Variance of the parental genome contribution to inbred lines derived from biparental crosses

The expectation of the parental genome contribution to inbred lines derived from biparental crosses or backcrosses is well known, but no theoretical results exist for its variance. Our objective was to derive the variance of the parental genome contribution to inbred lines developed by the single-seed descent or double haploid method from biparental crosses or backcrosses. We derived formulas and tabulated results for the variance of the parental genome contribution depending on the chromosome lengths and the mating scheme used for inbred line development. A normal approximation of the probability distribution function of the parental genome contribution fitted well the exact distribution obtained from computer simulations. We determined upper and lower quantiles of the parental genome contribution for model genomes of sugar beet, maize, and wheat using normal approximations. These can be employed to detect essentially derived varieties in the context of plant variety protection. Furthermore, we outlined the application of our results to predict the response to selection. Our results on the variance of the parental genome contribution can assist breeders and geneticists in the design of experiments or breeding programs by assessing the variation around the mean parental genome contribution for alternative crossing schemes.