Abstract
In plant breeding, the dialelic models univariate have aided the selection of parents for hybridization. Multivariate analyses allow combining and associating the multiple pieces of information of the genetic relationships between traits. Therefore, multivariate analyses might refine the discrimination and selection of the parents with greater potential to meet the goals of a plant breeding program. Here, we propose a method of multivariate analysis used for stablishing megatraits (MTs) in diallel trials. The proposed model is applied in the evaluation of a multienvironment complete diallel trial with 90 F_{1}’s of simple maize hybrids. From a set of 14 traits, we demonstrated how establishing and interpreting MTs with agronomic implication. The diallel analyzes based on megatraits present an important evolution in statistical procedures since the selection is based on several traits. We believe that the proposed method fills an important gap of plant breeding. In our example, three MTs were established. The first, formed by plant staturerelated traits, the second by tassel sizerelated traits, and the third by grain yieldrelated traits. Individual and joint diallel analysis using the established MTs allowed identifying the best hybrid combinations for achieving F1’s with lower plant stature, tassel size, and higher grain yield.
Key words
Zea mays L.; multivariate analysis; selection multivariate; multienviroments
INTRODUCTION
Experimental mating designs, especially diallel crosses, are widely used in maize breeding for the selection of superior hybrid combinations. These types of trials allow one to estimate the general combining ability (GCA), related to the additive gene effects and the specific combining ability (SCA), related to nonadditive gene actions (Feher et al. 2014FEHER K, LISEC J, RÖMISCHMARGL L, SELBIG J, GIERL A, PIEPHO HP, NIKOLOSKI Z & WILLMITZER L. 2014. Deducing Hybrid Performance from Parental Metabolic Profiles of Young Primary Roots of Maize by Using a Multivariate Diallel Approach, Lukens L (Eds). PLoS One 9:e85435., Oliveira et al. 2016OLIVEIRA GH, BUZINARO R, REVOLTI LT, GIORGENON CH, CHARNAI K, RESENDE D & MORO GV. 2016. An accurate prediction of maize crosses using diallel analysis and best linear unbiased predictor (BLUP). Chil J Agric Res 76: 294299.). With the estimates of the genetic parameters the breeder can define which are the combinations of crosses that reveal greater heterosis in F_{1} for the desired trait.
The genotype × environment interaction is characterized by the phenotypic performance of the hybrids not being consistent in the multienvironments. Responses can be modified by changes that occur intrinsically in the environment, that is, reflect differences in the sensitivity of hybrids to changes in the environment (Ramalho et al. 2012RAMALHO MAP, ABREU A, SANTOS JB & NUNES JAR. 2012. Aplicações da genética quantitativa no melhoramento de plantas autógamas. UFV, Viçosa, MG., Allard 1999ALLARD RW. 1999. Principles of plant breeding. 2ª ed. New York: J Wiley & Sons, 254 p.). The genetic causes of genotype × environment interaction can be attributed to physiological, biochemical, adaptive and related to scale representation of traits (Cruz et al. 2012CRUZ CD, REGAZZI AJ & CARNEIRO PCS. 2012. Modelos biométricos aplicados ao melhoramento genético. 4th ed., UFV, Viçosa, MG.).
Multienvironment diallel trials aim at obtaining hybrids for a broad region, or for specific regions that enable the hybrid to express its maximum agronomic potential (Hallauer et al. 2010HALLAUER AR, CARENA MJ & MIRANDA FILHO JB. 2010. Quantitative genetics in maize breeding. Springer New York, New York, NY., Ramalho et al. 2012RAMALHO MAP, ABREU A, SANTOS JB & NUNES JAR. 2012. Aplicações da genética quantitativa no melhoramento de plantas autógamas. UFV, Viçosa, MG.). Thus, in these types of trials it is possible to detect the interaction of combining ability×environment (Nardino et al. 2016bNARDINO M, SOUZA VQ, BARETTA D, KONFLANZ VA, FOLLMANN DN, CARVALHO IR, FERRARI M, CARON BO & SCHMIDT D. 2016b. Partial diallel analysis among maize lines for characteristics related to the tassel and the productivity. African J Agric Res 11: 974982., Ogut et al. 2014OGUT F, MALTECCA C, WHETTEN R, MCKEAND S & ISIK F. 2014. Genetic analysis of diallel progeny test data using factor analytic linear mixed models. For Sci 60: 119127., Zhang et al. 2016ZHANG YD, FAN X, YAO W, PIEPHO HP & KANG MS. 2016. Diallel analysis of four maize traits and a modified heterosis hypothesis. Crop Sci 56: 11151126., Mutimaamba et al. 2017MUTIMAAMBA C, MACROBERT J, CAIRNS JE, MAGOROKOSHO CE, NDHLELA T, MUKUNGURUTSE C, MINNAARONTONG A & LABUSCHAGNE MT. 2017. Diallel analysis of acid soil tolerant and susceptible maize inbred lines for grain yield under acid and nonacid soil conditions. Euphytica 213: 88.). Therefore, it is assumed that gene effects are heterogeneous among the environments under study. In this case, when the interaction is significant, the best way to achieve satisfactory results is regionalizing the recommendation of hybrid cultivars.
