Influence of the mating design on the additive genetic variance in plant breeding populations

Mating designs determine the realized additive genetic variance in a population sample. Deflated or inflated variances can lead to reduced or overly optimistic assessment of future selection gains. The additive genetic variance [Formula: see text] inherent to a breeding population is a major determinant of short- and long-term genetic gain. When estimated from experimental data, it is not only the additive variances at individual loci (QTL) but also covariances between QTL pairs that contribute to estimates of [Formula: see text]. Thus, estimates of [Formula: see text] depend on the genetic structure of the data source and vary between population samples. Here, we provide a theoretical framework for calculating the expectation and variance of [Formula: see text] from genotypic data of a given population sample. In addition, we simulated breeding populations derived from different numbers of parents (P = 2, 4, 8, 16) and crossed according to three different mating designs (disjoint, factorial and half-diallel crosses). We calculated the variance of [Formula: see text] and of the parameter b reflecting the covariance component in [Formula: see text] standardized by the genic variance. Our results show that mating designs resulting in large biparental families derived from few disjoint crosses carry a high risk of generating progenies exhibiting strong covariances between QTL pairs on different chromosomes. We discuss the consequences of the resulting deflated or inflated [Formula: see text] estimates for phenotypic and genome-based selection as well as for applying the usefulness criterion in selection. We show that already one round of recombination can effectively break negative and positive covariances between QTL pairs induced by the mating design. We suggest to obtain reliable estimates of [Formula: see text] and its components in a population sample by applying statistical methods differing in their treatment of QTL covariances.