DIALLEL ANALYSIS AND PREDICTION OF UNTESTED MAIZE SINGLE CROSS HYBRIDS

Popcorn (Zea mays everta) is a popular snack food and very appreciated in Brazil, presenting higher aggregate value when compared with field corn. The aim of this study were to identify superior inbred lines and single crosses hybrids (SH) for popcorn traits, as well as the prediction of the performance of untested single cross hybrids. Sixteen maize inbred lines were crossed in a 9x7 partial diallel, but it was possible to evaluate 47 single crosses in two distinct locations. Predicted genetic values, diallel analysis and the prediction of untested HS were performed by mixed models. Deviance effects for treatments x locations were considered non-significant (p>0.05) for grain yield (GY) and popping expansion (PE), showing an average performance from the HS in the locations. Inbred lines P5-1, P3.3T, GER-P3, P9-1, P12-2 and GER-P12 were selected considering the general combining ability, and should be used for obtaining superior genotypes. Based on the non-additive effects, the single hybrid P3.3T x GERP-P12 was selected for grain yield and popping expansion, and could be exploited in future trials. Neither of the untested single crosses showed desirable performance for grain yield and popcorn expansion.


INTRODUCTION
Popcorn (Zea mays everta) is a popular snack food and it is very appreciated in Brazil, presenting higher aggregate value when compared with field corn.Popping expansion is conferred by pericarp resistance and grain moisture, differing from the field corn and being classified as specialty corn, although both belong to the same genus and species (LEONELLO et al., 2009;DE CARVALHO et al., 2013).When popcorn grains are exposed under heat, the oil and moisture content make pressure over pericarp, bursting it and exposing the endosperm, the so-called "popcorn flower".
According with Cruz et al. (2015), among the 477 maize cultivars available for Brazilian farmers at 2015/16 growth season, only the open pollinated variety RS-20 and the topcross hybrid IAC 125 are indicated for popcorn production.The lack of genotypes that aggregate agronomic and quality traits, associated with low production technology, are the main problems that limits the economical raise of the popcorn national market, favoring seed and grain importation (AMARAL JUNIOR et al., 2010;SILVA et al., 2013).Considering this scenario, the generation of new genotypes able to be used as popcorns, especially to small farmers and industries, it is essential for this specialty corn in Brazil.
The development of popcorn hybrids depends on genetic distance and gene complementation effect, thus, it is necessary to select inbred lines based on genetic effects and heterotic groups in order to obtain single cross hybrids with superior characteristics (HALLAUER et al., 2010).Diallel analysis is one of the most used techniques to obtain genetic information in any breeding program.This controlled mating system allows the estimation of the general combining ability (GCA) and the specific combining ability (SCA), which are associated to the additive and non-additive genetic effects (GRIFFING, 1956).According to the genetic base of the parents involved, the results of the diallel analysis allows the selection of parents for development of superior genotypes.
In situations with a high number of inbred lines, diallel systems results on a large quantity of single crosses for field evaluation.The most expensive part of a plant breeding program is comparing this crosses in field trials, since it is essential to evaluate them in multiple environments for years and different growth seasons (FRITSCHE-NETO et al., 2010;HALLAUER et al., 2010).
Therefore, this situation may lead on unbalanced data, especially due to differences between seed production and germination, soil fertility, pests, diseases and adverse climatic conditions, that affect the genotype development on field conditions.
It is essential, in any breeding program, a precise estimation of genetic components for accurate selection among a large data set, for development and recommendation of new improved genotypes (PIEPHO et al., 2008).Considering unbalanced data sets in annual and perennial species, the estimation and maximization of genetic gains can be achieved by mixed linear models (MLM) using REML/BLUP (restricted maximum likelihood/best linear unbiased predicted) procedure (PATTERSON; THOMPSON, 1976;SEARLE et al., 1992;RESENDE, 2002).Thus, it is also possible through MLM to predict the performance of untested hybrids in diallel crosses, using the information about the pedigree of the inbred lines or genetic distance based on molecular markers, allowing breeders to select single hybrids based on their performance without testing them in field trials (BERNARDO, 1996).
The aim of the present study was to select, based on their general and specific combining ability, inbred lines and single crosses with superior values for popcorn traits and to predict the performance of untested single crosses.

