Analysis and Interpretation of the Variety Cross Diallel and Related Populations

The parametric restrictions of the Griffing diallel analysis model: combining ability analysis

“…For one gene and populations with p ij values equal to 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1, the correlation between the effect of SCA of two populations and specific heterosis is 0.998, independent of the degree of dominance (d/a ≠ 0). This and the other results given above show that the methods of Griffing (1956b) and of Gardner and Eberhart (1966) where e jj and e jj' are the average values of the residues associated with the observations for population j and the hybrid of parents j and j', respectively.…”

“…For one gene and populations with p ij values equal to 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1, the correlation between the absolute values of g j and s jj is 0.965 for any degree of dominance (d/a ≠ 0). The s jj values thus provide the same inferences as the estimates of the parameters 'average heterosis' and 'variety heterosis' of the Gardner and Eberhart (1966) model. Although s jj is a measure of the population divergence relative to the diallel's parents and 'variety heterosis' is an indicator of the differences between the gene frequencies in the population and the average frequencies in the other genitors, the correlation between the absolute values of these parameters for one gene is 1, independent of the populations and of the degree of dominance (d/a ≠ 0).…”

“…If the parents are inbred lines or pure lines, the greater the value of the GCA effect of a population, the greater the number of genes that increase the trait expression and, consequently, the greater the number of positive differences between the gene frequency of the population and the average frequency in the diallel's parents. Therefore, the effect of GCA is an indicator of the superiority of the population and of its divergence relative to the diallel's parents, thus providing the same information as the parameters 'population effect' (v j ) and 'variety heterosis' (H j ) of the Gardner and Eberhart (1966) model. The correlation between the GCA effect and v j approaches close to 1 as the degree of dominance approaches zero.…”

“…If the s jj' value equals zero, the gene frequencies in one of the populations are equal to the average frequencies in the diallel's parents. The average value of the SCA effects of different populations is Therefore the SCA of populations j and j' is an indicator of the divergence between them and of their divergence from the diallel's parents, in a manner similar to the parameter 'specific heterosis' (S jj' ) of the Gardner and Eberhart (1966) model. For one gene and populations with p ij values equal to 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1, the correlation between the effect of SCA of two populations and specific heterosis is 0.998, independent of the degree of dominance (d/a ≠ 0).…”

Diallel designs, analyses, and reference populations

“…Morley-Jones (1965) modified this analysis for the half diallel. Gardner and Eberhart (1966) proposed an analysis for a half diallel among the parents which are themselves random mating populations, and although both Baker (1979) and Singh and Paroda (1984) have treated it as distinct from the MorleyJones (1965) analysis, it is in fact identical if the same parentage is used.…”