Synthetic varieties (SVs) are populations generated by randomly mating their parents. They are a good alternative for low-input farmers who grow onions, maize, and other allogamous crops since the seed produced by a SV does not change from one generation to the next. Although SV progenitors are commonly pure lines, in this case a synthetic (Syn_TC) whose parents are t three-way line crosses, a very common type of maize hybrid grown in Mexico, is studied. The aim was to develop a general and exact equation for the inbreeding coefficient of a Syn_TC Syn_TC because of its relationship with the mean of economically important traits. This objective arose due to the need for a more advanced study in terms of determining whether Syn_TC can be applied specifically and accurately for any number of parents (t), plants per parent (m) and inbreeding coefficient (IC) of the initial lines (F_L). A formula for the IC of the Syn_TC was derived that, given any values of F_L (0 ≤ F_L ≤ 1) and t, is specific for any value of m, not just for “large” numbers associated with the context in which the Hardy-Weinberg law is stated. It was found that Syn_TC is very sensitive to changes in m when m is not greater than eight, after which it tends to stabilize very quickly. In summary, unlike previously derived formulas, Syn_TC is exact for any values of t, m and F_L.

Genotypic array; genotypic mean; hybrid; random mating; Zea mays