MATERIAL AND METHODS
Sixteen maize inbred lines were selection from the State University of Maringá breeding program (Table 1).The lines were divided in two groups for a partial diallel scheme, with nine inbred lines on group I and seven inbred lines on group II.Groups were divided according with genetic base, grain type, and based on previous experiments.The sixteen inbred lines were grown in 10 meters' rows, 0.9 meters spaced between rows and 0.20 meters between plants, in the second growth season of 2012 at Fazenda Experimental de Iguatemi, located at Maringá/PR.Due to low seed production, it was possible to obtain enough seed for evaluating 47 single hybrids among the 63 possible crosses.
Two trials were carried out in the main crop season of 2012/13.The first one was evaluated at Fazenda Experimental de Iguatemi, State University of Maringá (lat 23º 25' S; long 51º 57' O, alt 550 m) located in Maringá/PR, in a soil characterized as Dystrophic Red Latosol (DRL).The second one was evaluated at Fazenda Escola of State University of Londrina PR (lat 23º 22' S; long 51º 22' O, alt 566 m), located in Londrina/PR, in a soil characterized as Eutrophic Red Latosol (ERL).Climate of both regions is Cfa, according to the Köppen classification, with an annual average temperature of 19°C and an annual rainfall of 1500mm.
The experiments were arranged in a complete randomized blocks with common treatments, as proposed by Pimentel Gomes and Guimarães (1958).The 47 regular treatments were divided in groups, with three commercial controls that were used as the common treatments between groups, with three replications.The hybrids IAC 125, IAC 112 and Jade were used as commercial checks.
Experimental plots were consisted by 5 meters' single row, spaced 0.9 meters between rows and 0.20 meters between plants.In Maringá, sowing fertilization was done with 280 kg ha -1 of 08-20-20, and in Londrina the sowing fertilization was done with 250 kg ha -1 of 04-14-08.Twenty days after seed germination, side-dressing fertilization was performed with 50 kg ha -1 of urea.At 45 days after plant emergence, a thinning operation was performed to adjust the row stand to five plants per meter, totalizing 55.555 plants ha -1 .Both experiments were performed according with normal agronomic practices.
The following traits were evaluated: average plant height (PH, in cm) from six competitive plants; average ear height (EH, in cm) from six competitive plants; grain yield (GY, in kg ha -1 ), corrected to a 15% moisture content; popping expansion (PE, in mL g -1 ), determined in laboratory using an electric popping device developed by EMBRAPA -Centro Nacional de Pesquisa e Desenvolvimento de Instrumentação Agrícola (CNPDIA).Samples of each plot were composed by grains from ten kernels, manually hulled and discarding the both ends of the kernels.Popping expansion measurement was performed by the ratio of the volume from 30g grain after popping, at 280 o C for 2.5 minutes and with 13 to 14% of moisture content, with two replications per plot.A 2000 mL graduated cylinder was used to measure the popcorn volume after expansion.Experimental data was analyzed with the following mixed linear model, where: y is the vector from observed data (y x 1), l is the fixed effect vector (l x 1) from the environments, β is the fixed effect vector (β x 1) from the replications-experiments, a is the fixed effect vector (a x 1) from the environments-replicationsexperiments interaction, g is the random effect vector (g x 1) for regular and common treatments, p is the random effect vector (p x 1) for the interaction between treatments and environments, W, T, X, S, Z and I are the incidence matrixes from the associated l, e, β, a, g, and p parameters, and ϵ is the residual random effect vector.The significance of the random effects was performed by deviance analysis using likelihood ratio test (LTR), with and without g and p, using the chi-square with one degree of freedom at 5% of probability.Fixed effects of the model were tested though ANOVA, using F test at 5% of probability.
The predicted genotypic values (µ+g) were obtained through the sum of the genotypic values (BLUPs) with the average of fixed effects (environments and replicates).These values (µ+g) were used for treatment comparison and for diallel analysis through mixed models.For the diallel analysis using the IV model proposed by Griffing (1956) adapted for partial diallel's (CRUZ et al., 2012), the following mixed linear model was considered: which y is the vector (y x 1) of the predicted genotypic values (µ+g) for the characteristic, β is the fixed effect vector (β x 1) for the environments, g 1 is the random effect vector (g 1 x 1) related with the general combining ability effects ) for the inbred lines on group I (GCAI), g 2 is the random effect vector (g 2 x 1) related with the general combining ability effects ) for the inbred lines on group II (GCAII), s is the random effect vector (s x 1) for the specific combining ability (SCA) effects ) for the tested single cross hybrids between the inbred lines from the two groups, and X, Z 1 , Z 2 and Z 3 are the incidence matrixes from the associated β, g 1 , g 2 and s parameters, respectively.
The solution for the fixed and random effects followed the equation system proposed by Henderson (1984): Variance components were solved using the Expectation-Maximization (EM) algorithm from REML method.Based on initial arbitrary values for error, GCAI, GCAII and SCA variance components, the solutions for β, g 1 , g 2 and s were obtained and used again for obtaining new estimations of variance components and so on, until convergence is achieved.Identity matrices were used on the matrixes of coefficients of relatedness between the inbred lines in group I (A 1 ), group II (A 2 ) and between the single cross hybrids (A 3 ).Prediction of untested single crosses for phenotypic values and SCA estimation were performed considering the methodology proposed by Bernardo (1996).Predicted genotypic values (µ+g) from the tested single crosses were corrected for the fixed effects (β) using the proposed equation: is the vector of the phenotypic means corrected by the fixed effects, Z 3 is the incidence matrix from the parameter associated with the tested single crosses, X is the incidence matrix from the fixed effects, y is the vector (y x 1) of estimated means for the characteristic, β is the fixed effect vector (β x 1) associated with the environments.Prediction of untested single hybrids were made using the following expression: which being the performance vector of untested single hybrids, C is the matrix of covariance's between the tested and untested hybrids, V -1 is the variance-covariance matrix between the tested hybrids, and is the vector of the phenotypic means corrected by the fixed effects.Estimation of SCA from the untested hybrids was performed using SCA values from the tested hybrids at vector.For all traits evaluated, analysis of variance and deviance were performed in SAS software version 9.3 (SAS, 2013), considering significance when p<0.05.Diallel analysis and the prediction of untested single hybrids were performed using a function programmed on R software 3.3.1 (R CORE TEAM, 2016).

