The parametric restrictions of the Griffing diallel analysis model: combining ability analysis

It was studied the parametric restrictions of the diallel analysis model of Griffing, method 2 (parents and F-1 generations) and model 1 (fixed), in o rder to address the questions: i) does the statistical model need to be res tricted? ii) do the restrictions satisfy the genetic parameter values? and iii) do they make the analysis and interpretation easier? Objectively, thes e questions can be answered as: i) yes. ii) not all of them. and iii) the a nalysis is easier, but the interpretation is the same as in the model with restrictions that satisfy the parameter values. The main conclusions were t hat: the statistical models for combining ability analysis are necessarily restricted: in the Griffing model (method 2, model 1), the restrictions rel ative to the specific combining ability (SCA) effects, [GRAPHICS] s(jj) = 0 and s(jj) [GRAPHICS] for all j, do not satisfy the parametric values, and the same inferences sh ould be established from the analyses using the model with restrictions tha t satisfy the parametric values of SCA effects and that suggested by Griffi ng. 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 s ums of squares.