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.