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An adaptation of griffing's method iv of complete diallel cross analysis for experiments repeated in several environments

Daniel Furtado Ferreira; Gabriel Dehon S.P. Rezende; Magno Antonio P. Ramalho

Departamento de Biologia, Escola Superior de Agricultura de Lavras (ESAI.), Caixa Postal 37, 37200-000 Lavras, MG, Brasil. Send correspondence to M.A.P.R.

ABSTRACT

Griffing's method of complete diallel crosses, which evaluates only hybrids (method IV), was adapted for several environments. This methodology is based on the following mathematieal model: Y_ii.k= m + 1_k + g_i+ g_i+ s_ii + (1g)_ik + (1g)_i.k + (IS)_ii.k+ e_ii.k ;i < i, where Y_ii.k is the mean of the hybrid from the cross between the ith and i'th varieties of the group in the kth environment; 1k is the kth environmental effect; m, g_i, g_i,S_iI, e_ii.k are as described by Griffing (Aust. J. Biol. Sci. 9: 463-493, 1956b); the remaining parameters correspond to the many interactions with environments. Parameter estimates and formulas to calculate sums of squares were obtained using a least squares method. Au example is presented, related to a complete diallel carried out in two environments, concerning number of days to flowering of the common bean.

Keywords: Griffing's method; Diallel cross.

REFERENCES

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