Analysis of diallel cross for the evaluation of maize populations across environments

Eleven open-pollinated maize (Zea mays L.) populations were crossed in a diallel scheme and evaluated in five locations in the State of Paraná: [1] Ponta Grossa, [2] Pato Branco, [3] Palotina, [4] Londrina and [5] Guarapuava. Two commercial hybrids (P 3230 and BR 201) were included as checks in the experiments, thus completing 68 entries (11 parents, 55 hybrids and 2 checks). Plots were represented by single rows 5 m long spaced 0.9m with 25 plants per plot after thinning. The following traits were analyzed: GYtotal plot grain yield expressed in kg/ha after adjustment to 14.5% grain moisture; PHplant height (cm); EHear height (cm); and FFdays for female flowering. Plant height and EH were not included in location [2]; FF was not include in locations [2] and [3]. The joint analysis of variance showed significance for all traits, only for the variation among location, entries, variety effects and average heterosis. For yield the total heterosis in mid-parent percentage varied from –0.96% (PMI 8403 x PMI 9304) to 32.4% (PMI 9302 x PMI 9307). Variety effects (vi) and general combining ability (gi) effects were in the range of –1483 to 772 kg/ha and from –847 to 448 kg/ha, respectively. Both gi (for yield) and vi (for the other traits) were used to select two populations to be used in a reciprocal recurrent selection program. BR 106 showed the highest estimates for both gi and vi for yield but also showed undesirable traits (tall plants and late flowering). Some outstanding populations for yield potential per se did not show a good performance in crosses. Other populations with outstanding performance in crosses exhibited lower variety effects for yield or high variety effects for the other traits. Some introduced populations who showed shorter plants and earliness should be submitted to selection for yield, adaptation and other agronomic traits before being indicated for crossing. However, they should be recommended as source populations for short architecture and early flowering. An overall analysis led to the decision of choosing the population IAPAR 26 to be used as contrasting parent of BR 106 in a reciprocal recurrent selection program at IAPAR (Londrina, State of Paraná).


INTRODUCTION
populations allow the synthesis of divergent composites which can be used in reciprocal recurrent selection program ( Hallauer and Miranda Filho, 1988).
Methods based on diallel crosses have been largely used in plant breeding, either to provide information on combining ability and/ or heterosis in crosses or to allow prediction of crosses that have not been directly evaluated (Miranda Filho and Chaves, 1992).Gardner and Eberhart (1966) suggested three ways for the analysis of diallel crosses of populations in equilibrium.Analysis I provides detailed information on the genetic effects but its use requires the inclusion of selfed parents besides the original parents and their crosses.Analyses II and III are based only on means of parent populations and their crosses.Analysis II provides a wide array of information including the effects of varieties and total heterosis and its components (average heterosis, variety heterosis and specific heterosis).Analysis III is a variation of Griffing (1956)'s Method 4, with partition of the sums of squares for hybrids into general and specific combining ability.
Short plant cultivars have long been recommended for the replacement of typically tropical varieties which are very tall with ears placed high in the stalk, bringing problems related to plant lodging and mechanical harvesting (Miranda Filho, 1974;Paterniani, 1993).On the other hand, early flowering cultivars have recently received special attention when short dry seasons may occur during the crop or they have also been recommended as second crop ("safrinha") in a double cropping system (Gama et al., 1995).
The IAPAR maize breeding program aims the introduction or synthesis of maize populations which have high yield, short architecture and earliness.In the present work, eleven open pollinated populations were evaluated using the diallel mating scheme.The objective of this study was to obtain information about the performance per se, heterotic pattern and combining ability of these populations for the choice of the most promising for use in recurrent selection and hybrid development progams.

MATERIAL AND METHODS
Eleven maize populations were chosen as parents in a diallel mating scheme for evaluation of their genetic potential as base germplasm for grain yield, short architecture and earliness.The origin and description of populations are shown in The analyses of variance were performed on each location and adjusted means were used in the analysis of variance across locations.Locations were considered as random effect and entries as fixed effect.The pooled error mean square was used to test the significance of entry by location interaction.Main effects were tested against their respective interactions with environment.
The diallel tables were analyzed according to Gardner and Eberhart (1966) model II.The model for each location is: Y ii' = µ + 2 Where Y ii' is the mean (over three replications) representing the cross i x i'; u is the mean of parent varieties or populations; v i is the effect of varieties or populations; h is the average midparent heterosis; h i is the variety heterosis; s ii' is the specific heterosis or specific combining ability; and e ii is the error term associated with the observed mean.The model can be applied to represent both variety or population mean (i = i'; q = 0) and hybrid mean (i ≠ i'; q = 1).The combined analysis over environments was performed according to the methodology given by Morais et al. (1991).

