Keywords: llium cepa L., Zea mays L., inbreeding, synthetic varieties, hybrids, genotypic array.
The use of synthetic varieties (SVs) derived from single (SynSC) or double (SynDC) crosses is a way of avoiding the high seed cost of hybrid maize (Zea mays L) and onion (Allium cepa L.) varieties, among others. In addition, these SVs could be used to more economically predict the genotypic means (GMs) of the SVs derived from the hybrid parental lines (SynL). It is known, however, that the inbreeding coefficients (ICs) of the SynL, SynSC, and SynDC derived from the same lines can differ, but the reason why is unknown. This lack of knowledge makes it difficult for the breeder to improve the representation of the SynL through the SynDC and SynSC and thereby to improve the estimation of the SynL GM. The objective of this study was to determine the reason why the SynL, SynSC, and SynDC can differ. From unrelated L lines whose IC is FL, L/2 single (SCs) and L/4 double crosses (DCs) were derived; and each line, SC, and DC were represented by m individu- als. By randomly mating each set of parents, the SynL, SynSC, and SynCD were formed. It was found that the genotypic arrays of the three SVs differ because with the same 4 initial lines the number of non-identical by descent genes contributed to the genotypic array is larger as fewer lines are involved in a parent [lines (1), single crosses (2), and double crosses (4)]. Thus, the ICs of SynL and SynDC are the smallest and largest, respectively; and it is expected that the GMs show the opposite ordering. In addition, as m and FL are smaller the differences among the genotypic arrays of the SVs are larger. On the contrary, when the L lines are pure, the genotypic arrays of SynL and SynSC are equal, and their IC must be equal as well. To be equal to SinL, SynDC requires, in addition, a large m. However, even with FL < 1, as m is larger the genotypic arrays of SynSC and SynDC tend to the genotypic array of SynL, although slowly, particularly for SynDC.