RESULTS AND DISCUSSION
The result of the deviance analysis for the random effects and the ANOVA for the fixed effects is presented in Table 2.The deviance values for the treatments differed significantly by the chi-square test at 5% probability for all the evaluated traits, indicating high genetic variability between the single hybrids.Considering the results for treatments x environments interaction, the deviance values were considered not significant for GY and PE, reflecting the similar performance of the treatments in both environments, an indication that the selection of the superior's single hybrids can be made considering the average performance in both environments.Hybrid performance differed for PH and EH according to the environment, indicating that selection must be made for each environment separately.
In popcorn breeding, the principal agronomic characteristics are grain yield and popping expansion (SILVA et al., 2013).Based on the predicted genotypic values, it is possible to conclude that none of the single hybrid crosses presented superior values in both traits, which is in agreement with the results obtained by Arnhold et al. (2006) and illustrates the difficulties for obtaining simultaneous positive gain selections, mainly due to the negative correlations.Nevertheless, the hybrid P3.3T x GER-P12 (2x4) presented the third higher values for PE and is among the six best hybrids for GY (4.53 t ha -1 ), performing better predicted genotypic values (µ+g) for these traits than the commercial checks, and can be considered promising for future experiments.
The results from the GCA for the mixed model diallel are shown on Table 4. Based on the additive effects, it is possible to select for GY the inbred lines P5-1 and P3.3T from group I and the inbred line GER-P3 from group II.Considering PE, the inbred lines P9-1 and P12-2 in group I and GER-P12 in group II were found to be superior in terms of frequency of favorable genes with additive effects.For PH and EH, the inbred lines P3.3T from group I and GER-P3 from group II showed the highest GCA effects. 1 GY: Grain Yield (kg ha -1 ). 2 PE: Popping expansion (mL g -1 ). 3 PH: Plant height (cm). 4EH: Ear height (cm).
Popcorn breeding programs seek genotypes that aggregate high grain yield and popping expansion.Based on GCA effects, it is possible to select the best inbred lines with superior additive effects for traits of interest, being a parental in future crosses for hybrids with large agronomic performance for producers and popcorn industry.Inbred line P3.3T showed the higher additive effect for GY and a good positive GCA effect for popping expansion, presenting a great potential for composing new genotypes with superior yield and popping expansion.These results suggest that, using a mixed linear model analysis, it is possible to select genotypes with satisfactory values for both grain yield and popping expansion.Similar results were found by Freitas et al. (2013), which recommended the use of selection index based on REML/BLUP methods for positive gains in grain yield and popping expansion, even with the negative correlation between the characteristics.
The SCA reflects the specificity between the parents involved in crosses, being explained by the effect of complementation between alleles derived from each parent (dominant gene action) and the effect of interactions between alleles of different loci involved in the trait transmission (epistatic gene action).High ij s ) values, regardless of the signal, indicates that the SCA performance were different than the expected based on the GCA of the parents.Although, for selecting the best crosses based on the SCA effects, at least one parent with high GCA should be present at the cross (CRUZ et al., 2012).Furthermore, SCA is also related with the genetic distance between the parents and demonstrate the importance of non-additive interactions to complement the performance of the hybrid combination.
