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: Yk = a1 sigmaVj + a2sigmaTj + a3<IMG SRC="Image156.gif" WIDTH=16 HEIGHT=18> - a4<IMG SRC="Image157.gif" WIDTH=14 HEIGHT=17>, with coefficients a1 = (n - 2k)/k²(n - 2); a2 = 2n(k - 1)/k²(n - 2); a3 = n(k - 1)/k(n - 1)(n - 2); and a4 = n²(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 varieties of a particular composite) and n is the total number of parent varieties. Vj is the mean of varieties and Tj is the mean of topcrosses (pool of varieties as tester), and <IMG SRC="Image158.gif" WIDTH=16 HEIGHT=18>and <IMG SRC="Image159.gif" WIDTH=14 HEIGHT=17>are the 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 "simulated" topcross means to illustrate the proposed procedure. The proposed prediction procedure was as effective as the prediction based on Yk = <IMG SRC="Image160.gif" WIDTH=16 HEIGHT=17>- (<IMG SRC="Image161.gif" WIDTH=16 HEIGHT=17> -<IMG SRC="Image156.gif" WIDTH=16 HEIGHT=18>)/k, where <IMG SRC="Image161.gif" WIDTH=16 HEIGHT=17>and <IMG SRC="Image158.gif" WIDTH=16 HEIGHT=18>refer to the mean of hybrids (F1) 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 treatments (varieties and topcrosses) can be orthogonally partitioned following the reduced model Yjj’ = mu + ½(v j + v j’) + <IMG SRC="Image162.gif" WIDTH=12 HEIGHT=18>+ h j+ h j’, thus making possible an F test for varieties, average heterosis and variety heterosis. Least square estimates of these effects are also given