The selection of cross combinations between lines is performed by the breeders after the evaluation of a set of traits, which are determinants for the definition of their superiority (Silva et al. 2008SILVA GO, PEREIRA A, SOUZA VQ, CARVALHO FIF & VIEIRA EA. 2008. Capacidade de combinação multivariada para caracteres de tubérculo em gerações iniciais de seleção em batata. Ciênc Rural 38: 321325.). However, in the majority of reports, each trait is analysed and interpreted separately, which are often insufficient to precisely predict the phenomenon. Multivariate analyses allow combining and associating the multiple pieces of information of the genetic relationships between traits. Therefore, multivariate analyses might refine the discrimination and selection of the parents with greater potential to meet the goals of a plant breeding program (Ledo et al. 2003LEDO CAS, FERREIRA DF & RAMALHO MAP. 2003. Análise de variância multivariada para os cruzamentos dialélicos. Ciênc Agrotec 27: 12141221.).
Although multivariate diallel analysis has been used in some studies, the selection of traits aiming at stablishing megatraits (MT) occurs empirically and often a priori (Ledo et al. 2003LEDO CAS, FERREIRA DF & RAMALHO MAP. 2003. Análise de variância multivariada para os cruzamentos dialélicos. Ciênc Agrotec 27: 12141221., Kostetzer et al. 2009KOSTETZER V, MOREIRA RMP & FERREIRA JM. 2009. Cruzamento dialélico parcial entre variedades locais do Paraná e variedades sintéticas de milho. Pesq Agropec Bras 44: 11521159., Nascimento et al. 2010NASCIMENTO IR, MALUF WR, GOLÇALVES LD, FARIA MV, DE RESENDE JTV & NOGUEIRA DW. 2010. Capacidade combinatória de linhagens de pimentão a partir de análise dialélica multivariada. Acta Sci Agron 32: 235240., Hu et al. 2017HU G, GU W, YANG R & WANG B. 2017. Multivariate diallel crossanalyses for body weight of rainbow trout, Oncorhynchus mykiss, in China. J World Aquac Soc 48: 240247.). The combined use of diallel cross designs and a posteriori multivariate analysis considering the correlations among traits to stabllishing the MTs, can provide important information for breeders in selecting crosses. In an innovative and unpreceded way in plant breeding, this study has aimed proposes and validates a linear model for multienvironments trial using multivariate analysis for stablishing megatraits (MTs) and selection of lines in diallel crosses.
MATERIALS AND METHODS
Plant Material
We carried out complete diallel crosses (F_{1}’s and reciprocals) with ten maize inbred lines (S_{9} generation, KSP 1 to KSP 10) of the Maize Breeding Program of the KSP Seeds and research Ltda, Pato Branco, PR, Brazil. The lines used at the crossing were selected from single and triple commercial hybrids with desirable agronomic traits, mainly for grain yield. The crosses were carried out in Campo Alto, Clevelândia, PR, Brazil, between October, 2011 and March, 2012. The lines were previously selected considering their performance per se, tolerance to the main leaf diseases, plant height, height of ear, resistance to lodging and culm breakage, yield of grain, mass of one hundred grains. At the flowering stage, the crosses were carried out according to the established genetic design by using artificial pollinations. The ears were manually harvested in field (with approximately 35% moisture), and later arranged in an airforced dryer up to moisture stabilization (14%). Afterwards, the ears were threshed and the seeds of each crossing were splitted into three equal parts, aiming at conducting the F_{1}’s in multienvironments.
Sites and experimental design
From the crosses, 90 hybrid combinations were obtained, which were evaluated in the 2012/2013 growing season in three growth sites in the Southern region of Brazil: Pato Branco (PB), Campos Novos (CN) and Frederico Westphalen (FW) (Figure 1). For all sites, the experimental design was a randomized complete block design with three replicates. The experimental units were composed of two 5m long rows spaced at 0.70 m. In the surroundings of the experiment four rows were sown to minimize the edge effects. Sowing was manually carried out using 300 kg ha^{1} of a 52020 NPKbased fertilizer. When the plants had six to eight fully emerged leaves, 140 kg ha^{1} of N was applied in a single topdressing, according to Coelho et al. (2002)COELHO AM, FRANÇA GE, PITTA GVE, ALVES VMC & HERNANI LC. 2002. Cultivo do milho: nutrição e adubação. Sete Lagoas: Embrapa, 12 p. (Comunicado Técnico, 44)..
