PREDICTING VARIETY COMPOSITE MEANS WITHOUT DIALLEL CROSSING

Prediction of variety composite means was shown to be feasible without diallel crossing the parental varieties. Thus, the predicted mean for a quantitative trait of a composite is given by: Y-k = a(1) Sigma V-j + a(2) Sigma T-j + a(3) (V) over bar - a(4) (T) over bar, with coeffi cients a(1) = (n-2k)/k(2)(n-2); a(2) = 2n(k-1)/k(2)(n-2); a(3)=n(k-1)/ k(n-1)(n-2); and a(4) = n(2)(k-1)/k(n-1)(n-2); summation is for j = 1 to k, where k is the size of the composite (number of parental varieti es of a particular composite) and n is the total number of parent vari eties. V-j is the mean of varieties and T-j is the mean of topcrosses (pool of varieties as tester), and (V) over bar and (T) over bar are t he respective average values in the whole set. Yield data from a 7 x 7 variety diallel cross were used for the variety means and for the ''s imulated'' topcross means to illustrate the proposed procedure. The pr oposed prediction procedure was as effective as the prediction based o n Y-k = (H) over bar - ((H) over bar - (V) over bar)/k, where (H) over bar and (V) over bar refer to the mean of hybrids (F-1) and parental varieties, respectively, in a variety diallel cross. It was also shown in the analysis of variance that the total sum of squares due to trea tments (varieties and topcrosses) can be orthogonally partitioned foll owing the reduced model Y-jj' = mu + 1/2(v(j) + v(j')) + (h) over bar + h(j) + h(j'), thus making possible an F test for varieties, average heterosis and variety heterosis. Least square estimates of these effec ts are also given.