the length of the intact donor chromosome segment around the target gene in recurrent backcrossing with selection for heterozygosity at the target locus and homozygosity for the recurrent parent allele at flanking markers for a diploid species. Assuming no interference in crossover formation, we derived the cumulative density function, probability density function, expected value, and variance of the length of the intact chromosome segment for the following cases: (1) backcross generations prior to detection of a recombinant individual between the target gene and the flanking marker; (2) the backcross generation in which for the first time a recombinant individual is detected, which is selected for further backcrossing; and (3) subsequent backcross generations after selection of a recombinant. Examples are given of how these results can be applied to investigate the efficiency of marker-assisted backcrossing for reducing the length of the intact donor chromosome segment around the target gene under various situations relevant in breeding and genetic research.