Deterministic Formulas and Procedures for Stochastic Trait Introgression Prediction
Key messageWe derive formulas for the background noise during trait introgression programs and use these formulas to quickly predict noise for up to five future generations without using simulation. Trait introgression is a common method for introducing valuable traits into breeding populations and inbred cultivars. The process involves recurrent backcrossing of a donor individual (and its descendants) with a desirable, inbred line that lacks the aforementioned traits. The process typically concludes with a final generation of selfing in order to recover lines with the traits of interest fixed in the homozygous state. The particular breeding scheme is usually designed to maximize the genetic similarity of the converted lines to the recurrent parent while minimizing a breeders cost and time to recovering the near isogenic lines. Thus, key variables include the number of generations, number of crosses, and how to apply genotyping and selection during the process. In this paper, we derive analytical formulas that characterize the stochastic nature of residual donor geneome (i.e., "background noise") during trait introgression. We use these formulas to predict the background noise in simulated trait introgression programs for five generations of progeny, as well as to construct a novel mathematical program to optimally allocate progeny to available parents. This provides a framework for the design of optimal breeding schemes for trait introgression involving one or more traits subject to the requirements of specific crops and breeding programs.