Analysis of partial diallel crosses in incomplete blocks

With a large number of lines in a diallel cross experiment, the number of crosses becomes unmanageable to be accommodated in homogeneous blocks. To overcome this problem, a sample of crosses, known as partial diallel cross (PDC) is often used. The selection of a PDC is based on the criterion of high efficiency for the estimation of general combining ability (gca) effects. Even with a moderately large number of crosses, the use of incomplete blocks is necessary to obtain homogeneous experimental units. The analysis of data from a general PDC grown in general incomplete block designs is being described. An iterative scheme is being developed for obtaining a generalized inverse of the information matrix used in estimating gca effects. Properties such as connectedness and efficiency of mating designs embedded in environment designs are being examined. The paper also examines the universal optimality of some designs in a class of designs. An illustration of the numerical procedure is also presented.