The diallel analysis has been used mainly to estimate general-(GCA) and spe
cific combining ability (SCA) effects for a fixed sample of parents and les
s frequently to estimate components of variance for a random sample of pare
nts of the reference population. In both cases, only additive and deviation
s due to dominance effects can be estimated, assuming thar epistasis is neg
ligible. The triallel analysis allows the estimation of epistasis variance
because more ancestors are available and more covariances among relatives c
an be estimated. The maize (Zea mays L.) population SA-8 was used to estima
te components of variance through the generation of single- and three-way c
rosses with a random sample of 50 S1 lines. Replicated trials were planted
in ten environments, including seven acidic and three non-acidic soils. Eac
h trial consisted of 400 entries, 100 single- and 300 three-way crosses. Yi
elds on non-acidic soils averaged 70% greater than on acidic soils. Within
a given soil type (non-acidic or acidic), single crosses were similar to th
ree-way crosses in overall mean, maximum, and minimum values for grain yiel
d, clays to 50% silk emergence, and plant height. For these traits, GCA and
SCA sum of squares were highly significant using the triallel and diallel
analyses For acidic soils, and across environments; although an overestimat
ion for GCA effects for the diallel analysis was observed. Estimation of co
mponents of variance using the triallel and diallel data for the full model
showed that sigma (2)(AD), and sigma (2)(AA) explained 79 and 19% of the g
enetic variance respectively, and both were highly significant; sigma (2)(A
) explained less than 2% of the generic variance. On the other hand, using
the reduced model, sigma (2)(A) and sigma (2)(D) were significant and expla
ined 37 and 63% of the genetic variation, respectively. The results, using
the diallel data only, are in agreement with the reduced model. These resul
ts suggest that epistasis was important in the SA-8 maize population. The s
imilar grain yields for single- and three-way crosses in the present study
suggest that both types of hybrids would be suitable to increase maize yiel
ds in acidic and non-acidic environments of the developing countries.