Abstract
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 (SynTC) 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 SynTC SynTC 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 SynTC can be applied specifically and accurately for any number of parents (t), plants per parent (m) and inbreeding coefficient (IC) of the initial lines (FL). A formula for the IC of the SynTC was derived that, given any values of FL (0 ≤ FL ≤ 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 SynTC 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, SynTC is exact for any values of t, m and FL.
Highlights
Synthetic varieties (SVs) of maize (Zea mays L.), called synthetics, are populations generated by randomly mating their parents, usually unrelated inbred lines
We will consider any values of t, FL and m in a SynTC to derive its inbreeding coefficient (IC) ðFmf SynTC Þ
If N1 (m) is the total number of self-fertilizations resulting from the random mating of each parent, the contribution to Fmf SynTC (C1) of the t parents must be:
Summary
Synthetic varieties (SVs) of maize (Zea mays L.), called synthetics, are populations generated by randomly mating their parents, usually unrelated inbred lines. They are highly heterozygous and heterogeneous populations that show high adaptability even to adverse environmental conditions such as drought, extreme temperatures, pests, diseases, nutritional problems, etc. A relevant difference between a SV and a hybrid is that the seeds produced by a synthetic must be genetically equal to that of its previous generation. This is not the case in a hybrid.
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