The theoretical distribution of lengths of intact chromosome segments around a locus held heterozygous with backcrossing in a diploid species.

When two different isogenic lines of a diploid species (or two different species) are crossed, the resulting F1 individuals should be heterozygous at all the loci fixed for different alleles in the two strains (in the limit, at all the loci of the genome). If one of these loci is then held heterozygous for several generations of repeated backcrossing to the same strain, the average length of intact chromosome segments (with reference to the original parental chromosome) on both sides of the selected locus, or, equivalently, the average length of segments surrounding that locus which are still heterozygous (with reference to the fully heterozygous F1 chromosome), may diminish, but cannot increase. Several authors have derived equations to predict this average. We show that the most widely used criterion, developed by R.A. Fisher, leads to serious overestimations of the true parametric values, when applied to early generation analyses, with the corresponding errors in the interpretation of experimental results. We then derive the exact equations both for the average and standard deviation of the lengths of intact chromosome segments surrounding a locus held heterozygous after any number of generations of backcrossing. Our results are in close agreement with those found by a former author, although involving a rather different approach.