Predicting mean and variance of all possible lines and hybrids from designs with partially inbred progenies

Two-factor mating designs at consecutive S_n and S_(n+1) levels (S₀ and S₁ S₁ and S₂, or F₂ and F₃) allow estimation of all components of the variation among homozygous lines and F₁ hybrids that can be derived from a given population. They also allow for the prediction of the mean of these lines and single-cross hybrids. Some tests for the presence of epistasis are possible at the levels of means and of variances. Such mating designs can be very useful for predicting the value of the best possible lines or the best possible F₁ hybrids when it is difficult to produce, at an experimental level for exploratory purposes, either lines or hybrids.