When plants reached emergency stage we carried out a manual thinning adjusting the plant density to 42 plants per plot. This number corresponds to a density of 60,000 plants per hectare. Weed control was performed using preemergence herbicide (Atrazine + Simazine) and postemergence herbicide (Tembotrione). At the harvest stage, aiming at avoiding edge effects, 0.5 m at each plot end was excluded.
Assessed traits
At flowering, harvest and post harvest stages 14 agronomic traits were evaluated in three plants per plot. Table I shows the traits and its assessment method.
Description and methodology of assessment of the 14 traits evaluated in 90 simple maize hybrids.
Statistical analysis
Analise of variance
As a first step, data on 14 assessed traits (Table I) were subjected to univariate ANOVA to verify the assumptions (normality, homogeneity, independence of residuals and additivity of the model). The following model was considered
Where, y_{ijk} is the espected value of the dependent trait in the jth block (j = 1, 2, and 3) of the kth environment (k = 1, 2, and 3) which received the ith genotype (i = 1, 2, ..., 90); μ is the overall mean; β_{j(k)} is the effect of the block j in the environment k; α_{i} is the additive effect of the ith genotype (fixed); τ_{k} is the additive effect of the kth environment (random); (ατ)_{ik} is the nonadditive interaction between the ith genotype in the kth environment (random); $${\stackrel{\xaf}{\epsilon}}_{ij(k)}$$and is the average error associated toassumed to be normally, identically and independently distributed [IID~N(0,σ^{2})].
Factor analysis
As the interaction was significant for all traits, the factor analysis was performed considering the individual environments. The following model was considered:
Where X_{j} is the jth trait estimated in each plot (j= 1, 2, ... 14), l_{jk} is the fator load of the jth trait linked to kth factor (k = 1, 2, ... m); F_{k} is the kth common factor, is the specific factor (Cruz & Carneiro 2003CRUZ CD & CARNEIRO PCS. 2003. Modelos biométricos aplicados ao melhoramento genético. 2nd ed., UFV, Viçosa, MG.). The initial fator load is: $${l}_{ij}={\lambda}_{i}{V}_{ij}^{2}$$, where λ_{ij} the ith eigenvalue greather than one estimated in the phenotypic correlation matrix and V_{ij} is the jth value of the ith vector being j the number of traits and k the number of factors. The commonality is represented by: $${\varsigma}_{j}^{2}=\underset{K=1}{\overset{m}{\sum}}{I}_{ik}^{2}=1{\stackrel{^}{\sigma}}_{\stackrel{^}{e}j}^{2}$$, where $${\stackrel{^}{\sigma}}_{\stackrel{^}{e}j}^{2}$$ is the variance of the specific factor linked to the jth trait and with the initial factor load of these factors. After the initial factor load was calculated, the Varimax rotation procedure was applied (Mardia et al. 1979MARDIA KV, KENT JT & BIBBY JM. 1979. Multivariate analysis. London: Academic Press, 521 p.) aiming at obtaining the final factor loads, with which megatraits were chosen.
For the factor analysis, we used the original data matrix of the crosses (90 hybrids, three environments, three replicates and 14 traits). A factor analysis was carried out for each environment. The number of common factors was defined as being equal to the number of eigenvalues greater than one and the orthogonal model was chosen (Ferreira et al. 2010FERREIRA FM, NEVES LG, BRUCKNER CH, VIANA AP, CRUZ CD & BARELLI MAA. 2010. Formação de supercaracteres para seleção de famílias de maracujazeiro amarelo. Acta Sci Agron 32: 247254.).
The scores of the factors were estimated by using the following matricial equation:
Where $${F}^{\ast}=[{E}_{1}{E}_{2}\dots {E}_{\mu}]$$ is the vector of 1×m dimension of the factor scores (E_{k}); $$G=\left(\begin{array}{cccc}{\ell}_{1,1}& {\ell}_{1,2}& \dots & {l}_{1,\mu}\\ {\ell}_{2,1}& {\ell}_{2,2}& \dots & {\ell}_{2,\mu}\\ \dots & \dots & \dots & \dots \\ {\ell}_{14,1}& {\ell}_{14,2}& \dots & {\ell}_{14,\mu}\end{array}\right)$$is the matrix of 14×m dimension of the final factor loads $$({\ell}_{j,k})$$; $$X=\left(\begin{array}{c}{\stackrel{^}{\mu}}_{1}\\ {\stackrel{^}{\mu}}_{2}\\ \dots \\ {\stackrel{^}{\mu}}_{14}\end{array}\right)$$is the vector of v×1 dimension of the traits of the kth cross.