RESULTS AND DISCUSSION
Means were obtained for four traits over three replications, across five locations (Table 2).Grain yield (GY), varied from 4959 to 7373 kg/ha for varieties and from 5820 to 8505 kg/ha for hybrid crosses; the highest yield was for the BR 106 x PMI 9307 cross which was practically equal to the best check (P 3230) and 6.9% higher than the average of the two checks.For the other traits, the total means range was from 185 to 244 cm for plant height, from 90 to 132 cm for ear height and from 67 to 81 days for female flowering.
In the analysis of variance (Table 3), for grain yield, a highly significant variation P<0.01 was detected for locations, entries, varieties, heterosis, average heterosis, and interactions of varieties and heterosis effects with environments (locations).Similar patterns of significance for the same sources of variation were reported by Santos et al. (1994), Gama et al. (1995), Sinobas and Monteagudo (1996) and San Vicente et al. (1998).Variety heterosis and specific heterosis were non significant as source of variation, as also reported by Miranda Filho and Vencovsky (1984) for one set of open-pollinated varieties.
From the total sum of squares in the analysis of variance for yield, a proportion of 61% resulted from the effects of varieties and 39% resulted from the total heterosis.A similar  Biotechnology, v. 1, n. 3, p. 255-262, 2001 proportion of the sums of squares was reported by Gardner and Paterniani (1967), Parentoni et al. (1990), Gama et al. (1995), and Sinobas and Monteagudo (1996).However, a more expressive effect of heterosis as source of variation was found by Santos et al. (1994) and San Vicente et al. (1998).
From the components of the total heterosis, the highly significant average heterosis for yield is indicative of an expressive superiority of hybrid mean over the variety mean; in fact an average heterosis of 14.3% over all crosses was considered fairly high for variety crosses.
Hallauer and Miranda Filho (1988) reported a 19.5% average heterosis in a set of 1,394 crosses, including highly heterotic crosses between old races of maize.A high average heterosis (33%) including crosses with heterotic effects as high as 101% were reported by Paterniani and Lonnquist (1963) in crosses between South-American races.On the other hand, lower estimates of the average heterosis, ranging from 8 to 10%, was reported by Vasal et al. (1992), Beck et al. (1990) and Crossa et al. (1990) in diallel crosses between Mexican populations or "pools".The effect of variety heterosis and specific heterosis for grain yield   Biotechnology, v. 1, n. 3, p. 255-262, 2001 (Table 3) was not significant.Overall results are indicative that high yield in hybrid crosses depends essentially on the average heterosis rather than variety heterosis or specific heterosis.
For PH, EH and FF, the variation of locations, populations and varieties effects showed to be highly significant (P<0.01).A less significant effect (P<0.05) for average heterosis.Heterosis and specific heterosis was significant only for PH.The interactions between location with entries and varieties were highly significant for EH and FF and the interactions of total heterosis and variety heterosis were highly significant for FF.However, a higher possibility to detect significance of effects occur under a low magnitude of the interaction between some genetic effects and random environmental effects, as verified for the traits listed above.It may also occur as reported by Gama et al. (1995) for all sources of variation for PH and EH.
Table 3 -Analysis of variance, means and coefficients of variation (CV) for four traits over five locations following Model II of Gardner and Eberhart (1966) for variety diallel crosses.
*, ** Significant at 0.05 and 0.01 probability levels, respectively. 1/ kg/ha x 10 -6 The partition of the sums of squares showed that the larger portion was due to the variation among populations, with values of 83.2%, 85.1% and 89.1% for PH, EH and FF, respectively, thus indicating a less pronounced effect of dominance for those traits as compared to grain yield.Similar proportions were found by Miranda Filho and Vencovsky (1984), ), Gama et al. (1995), and Sinobas and Monteagudo (1996) Biotechnology, v. 1, n. 3, p. 255-262, 2001 and PMI 9307.IAPAR 51 was not included because, despite its high v i estimate, it showed a negative h i estimate (variety heterosis effect), leading to a positive but low g i value (general combining ability effect).Miranda Filho and Vencovsky (1984) emphasized that the v i are very important when h i 's are not significant.Otherwise, g i effects are useful for selection among populations because of the relation g i = v i + h i (Miranda Filho and Chaves, 1992).In this sense, the most promising variety in the set is unquestionably BR 106.
For the other traits (PH, EH and FF), the interest is for populations with lower effects of v i , as determined by the objectives of the program; i.e., identification of populations with lower architecture and early flowering.Population PMI 9303 showed the lowest v i estimates for the mentioned traits.O n the other hand, the highest effects were observed for BR 106 and IAPAR 26.
(PMI 9302 x PMI 9307).The later also showed a high and positive estimate for specific combining ability (s ii' ) and high grain yield mean (8279 kg/ ha).Estimates of specific combining ability (data not shown) varied from -904 (PMI 9303 x PMI 9307) to 788 kg/ha (IAPAR 51 x PMI 9303).Vencovsky (1970) emphasized that higher specific combining ability estimates result from large differences in allele frequencies.One cross that showed high negative estimate for s ii' (-611 kh/ha) was PMI 8701 x PMI 9301.Although PMI 9301 has been introduced from Paraguay, from a region close to the border with the State of Paraná, it exhibited morphological characteristics that are very similar to PMI 8701.Therefore, the possibility that PMI 9301 has been introduced from CIMMYT and thus have a genetic base similar to PMI 8701 cannot be ruled out.
As mentioned above, some intervarietal hybrids showed an yield expression of the same level as the checks, which showed by themselves a fairly high yield potential for the conditions of the State of Paraná.Hallauer and Miranda Filho (1988) emphasized that the general use of variety crosses is not recommended due to their lack of uniformity for several important traits, which contributes to a lower yield when compared to more uniform types of hybrids.In addition, the lack of uniformity may also raise difficulties for detasseling in the seed production fields and compromise uniform patterns of the harvested hybrid seeds.
However, the identification of outstanding varieties and variety crosses may indicate outstanding sources of inbred lines to be used in crosses toward the development of more uniform hybrid crosses.In this sense, the

Table 1 -
Origin and description of maize populations used in diallel crosses.

Table 2 -
Observed means for grain yield (Kg/ha), plant height (cm), ear eight (cm) and female flowering (days) in eleven populations and their crosses (diallel scheme).
1/ See table one for pedigree and cross designation

Table 4 -
Estimates of variety effects ( v ˆi) , general combining ability ( g ˆi), variety mean (m), and average heterosis ( h ) for four traits following Model II of