The parametric restrictions of the Gardner and Eberhart diallel analysis model: heterosis analysis

It was studied the parametric restrictions of the diallel analysis model of Griffing, method 2 (parents and F1 generations) and model 1 (fixed), in order to address the questions: i) does the statistical model need to be restricted? ii) do the restrictions satisfy the genetic parameter values? and iii) do they make the analysis and interpretation easier? Objectively, these questions can be answered as: i) yes, ii) not all of them, and iii) the analysis is easier, but the interpretation is the same as in the model with restrictions that satisfy the parameter values. The main conclusions were that: the statistical models for combining ability analysis are necessarily restricted; in the Griffing model (method 2, model 1), the restrictions relative to the specific combining ability (SCA) effects, <img src="http:/img/fbpe/gmb/v23n4/6246s1.gif" align="absmiddle"> and <img src="http:/img/fbpe/gmb/v23n4/6246s2.gif" align="absmiddle"> for all j, do not satisfy the parametric values, and the same inferences should be established from the analyses using the model with restrictions that satisfy the parametric values of SCA effects and that suggested by Griffing. A consequence of the restrictions of the Griffing model is to allow the definition of formulas for estimating the effects, their variances and the variances of contrasts of effects, as well as for calculating orthogonal sums of squares.