Environmental stratification based on a 28 x 28 diallel of open-pollinated maize varieties

The objective of this study was to assess the representativeness of the test environments used by the maize breeding program of Embrapa in the first phase of genotype evaluation. Ear weight of 378 hybrids from a diallel of 28 openpollinated varieties (OPVs) evaluated in ten environments were used. The following environments were evaluated: two growing seasons (1991-92 and 1992-93), at three locations (Sete Lagoas, MG, Londrina, PR, and Goiania-GO); in two growing seasons (1991/92 and 1993/94) in Aracaju-SE; and in two growing seasons (1992-93 and 1993-94), in Ponta Grossa-PR. The complex part of the interaction accounted for nearly 75% of the genotype by environment interaction (G x E). The environments of Londrina-91/92, Ponta Grossa-93/94 and Aracaju-93/94 differed from the others and also from each other, as shown by stratification analysis. The phenotypic correlation between genotype means in the pairwise grouped environments, interpreted as coefficient of genotypic determination, indicated that non-genetic causes were responsible for 64.40% of the mean phenotypic variances. The results confirmed the discrimination of three major environmental groups, representing the Northeast (Aracaju), Central Southeast (Sete Lagoas, Goiania and Londrina) and South (Ponta Grossa) regions.


INTRODUCTION
In most cases in the literature, the complex part of the interaction was the major component of the total interaction, and sometimes even confused with the G x E. Even in studies where the G x E caused some inconvenience in the selection but was not partitioned, the difficulty was due to the inconsistency of the cultivar response to environmental changes. The answer to this question would enable breeders to determine the environment where trials should be conducted in the most practical, inexpensive and efficient way within a subset of environments grouped by non-significant interaction, based on the similarity patterns of the genotype response and other aspects.
The objective of this study was to verify the representativeness of the main environments used in the maize breeding program ofEmbrapa Milho e Sorgo, for the first year of evaluation of hybrids

MATERIAL AND METHODS
Data from 441 treatments were used. The treatments comprised 28 open-pollinated populations (P), the 378 interpopulation hybrids (F I) obtained from a diallel cross of these 28 populations, the first selfing generation (S I) of each of the 28 populations, and 7 checks (see Pacheco  Environmental effects were considered random factors, since the geographical distribution of lhe experi ments consti tuted a representative sample of the environmental conditions of maize-growing areas in Brazil. Population effects were considered fixed factors, since the populations represented a selected set of the best and/or most promising populations of the corn breeding program of the CNPMS, and are unlikely to be a representative random sample of the populations of the Maize Germplasm Bank (BAG).
Adjusted means of treatments involved in the diallel were used for the analysis. Joint analyses of environments, two at a time, were performed to estimate the cornplex part of interaction (C), using software Genes (Cruz 1997). The methodology was based on the expression ofCruz and Castoldi (1991): q%) J~-rJQ,Q'xloo Q" where: C (%) is the percentage of the cornplex part of interaction; r, is the phenotypic correlation between the means of the sarne genotype, in two environments; QI and Q2 are the mean squares of genotypes in environments 1 and 2 ; QI2 is the mean square of in teraction between genotypes and en v iron men ts, considering environments J and 2.
The stratification methodology of Lin (1982) was used, as proposed by Cruz and Regazzi (1994). It consists of the estimation o f the surn s of squares of the interaction between genotype and environments pairs, with subsequent grouping of the two environments with srnaller and non-significant interaction, based on the F test. The process is then repeated, in an attempt to include a new environment in the first group of two environments, thus grouping the environments in groups of three , then four , and so on, unti I the F test is significant, indicating that no other environment can be included. The process should then be restarted with the still ungrouped environments.

