Analysis of diallel tables with reciprocal crosses

The methodology of diallel crosses is extended to provide procedures for the analysis of variance and estimation of effects when the reciprocal crosses are included. The model of Gardner and Eberhart (Biometrics 22: 439-452, 1966) was used for the analysis of variety dialiel crosses when reciprocal crosses are included. The least square procedure was used to derive the formulas for estimation of effects (components of means) and for the analysis of variance. It was found that the estimates of effects is the same if the analysis is performed according to the original model, with varieties and the average of reciprocal crosses to represent any hybrid combination. The standard errors of the estimates of effects, however, change in the proposed procedure. The sums of squares in the analysis of variance are different from those obtained according to the original model. Some comparisons are made and an example is given for illustration.