Data on the 14 traits were standardized and subjected to factor analysis, according to the model described above. Three megatraits were established, called here as plant stature (MT1), tassel size (MT2) and grain yield (MT3).
Analysis of diallel crosses
The three MTs were subjected to diallel analysis, to verify the significance of the interaction and to obtain the estimates of the combinatorial abilities, according to the model 3, method I of Griffing (1956)GRIFFING B. 1956. Concept of general and specific combining ability in relation to diallel crossing systems. Aust J Biol Sci 9: 463493.. The following estimates were obtained: general combining ability (GCA), specific combining ability (SCA) and reciprocal specific combining ability (RSCA).
Firstly, an individual diallel analysis was carried out according to the followig model:
Where y_{ij}: is the average value of the F_{1}’s and reciprocal hybrids (i, j = 1, 2, ..., p); μ is the overall mean; g_{i} and g_{j} are the effects of the GCA of the ith and jth parent, respectively; S_{ij}is the effect of the SCA for the crosses between parents of i and j order; r_{ij} is the reciprocal effect wich reveals the differences of parents i and j, when used as male or female lines (in the cross ij); and $${\stackrel{\xaf}{\epsilon}}_{ij}$$ is the average error assumed to be IID~N(0,σ^{2}). The following resctrictions were considered: $$\mathrm{\Sigma}{\stackrel{^}{g}}_{i}=0$$, $$\mathrm{\Sigma}{\stackrel{^}{s}}_{ij}=0$$, and $${s}_{ij}={s}_{ji}$$.
Subsequently, a joint diallel analysis was performed considering the three sites. All the effects were assumed to be fixed, except the experimental error. The same restrictions of individual diallel analysis were considered. The statistical model adopted for each MT was the following:
Where, Y_{ij} is the value of hybrid combination between the parents i and j; μ is the overall mean; g_{i} and g_{j} are the effects of the GCA of the ith and jth parent, respectively; s_{ij} is the effect of the SCA for the crosses between parents of i and j order; a_{k} is the effect of the environment k; ga_{ik} and ga_{jk} is the effect of the interaction between GCA associated to the parents i and j and the environment k, respectively; sa_{ijk} is the effect of the interaction between SCA associated to the parents i and j and the environvent k; $${\stackrel{\xaf}{\epsilon}}_{(k)ij}$$and is the average error assumed assumed to be IID~N(0,σ^{2}).
Estimates of the quadratic components that express the genetic variability of the genotypes studied in terms of general and specific combining ability and reciprocal effect were obtained according to the following expressions, assuming the components as fixed.
where $${\stackrel{^}{\varphi}}_{g}$$is the quadratic component associated to the general combining ability; $${\stackrel{^}{\varphi}}_{s}$$ is the quadratic component associated to the specific combining ability; $${\stackrel{^}{\varphi}}_{r}$$ is the quadratic component associated to the reciprocal effect; MSG, MSS, MSR and MSE are the mean squares of the general combining ability, specific combining ability, reciprocal effect and error, respectively; p is the number of lines used in the diallel analysis (Cruz et al. 2012CRUZ CD, REGAZZI AJ & CARNEIRO PCS. 2012. Modelos biométricos aplicados ao melhoramento genético. 4th ed., UFV, Viçosa, MG., 2013).
The geneticstatistical analyses were carried out with the softwares Genes (Cruz 2013CRUZ CD. 2013. GENES  a software package for analysis in experimental statistics and quantitative genetics. Acta Sci Agron 35: 271276.) and SAS 9.22 (SAS Institute Inc 2010SAS Institute Inc. 2010. SAS/STAT 9.22 User’s Guide. SAS Institute Inc., Cary, NC.).
RESULTS AND DISCUSSION
Factor analysis
It was initially intended to obtain the grouping of all the traits within the factors, but the trait aggressiveness of the root system was not grouped in any of the three established factors. Then the script of Johnson & Wichern (2002)JOHNSON R & WICHERN D. 2002. Applied multivariate statistical analysis. 5th ed., Upper Saddle River, NJ. Prentice Hall, Englewood Cliffs. was followed. The analyses were carried out with four and five factors. In all, a factor related to the aggressiveness of the root system was obtained, but a factor that demonstrated simultaneous relations of this trait with the other evaluated traits was not obtained, which reveals the absence of correlation of this variable with the other studied. Thus, a minimum number of factors (in this case three factors) was maintained, which according to Granate et al. (2008)GRANATE MJ, CRUZ CD, CECON PR & PACHECO CAP. 2008. A análise de fatores na predição de ganhos por seleção em milho (Zea mays L.). Acta Sci Agron 23: 12711279., made the interpretations more concise. We also chose to maintain three factors, because the first three eigenvalues explain approximately 70% of the total variation.
