The advantage of factorial mating under selection is uncovered by deterministically predicted rates of inbreeding.

Rates of inbreeding (DeltaF) in selected populations were predicted using the framework of long-term genetic contributions and validated against stochastic simulations. Deterministic predictions decomposed DeltaF into four components due to: finite population size, directional selection, covariance of genetic contribution of mates, and deviation of variance of family size from that expected from a Poisson distribution. Factorial (FM) and hierarchical (HM) mating systems were compared under mass and sib-index selection. Prediction errors were in most cases for DeltaF less than 10% and for rate of gain less than 5%. DelatF was higher with index than mass selection. DeltaF was lower with FM than HM in all cases except random selection. FM reduced the variance of the average breeding value of the mates of an individual. This reduced the impact of the covariance of contributions of mates on DeltaF. Thus, contributions of mates were less correlated with FM than HM, causing smaller deviations of converged contributions from the optimum contributions. With index selection, FM also caused a smaller variance of number of offspring selected from each parent. This reduced variance of family size reduced DeltaF further. FM increases the flexibility in breeding schemes for achieving the optimum genetic contributions.