A method for combined analysis of the diallel crosses repeated in several environments

• Autor(a) principal: Morais, Augusto Ramalho de
• Data de Publicação: 1991
• Outros Autores: Oliveira, Antonio Carlos de, Gama, Elto Eugenio Gomes e, Junior, Claudio Lopes de Souza
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Pesquisa Agropecuária Brasileira (Online)
• Texto Completo: https://seer.sct.embrapa.br/index.php/pab/article/view/3352
• topic: parameters; combining ability; environment x effect interaction; parâmetros; capacidade de combinação; interação efeito x ambiente

This paper presents a metodology derived from the model proposed by Gardner & Eberhart For computing combined analysis of variance of diallel crosses tested in several environments, aiming to obtain estimators for the parameters and sums of squares formulae. The following mathematical model was adapted for a combined analysis of the complete diallel crosses:yijj’ = m + ½ (vj + vj’) + ei + ½ (evij + evij’) + θ(h + ehi + hj + ehij + hj’ + ehij’ + sjj’ + esijj’) + εijj’,where: Yijj' is the variety mean if j = j' or the cross mean if j≠j' in the ith environment; ei is the environment effects; evjj and evij, are the effects of the interaction environment x variety, ehi is the effect of the interaction environment x average heterosis; ehij and ehij' are the effects of the interaction environment x variety heterosis and esijj' is the interaction environment x specific heterosis. The other parameters of this model are similarly defined in Gardner & Eberhart work. When j = j' then θ=0 and for j≠j' then θ=1. The estimators for the parameters and the sums of squares formulas were determined through the least squared method. Variances of the parameters estimators and the analysis of variance were also determined. An example is presented with its correspondent analysis.