The initial factorial loads, initial commonalities and final factorial loads were calculated (^{Table SI – Supplementary Material} Table SI ). By analyzing the final factorial loads, the factors for FW were identified, as the first related to plant stature (MT1), since it was the one that presented greater final factorial loads for the traits related to plant stature, which in this work are EH, PH and EH/PH (Table SI). The second factor was the one that was mostly related to the grain yield (MT2), because it presented high factorial loads for the traits FKM, GYP and GYH (Table SI). The third factor presented the highest final factorial load for the traits FLD, TL and NTB (Table SI), called the megatrait Tassel Size (MT3). For the PB and CN environments in the first factor, the megatrait Grain Yield was grouped; in the second factor Tassel size; and in the third factor the plant stature. In this way, the MTs were stablished by the magnitudes and the signals of the final factorial loads. The signs revealed by the factorial loads reflect the direction of the selection of the trait, considering the aims of the breeding programs. The MT can vary according to the biological interpretation, i.e., breeders can establish a MT based on the aims of their own breeding program (Ferreira et al. 2010FERREIRA FM, NEVES LG, BRUCKNER CH, VIANA AP, CRUZ CD & BARELLI MAA. 2010. Formação de supercaracteres para seleção de famílias de maracujazeiro amarelo. Acta Sci Agron 32: 247254.).
The canonical loads were used as weighting coefficients of the standardized traits, to obtain the scores of the new MTs, obtained from the factor analysis. The analysis of factors has in theory, that the traits of a given factor are weakly correlated with the traits of other factors, to the point that the factors are uncorrelated (Cruz & Carneiro 2003CRUZ CD & CARNEIRO PCS. 2003. Modelos biométricos aplicados ao melhoramento genético. 2nd ed., UFV, Viçosa, MG.).
The sites conducting the trials present particularities for the climatic elements that have a strong influence on the growth and development of maize. Initially, the three sites were chosen because they represent a representation of the edaphoclimatic conditions for the southwest of Paraná, midwest of Santa Catarina and northwest of Rio Grande do Sul, with corn cultivation in small and medium rural properties. In these environments a variation of the climatic elements occurs, such as the altitude of CN for FW and PB, which gives T° colder the ideal night for the cultivation of maize hybrids, as it is perceived in Figure 1, which shows that the T° average are lower. The identification of promising crosses for the three environments simultaneously is desired, as well as for each environment individually.
Analysis of variance of the megatraits
The sum of squares of multivariate diallel analysis via factor analysis (Table II) revealed that there were significant effects for the crossing (C) in MT1. The same significance was observed for GCA and SCA. The presence of significance for GCA and SCA points to the existence of variability between GCA, associated with additive gene effects, and between SCA, associated with nonadditive effects. The GCA with significant effects indicates that the inbred line contribution was different according to the crosses to which they were involved. However, the variability between the effects of SCA indicate that there are hybrid combinations that presented different performance than it was expected only based on the GCA effects (Aguiar et al. 2004AGUIAR CG DE, SCAPIM CA, PINTO RJB, DO AMARAL JÚNIOR AT, SILVÉRIO L & ANDRADE CAB. 2004. Análise dialélica de linhagens de milho na safrinha. Ciênc Rural 34: 17311737.).
Multivariate diallel analysis of variance for the three megatraits assessed in 90 simple hybrids grown in three sites.
Given the great importance of SCA estimates for selecting the best hybrid combinations, the selection of which line(s) will be male or female in the crosses is not specified. In this sense, reciprocal effect information is needed (Cruz et al. 2012CRUZ CD, REGAZZI AJ & CARNEIRO PCS. 2012. Modelos biométricos aplicados ao melhoramento genético. 4th ed., UFV, Viçosa, MG.). In this study, no megatrait presented significant reciprocal effects (Table II), the magnitude of the traits is not influenced by the direction of the crosses. In this sense, it is suggested that the inheritance of the traits associated to these MTs is mainly controlled by nuclear genes (Vivas et al. 2013VIVAS M, SILVEIRA SF, DA PEREIRA MG, CARDOSO DL & FERREGUETTI GA. 2013. Análise dialélica em mamoeiro para resistência a manchadephoma. Ciênc Rural 43: 945950.).
