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Analise de cruzamentos dialelicos parciais repetidos em varios ambientes (Analysis of partial-diallel crosses repeated over locations)

Antonio Carlos de Oliveira^I; Augusto Ramalho de Morais^I; Cláudio Lopes de Souza Júnior^II; Elto Eugênio Gomes Gama^I

^IEMBRAPA/CNP Milho e Sorgo, Caixa Postal 151, 35700 Sete Lagoas, MG, Brasil. Enviar correspondência para A.C.O.
^IIDepartamento de Genética, ESALQ.USP, Caixa Postal 83, 13400 Piracicaba, SP, Brasil.

ABSTRACT

This work deals with á methodology derived from the model proposed by Miranda Filho and.Geraldi (Rev. Brasil. Genet. VII, 4: 677-688, 1984) and adapted from Gardner and Eberhart (Biometrics, 22: 439-452, 1966), to compute combined analysis of variance of partial diallel crosses. The experiments comprise two sets of varieties, chosen in accordance with breeder's concern, and the hybrids among sets. The methodology of the analysis was based on the following mathematical model: Y_ijj,. = µ + ad + Q_i + ã (v_i + v_i,) + 9 ₍h + h_j + h., + sÿ,) + CYQdi + Z (Qv_ij + Qg_q,) + O (Qh. + Qh.. + Qh.., + Qs...,) + é_ij., , where Y..., is the hybrid mean resulting from the cross between the j^th variety of set 1 and the j'^th variety of set 2 in the _ith environment (CY= 0 and e = 1); Y... and Y_ij,., are variety means in the i^th environment (QC= 1, for Y_id , Or= -1 for _\riff and e =_-0); d is a measure of the difference between means of the two sets of varieties; Q_i is the effect of _i^th environment; m, v., v. , h, 1 _j, h „ s. and é_ijj, are defined analogous to the model of Gard- ner and Eberhart (1966) and the remaining parameters are the various interactions with the environment. The estimators of the parameters and formulas to compute the sums of squares in the analysis of variance were obtained by the least squares procedure. An example is given for illustration.

Keywords: partial-diallel; crosses.

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