General inbreeding coefficient of maize synthetics derived from three-way line hybrids
The scarcity of pure and unrelated maize inbred lines that possess high combining ability in Mexico has led breeders wishing to form single crosses to develop double-cross or three-way line hybrids (TWLHs) instead. However, some of the farmers who grow these hybrids cultivate their advanced generations later on. Although the resulting populations can be viewed as the synthetics that the random mating of the parental lines (SynL) of these hybrids would produce, there may be differences. The synthetic variety whose parents are t TWLHs (SynT) is interesting because the contributed gene frequencies of the three lines that are parents of a TWLH are not balanced and this may generate a difference between the inbreeding coeff icients (ICs) of the SynL and SynT. Since an unbiased and general inbreeding coeff icient of the SynT and a prediction formula for the SynT genotypic mean (GM) are not yet known, the objective of this study was to derive formulae for these two important parameters of SynT. To form the t TWLHs, it was assumed that 3t unrelated lines whose IC was F (0 ≤ F ≤ 1) were used. Unbiased and general formulae for FSynT and GM were derived for the f irst time. In particular, it was found that FSynT = [3(1 + F)]/(16t). Since the inbreeding coeff icient of the SynL derived from the same 3t lines is (1 + F)/(6t), then FSynT > FSynL. These f indings suggest that the genotypic mean of the SynL grain yield is larger than the SynT’s.