In the multivariate diallel analysis considering the effects of the interaction (Table II) a significance (p < 0.01) was observed for the three MTs for interaction between crosses×environment (C×E), general combining ability×environment (GCA×E), specific combining ability (SCA×E) and for the reciprocal effects×environmental (R×E). The nonsignificant effect for GCA and SCA of the MT2 and MT3 with the environment indicate that the selection of the lines aiming at hybrid formation is specific for each environment. Thus, the heterotic groups used for one cannot be generalized to the other environments, due to the significant effect revealed by the interaction.
The presence of significant C×E interaction shows that the hybrids present a differential response depending on modifications of the environment. For maize, GxE interaction has been widely studied due to its high breeding level, narrow genetic base, and its modelcrop role among outcrossing species. Furthermore, the wide range of environments in which this crop can grow is also a factor (Souza Neto et al. 2015BARETTA D, NARDINO M, CARVALHO IR, DANIELOWSKI R, LUCHE HS, DE OLIVEIRA VF, DE SOUZA VQ, DE OLIVEIRA AC & DA MAIA LC. 2016. Characterization of Dissimilarity among Varieties in Brazilian Maize Germplasm. Aust J Crop Sci 10: 112.). This type of interaction was also reported in previous studies (Locatelli et al. 2002LOCATELLI AB, FEDERIZZI LC & NASPOLINI FILHO V. 2002. Capacidade combinatória de nove linhagens endogâmicas de milho (Zea mays L.) em dois ambientes. Ciênc Rural 32: 365370., Oliboni et al. 2013OLIBONI R, FARIA MV, NEUMANN M, RESENDE JTV, BATTISTELLI GM, TEGONI RG & OLIBONI DF. 2013. Análise dialélica na avaliação do potencial de híbridos de milho para a geração de populaçõesbase para obtenção de linhagens. Semina Ciênc Agrár 34: 718.).
The presence of significant effects of SCA on the MT1 megatraits indicates that the parents’ mean and their GCAs cannot explain the performance oscillation that occurs in specific hybrid combinations (Cruz et al. 2012CRUZ CD, REGAZZI AJ & CARNEIRO PCS. 2012. Modelos biométricos aplicados ao melhoramento genético. 4th ed., UFV, Viçosa, MG.). With the manifestation of significant effects of the SCA×E, we point out to the differentiated performance of the hybrid combinations in the three environments, related to their performance and the combinatorial ability of the evaluated traits, indicating that the selection of the best hybrids (crosses) should be made within each environment (site). According to Rocha et al. (2014)ROCHA F, STINGHEN JC, GEMELI MS, COIMBRA JLM & GUIDOLIN AF. 2014. Análise dialélica como ferramenta na seleção de genitores em feijão. Rev Ciênc Agron 45: 7481. higher values are given to genotypes that are dissimilar in their frequencies of genes with dominance, although they are also influenced by the average gene frequency of the diallel.
GCA and SCA estimates in fixed diallel models are limited to the group of lines evaluated in the crosses. Thus, the quadratic components express the genetic variability present only in the studied constitutions, allowing estimates of predominant gene actions for each MT (Cruz et al. 2012CRUZ CD, REGAZZI AJ & CARNEIRO PCS. 2012. Modelos biométricos aplicados ao melhoramento genético. 4th ed., UFV, Viçosa, MG.). The quadratic component estimates (Table II) for GCA ($${\stackrel{^}{\varphi}}_{\text{GCA}}$$), SCA ($${\stackrel{^}{\varphi}}_{\text{SCA}}$$) and GCA/SCA ratio ($${\stackrel{^}{\varphi}}_{\text{GCA}}/{\stackrel{^}{\varphi}}_{\text{SCA}}$$), indicate that the additive genetic variance was the most relevant component for all megatraits in all environments, except for MT3 in environment 1. Superiority in the environments for virtually all megatraits indicates predominance of additive gene effects on the expressiveness of these traits and demonstrates that the progenies perform according to the GCA between the parents (Drumond et al. 2014DRUMOND ESC, PIRES AV, BONAFÉ CM, MOREIRA J, VELOSO RC, ROCHA GMF, BALLOTIN LMV & ALCÂNTARA DC. 2014. Rendimento de carcaça de codornas de corte em cruzamentos dialélicos. Ciênc Rural 44: 129134.).
The partitioning of the sum of squares of the GCA×E interaction is shown in Table III for the three MTs. The results, as well as the discussion, will be presented for each MT separately.
