Recombination fraction in pre-recombinant inbred lines (PRERIL) - revisiting a century old problem in genetics

Traditional recombinant inbred lines (RILs) are generated from repeated self-fertilization or brother-sister mating from the F₁ hybrid of two inbred parents. Compared with the F₂ population, RILs cumulate more crossovers between loci and thus increase the number of recombinants, resulting in an increased resolution of genetic mapping. Since they are inbred to the isogenic stage, another consequence of the heterozygosity reduction is the increased genetic variance and thus the increased power of QTL detection. Self-fertilization is the primary form of developing RILs in plants. Brother-sister mating is another way to develop RILs but in small laboratory animals. To ensure that the RILs have at least 98% of homozygosity, we need about seven generations of self-fertilization or 20 generations of brother-sister mating. Prior to homozygosity, these lines are called pre-recombinant inbred lines (PRERIL). Phenotypic values of traits in PRERILs are often collected but not used in QTL mapping. To perform QTL mapping in PRERILs, we need the recombination fraction between two markers at generation t for t < 7 (selfing) or t < 20 (brother-sister mating) so that the genotypes of QTL flanked by the markers can be inferred.

In this study, we developed formulas to calculate the recombination fractions of PRERILs at generation t in self-fertilization, brother-sister mating, and random mating. In contrast to existing works in this topic, we used computer code to construct the transition matrix to form the Markov chain of genotype array between consecutive generations, the so-called recurrent equations.

We provide R functions to calculate the recombination fraction using the newly developed recurrent equations of ordered genotype array. With the recurrent equations and the R code, users can perform QTL mapping in PRERILs. Substantial time and effort can be saved compared with QTL mapping in RILs.