THE BEST LINEAR UNBIASED PREDICTORS (BLUP) IN DESIGNS ONE AND THREE OF GRIFFING

Abstract

In diallel cross experiments, when we wish to estimate the maternal effect, it is necessary to include the reciprocal crosses. In particular, Griffing?s treatment designs one and three are used when all simple crosses and their reciprocal crosses among p parents are included in the experiment. In most applications, the genetic and environmental components in these experiments are random; however, the estimation of general combining abilities and maternal effects has been commonly carried out considering a fixed effect model, reducing in this way the precision of the estimation. In this paper, based upon the random nature of these components, in Griffing?s treatment designs one and three laid out in a complete randomized blocks design, the best linear unbiased predictors are obtained for the effects of general combining abilities and for the maternal effect. Furthermore, a computational algorithm is provided in SAS-IML to obtain such predictors and the analysis of the experiment.