Estimates of general combining ability (GCA) for three megatraits in a joint diallel analysis with F1’s and reciprocal grown in three sites. Boldhighlighted values are the favorable combining for each megatrait.
General combining ability for the megatrait plant stature
The morphological traits of plant stature grouped into MT1 have been taken special attention of breeders in recent years. Currently, maize breeders have directed their efforts aiming at reducing plant stature (Aguiar et al. 2004AGUIAR CG DE, SCAPIM CA, PINTO RJB, DO AMARAL JÚNIOR AT, SILVÉRIO L & ANDRADE CAB. 2004. Análise dialélica de linhagens de milho na safrinha. Ciênc Rural 34: 17311737.). Thus, negative GCA estimates are of greater interest since the additive gene contributions of the lines with such estimates are favorable for stature reduction. The lines 4, 5, 7, 8 in FW, 4, 5, 6, 7 in PB, and 4, 5, 7, 8, 9, 10 in CN showed estimates of additive gene effecs favorable for reduction of plant stature (Table III). Therefore, the lines 4, 5 and 7 present negative estimates for the three studied environments. Negative estimates of GCA obtained for the three traits (that compose the MT1) simultaneously, present high importance in maize breeding programs. Taller plants make harvesting more difficult, and are more susceptible to lodging and breaking, in regions with a high incidence of winds (Freitas et al. 2013FREITAS ILJ, AMARAL JUNIOR AT, VIANA AP, PENA GF, CABRAL PS, VITTORAZZI C & SILVA TRC. 2013. Ganho genético avaliado com índices de seleção e com REML/Blup em milhopipoca. Pesq Agropec Bras 48: 14641471.).
General combining ability for the megatrait tassel size
Regarding the traits related to tassel size, grouped into MT2, maize breeding programs have worked aiming at reducing their magnitudes. Thus, lines with negative estimates are desirable. The lines 2, 3, 6, 7, 10 for FW, 2, 5, 6, 9 10 for PB and 5, 6, 7, 9, 10 for CN presented favorable estimates of additive gene effects for reduction of tassel size (Table III). The lines 6 and 10 showed negative estimates in the three environments. These estimates are desirable in maize breeding programs, since lines that contribute for reduction of tassel size are desired.
This new approach was an important modification on aims of maize breeding programs in the corn belt (Duvick & Cassmann 1999DUVICK DN & CASSMAN KG. 1999. Post–Green Revolution Trends in Yield Potential of Temperate Maize in the NorthCentral United States. Crop Sci 39: 16221630.). These same authors pointed out that tassels with smaller size have lower apical dominance on the ears, a very relevant feature under stress conditions. It is important to mention that a lower cost of photoassimilates also occurs in the development of the tassel, which refers to a greater adaptation of the crop to higher plant densities. Both negative phenotypic and genetic associations between tasselrelated traits and grain yield have been described by correlation and path analysis studies in maize (Nardino et al. 2016aNARDINO M, SOUZA VQ, BARETTA D, KONFLANZ VA, CARVALHO IR, FOLLMANN DN & CARON BO. 2016a. Association of secondary traits with yield in maize F1’s. Ciênc Rural 46: 776782., b). The same authors, analyzing a partial diallel cross, showed that there were lines with negative (favorable) effects for reduction of tassel size. Sangoi et al. (2006)SANGOI L, GUIDOLIN AF, COIMBRA JLM & DA SILVA PRF. 2006. Resposta de híbridos de milho cultivados em diferentes épocas à população de plantas e ao despendoamento. Ciênc Rural 36: 13671373. reported that the tassel can suppress the development of the ear by three different ways: by shading the upper leaves, by competing for photoassimilates and by producing and exporting growth regulators that would be used in the development of the ear.
General combining ability for the megatrait grain yield
The selection of lines with positive estimates of GCA for the traits related to grain yield grouped in MT3, point to the presence of genes with favorable additive effects to increase yield and their respective components. Thus, line 5 showed positive and elevated estimates in FW. In PB and CN, lines 2 and 6 revealed higher estimates of GCA and may be considered superior to the average of the lines involved in the diallel. Thus, these lines might be used to provide an increase of yield components and consequently increase grain yield. The oscillation in the GCA estimates is linked to the presence of significant interactions for this MT.
This was expected, considering the quantitative inheritance of the genes that control the components and the grain yield. Optimal conditions could be achieved if it were possible to identify a population where two parents have the highest estimates both for GCA and SCA. This would be very important because the population would have a high average since the GCA of the parents is associated with the high frequency of favorable alleles and the two lines would have good complementarity provided by the high SCA. Thus, the population would have a large number of loci in heterozygosity and consequently greater potential genetic variability (Ramalho et al. 2012RAMALHO MAP, ABREU A, SANTOS JB & NUNES JAR. 2012. Aplicações da genética quantitativa no melhoramento de plantas autógamas. UFV, Viçosa, MG.).
