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 GaussMarcov 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.
Phaseolus vulgaris; parents; hybrids; combining ability; quantitative genetics; pest resistance; breeding methods; bacterial blight; Xanthomonas axonopodis