The results for SCA effects are presented on Table 5.Based on the additive effects, the genitors P5-1, P3.3T and GER-P3 were selected for GY.The single hybrids P5.1 x GER-P14 (3x6), P3.3T x GER-P15 (2x7) and P8.1.1 x GER-P3 (4x1) showed the higher effect and also presented higher estimated means for GY (Table 3).Although, all these hybrids presented negative effects for PE and estimated means below 20 mL g -1 , indicating negative effects for this characteristic, which is not desirable in popcorn breeding programs (BARRETO et al., 2012).
The effects for PE and also for PH and EH were low and close to zero, indicating that the additive effects were more important to the estimated mean.Similar results were also observed by Vieira et al. (2011), highlighting the importance of GCA than SCA for popping expansion.The inheritance of bi-directional dominance may also explain the low participation of non-additive effects for PE (SILVA et al., 2010).
Inbred lines P9-1, P12-2 and GER-P12 had superior additive effects, and the best hybrids for this characteristic should have at least one of these inbred lines.Thus, considering effects, the single hybrids P12-2 x GER-P12 (9x4), P3.3T x GER-P12 (2x4) and P9-1 x GER-P13 (7x5) were selected, but only P3.3T x GER-P12 (2x4) showed positive effects for GY.Regarding the estimated means (Table 3), this single hybrid was ordered between the six higher means for GY (4.53 t ha -1 ) and also between the three best ones for PE (27.98 mL g -1 ).Therefore, it is possible to achieve proper GY and PE means in single hybrids by selecting inbred lines with higher additive effects for GY (P3.3T) and PE (GER-P12), allowing a positive effect in the single hybrid, evidencing the potential of these inbred lines for popcorn breeding programs.
The results of the estimated means and SCA for the untested single hybrids, as well as Pearson correlation with the predicted genotypic values (µ+g) and ij effects obtained from the tested single hybrids, are showed at Table 6.Considering the selected inbred lines based on general combining ability (Table 4), the untested single crosses P5-1 x GER-P12 (3x4) and P8.2 x GER-P3 (5x1) presented higher performance for GY, with positive effects for SCA.For popping expansion, the single hybrid P9-1 x GER-P12 (7x4) showed positive ij and acceptable estimated mean.For PH and EH, the cross P3.3T x GER-P13 (2x5) was the best hybrid, with estimated means of 219.1 and 125.2 cm, in addition too positive ij effects.Although, none of the untested single crosses obtained satisfactory performance for GY and PE simultaneously.

Table 1 .
Groups, origin and number from the inbred lines used on the single cross formation.

Table 2 .
Deviance analysis, p-values and general means for the characteristics evaluated in both environments, at 2012/2013 growth season.

Table 3 .
Predicted genotypic values (µ+g) for the single cross hybrids and for the commercial checks evaluated in two environments, at 2012/2013 growth season.

Table 4 .
General combining ability effects from the group I and group II inbred lines, for the characteristics evaluated at two environments, at 2012/2013 growth season.

Table 5 .
Specific combining ability effects from the single crosses hybrids, for the characteristics evaluated at two environments, at 2012/2013 growth season.

Table 6 .
Estimated means, specific combining ability (SCA) from the untested single crosses, and Pearson correlation between tested and untested single crosses, for the characteristics evaluated at two environments, at 2012/2013 growth season.