Exact inbreeding coefficient of maize synthetic varieties derived from mixed lines and single crosses

Abstract There is an apparent overvaluation in the inbreeding coefficient (IC) formula for a synthetic variety (SV) derived from a mixture of S single crosses and L lines (FSynL,SC) in Zea mays. Therefore, our goal was to derive the exact and general FSynL,SC. For the development of this SV (SynL,SC), an even number of L + 2S unrelated lines whose IC was F (0 ≤ F ≤ 1) was considered. We show that the exact and general formula for FSynL,SC is: FSynL,SC = (2L + S)(1 + F)/[4(L + S)2], and that the ICs and genotypic means of two additional synthetics developed from the same lines (one derived from (L + 2S)/2 single crosses and the other derived from the L + 2S lines) must be equal. Among these three SVs, SynL,SC shows the largest IC.