A METHOD FOR COMBINED ANALYSIS OF THE DIALLEL CROSSES REPEATED IN SEVERAL ENVIRONMENTS

This paper presents a metodology derived from the model proposed by Gardner & Eberhart for computing combined analysis of variance of diallel crosses tested in several environments, aiming to obtain estimators for the parameters and sums of squares formulae. The following mathematical model was adapted for a combined analysis of the complete diallel crosses: Y(ijj)' = m + 1/2(v(j) + v(j')) + e(i) + 1/2(ev(ij') + ev(ij')) + theta-(hBAR + ehBAR(i) + h(j) + eh(ij) + h(j') + eh(ij') + s(jj') + es(ijj') + epsilon-BAR(ijj'), where: Y(ijj') is the variety mean if j = j' or the cross mean if j not-equal j' in the i(th) environment; e(i) is the environment effects; ev(ij) and ev(ij), are the effects of the interaction environment x variety, ehBAR(i) is the effect of the interaction environment x average heterosis; eh(ij) and eh(ij), are the effects of the interaction environment x variety heterosis and es(ijj') is the interaction environment x specific heterosis. The other parameters of this model are similarly defined in Gardner & Eberhart work. When j = j' then theta = 0 and for j not-equal j' then theta = 1. The estimators for the parameters and the sums of squares formulas were determined through the least squared method. Variances of the parameters estimators and the analysis of variance were also determined. An example is presented with its correspondent analysis.