Generalized method for analysis of unbalanced diallels

Abstract

A general procedure for estimation of general and specific combining ability in diallelic crosses with unequal number of replications for treatments (parents and F₁ hybrid combinations), evaluated in a design with restricted randomization, is presented. In this case, the estimates of adjusted means are interdependent and heterocedastic, demanding the use of the Gauss-Marcov generalized linear model. The objective of this study was the theoretical deduction of the model and its application to a practical example. A complete diallel crossing without reciprocals was performed, including five parents: CB 511687-1, CB 733753, Diamante Negro, Rosinha G-2 and Compuesto Chimaltenango 2. The parents CB 511687-1, CB 733753 and Diamante Negro contribute genetically for resistance while Rosinha G-2 and Compuesto Chimaltenango 2 contribute for susceptibility of dry bean to common bacterial blight. Most of the crosses analyzed showed partial dominance for susceptibility of bean to Xanthomonas axonopodis pv. phaseoli