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

Abstract

The parametric restrictions of the diallel analysis model of Gardner and Eberhart (analysis II) were studied in order to address the following questions: i) does the statistical model really have to be restricted? ii) Do the restrictions satisfy the genetic parameter values? iii) Do the restrictions make analysis and interpretation easier? Objectively, the answers to these questions are: i) no, ii) not all, and iii) they facilitate the analysis, but the interpretation is the same as for the unrestricted model. The main conclusion was that the restrictions of the Gardner and Eberhart model related to specific heterosis effects, for all j, do not satisfy the parametric values. The Gardner and Eberhart's estimators of the variety heterosis effects, the specific heterosis effects and their variances, differ from those of the unrestricted model. Any analysis using the unrestricted model and that of Gardner and Eberhart should lead to the same inferences, at least for those based on assessment of the population effects expressed as deviations from the average value, the heteroses, the average heterosis and the variety heteroses (the correlation between the estimates of the two models is 1). The limiting factor for the use of the unrestricted model is the lack of formulas for computing the sums of squares and for estimating the estimable function variances.