RESULTS AND DISCUSSION
Despite thelarge number of treatrnents, the efficiency of the lattice cornpared to the randomized block design was low (Table J). The performance of the lattice design was bestin Aracaju -91/92 (44.54%) and poorest in Ponta Grossa -92/93 (0.08%). The use of a randomized block design would result, in the mean, in mean squares that would exceed the effective errors of lattice by 15.73%.
The complex part of interaction (values above Lhe diagonal in Table 2) accounted for a rnean of about 75% of the G x E, indicating differences in the ranking of populations among environments. By the significance of the F test for the G x E in the environments, considered two by two, it was observed that the responses were always different (p<O.OI) when the environments 2,9 and 10 were involved (Londrina -91/92, Ponta Grossa-93/94 and Aracaju-93/94).
Due to the imbalance of growing seasons, it was not possible to perform the analysis of variance, which would provide results on the genotype-year interaction,  The coefficient of variation (CY) ranged from 9.07% to 23.22%, allowing the following c1assification of the experirnents, according to Scapim et al. (1995): 2 environments -low; 7 environments -rnedium, and 1 environment -high. The mean CY of 15.11 % is below the mean of 16.22% estimated by the authors for the trait ear yield, based on 66 other maize breeding trials.
The ratio of 2.86 times between the largest and the smallest effecti ve error is well below the ratio of 7: 1, indicated by Gomes (1990) as a threshold to perforrn combined ANOVA from trials with different residual mean squares. Table 2. Pari of the complex genotype x environment interaction, according 10 Cruz and Castoldi (1991), in % (in bold above lhe rnai n diagonal) and estimares of simple correlation coefficients between genotype means, of lhe 10 pairwise environmcnt cornbinauons (in bold below the main diagonal) considering alllocations. However, the estimates based on data obtained in different years at the same location (values in bold in Table 2) show that G x E was nonsignificant in Goiania only, indicating the strong contribution of the effects of different growing seasons to the differential genotype response. It is possible that the genotype-year interaction at a same location is more important than the genotype-site interaction in a same year. Vencovsky and Torres (1988) found that these two forms of interaction were not correlated and may have distinct genetic bases.
lt may seem strange that sometimes a lower value for the complex part of interaction was significant, e.g., 68.9% among environments 4 and 5, while a much higher one, e.g., 84.9% among environments 8 and 5, was not. It must be stressed, that although the data in Table 2 referred specifically to the percentage of the interaction between genotypes and environments, considered pairwise, the F test was based on the total magnitude of the G x E due to complex causes.
The agreement of estimates of simple correlation coefficients between genotypemeans (phenotypic correlation) in the pairwise combinations of the 10 environments (Table 2, below the main diagonal), with esti mates of the respecti ve percentages of the complex part of interaction was good. Comparing the means, on the sides ofTable 2, it can be noted that the higher the correlation, the lower lhe contri bution of the complex part, as expected.
The correlation coefficient between phenotypic means of genotypes (r,) was estimated by the following ex pression:

Cov(P\,FJ r,= )V(Fl}V(F2)
where: Cov (Fj , F 2 )is the covariance between means of the same genotype in environments I and 2; V(FI)' V(F2) are the phenotypic variances of the genotype means within the environments I and 2, respectively.
If the environments were considered random, it can be assumed that Based on a general expression proposed by Cruz and Regazzi (1994) considering only two environments, it can be shown that: \1 2 (J g(12)+(Jgxa(12)= U g(I)+(J g(2») Based on this assumption, another, equally important 'expression can be inferred: Thus, if the denominator of expression (i) is used 10 compute the phenotypic variances, it could be replaced by the mean values of the second expression(ii), anel we woulcl have: In this final form (i v), it is easier to see that rf, under certain assumptions, is an indirect measure of the heritability coefficient (h 2 ) and can therefore be interpreted as an indicator of the mean fraction of lhe phenotypic variance between two environrnents, which is due to genotypic causes, also means, between the two environments.
Considering the genotype effccts as fixed, the interpretation rnay still be true, although ri would corresponcl to a genotypic coefficient o f determination.
Thus, the highest phenotypic correlation of 0.60 between Londrina and Sete Lagoas in 1992-93, interpreted as genotypic coefficient of deterrnination, indicates that 60% of'the variation in the treatments oeeurred due to genotypic causes. In this case, one may say that the phenotypic value was a good predictor of the genotypic value. However, in the mean of the 10 pairwise environment combinations, it was observed that as a mean effect, non-genotypic causes were responsible for 64.40% of lhe phenotypic variation.
Data shown in Table 3 refer to the grouping of environrnents with non-significant G x E, according to Cruz and Regazzi (1994). The environmental stratification was in full agreernent with the above explanations and conclusions on thecomplex part of G x E, evidencing that the results of the environrnents 2, 9 and 10 were di fferent from the other seven and also from each other. Environrnental stratification based on a 28 x 28 di al lel of opcn-pollinated rnaize varieties Table 3. Groups of environments with non-significant genotypeenvironrnent interaction for the treatments involved in the di aliei Groups Environrnents 11 I n m IV 1583764 10 2 9 11where 1 and 6 correspond to two different growing seasons in Sete Lagoas (MG) and, respectively, 2 and 7 to Londrina (PR), 3 and 8 to Goiânia (GO), 4 and 9 to Ponta Grossa (PR) and 5 and 10 to Aracaju (SE) The results of the clustering analysis represent exactly the order in which the environments were grouped.