Nonorthogonal Optimal Partial Diallel Cross Designs for Consistent Estimation of Heritability

Abstract

Diallel cross designs in the framework of random effects model are considered for the estimation of ratio of variance components, viz. heritability of crosses of inbred lines. New methods for construction of partial diallel cross (PDC) design sunder unblocked and blocked set up are proposed. The resulting designs of these methods are capable of minimizing variance of the estimator of heritability. Consistency of the estimator is also established. One of the practical advantage of the proposed series of designs is attributed to its ability to reduce number of distinct crosses over those for complete diallel cross (CDC) to an extent of 10 to 20 percent. Another heartening aspect of the proposed methods is that the blocks of these designs are incomplete and have smaller block sizes up to one-third than those of complete block designs. Note that, the variance-minimization criterion for optimality reduces to MS-optimality criterion of PDC designs defined in the context of fixed effects model. Further, the newly constructed designs are proved to be asymptotically universally optimal under fixed effects model. Since construction of these designs under blocked set up is quite involved, therefore a computer program is written in C++ for generating these designs which is provided in the Appendix.