Analytical prediction of genetic contribution across multiple recurrent backcrossing generations

We derive formulas for the residual donor genome content during trait introgression via recurrent backcrossing and use these formulas to predict (without simulation) residual donor genome content for five future generations. Trait introgression is a common method for introducing valuable genes or alleles into breeding populations and inbred cultivars. The particular breeding scheme is usually designed to maximize the genetic similarity of the converted lines to the recurrent parent while minimizing cost and time to recover the near isogenic lines. Key variables include the number of generations and crosses and how to apply genotyping and selection. One form of trait introgression, which is our focus, involves an initial cross of an elite, homozygous recurrent parent line with a non-recurrent, homozygous donor line. The descendants of this cross are backcrossed with the recurrent parent for several generation before self-pollination in the final generation to recover lines with the alleles of interest. In this paper, we derive analytical formulas that characterize the stochastic nature of residual donor genome content during this form of trait introgression. The development of these formulas expands the mathematical methods one can integrate into breeding design. In particular, we show we can use our formulas in a novel mathematical program to allocate resources to optimize the reduction of residual donor genome content.