Estimates of SCA were significant for only MT1, but interactions of SCA×E were significant for all MTs (Table II). Estimates of reciprocal effects (RSCA) and SCA for 90 hybrids related to the three MTs are shown in Figures 2, 3, 4, 5, 6 and 7.
Specific combining ability for megatrait plant stature
The significance of SCA is not sufficient to recommend a cross since the selection of hybrid combinations should involve lines with high estimates of SCA, where at least one of the parents has high GCA (Benin et al. 2009BENIN G, SILVA GO, PAGLIOSA ES, LEMES C, SIGNORINI A, BECHE E & CAPELIN MA. 2009. Capacidade de combinação em genótipos de trigo estimada por meio de análise multivariada. Pesq Agropec Bras 44: 11451151.). Thus, GCArelated additive alleles may provide greater accuracy in the selection of crosses.
Estimates of SCA considering the ten negative estimates of increasing order of s_{ij} (Figure 2) revealed as promising for the plant staturerelated traits, the following combinations: 4×10, 2×10, 2×5, 7×9, 3×9, 2×6, 1×3, 1×9, 1×2, and 4×8 for FW (Figure 2a); 5×10, 3×9, 2×6, 6×7, 2×9, 5×8, 2×7, 4×10, 1×3 e 4×8 for PB (Figure 2b); and 1×2, 3×9, 1×9, 4×10, 2×10, 5×9, 2×6, 6×8, 1×3, and 4×8 for CN (Figure 2c).
Specific combining ability for megatrait 1 (plant stature) of 90 crosses conducted in Frederico Westphalen (a), Pato Branco (b) and Campos Novos (c).
Specific combinations with significant SCA×E interation, as well as one parent with high GCA are preferred. The crosses 4×10, 2×5, 7×9 and 4×8 are the best, considering FW. All these combinations have negative estimates favorable for reduction of plant stature and one genitor with high GCA. The same rule can be applied to crosses regarding PB (5×10, 2×6, 6×7, 5×8, 2×7, 4×10 and 4×8) and CN (3×9, 1×9, 4×10, 2×10, 5×9, 6×8 and 4×8). These specific combinations for each environment are considered the most promissing crosses aiming at obtaining F_{1}’s with reduced plant stature.
On the other hand, the simultaneous selection of crosses in the three environments would be feasible, since the hybrid combinations 3×9, 2×6, 1×3 and 4×8 were common to all studied environments, which revealed estimates of negative SCA, favorable for the reduction of megatrait plant stature. However, these combinations with lower PH and EH can be important source of genes/alleles favorables for selection of populations/strains to reduce plant height. Taller plants with high inserted ears can cause increased susceptibility to lodging and may sometimes not be suitable for cultivation in areas with highwind events and to farmers working with high nitrogen doses (Paixão et al. 2008PAIXÃO SL, CAVALCANTE M, FERREIRA PV, DA SILVA MADALENA JÁ & PEREIRA RG. 2008. Divergência genética e avaliação de populações de milho em diferentes ambientes no estado de Alagoas. RC 21: 191195., Baretta et al. 2016BARETTA D, NARDINO M, CARVALHO IR, DANIELOWSKI R, LUCHE HS, DE OLIVEIRA VF, DE SOUZA VQ, DE OLIVEIRA AC & DA MAIA LC. 2016. Characterization of Dissimilarity among Varieties in Brazilian Maize Germplasm. Aust J Crop Sci 10: 112.).
Specific combining ability for the megatrait tassel size
Considering the ten negative estimates of increasing order of s_{ij} (Figure 3) SCA estimates indicated the best combinations for reduction of tassel size. Crosses in FW the Combinations 6×9, 2×3, 1×5, 1×10, 3×4, 9×10, 8×9, 2×8, 3×8 and 3×5 for FW (Figure 3a); 5×7, 6×8, 1×6, 1×9, 4×8, 1×5, 4×7, 5×10, 2×10, and 3×6 for PB (Figure 3b); and 1×3, 4×7, 4×8, 5×10, 1×2, 2×5, 2×7, 7×9, 6×8 and 2×10 for CN (Figure 3c). From these, the combinations 6×9, 2×3, 3×4, 3×8 and 3×5 for FW, 5×10, 2×10, 1×9, 5×7, 1×5 and 5×10 for PB; and 6×8, 5×10, 2×5, 4×7, 2×7 and 2×10 for CN presented at least one genitor with high value for this megatrait.
Specific combining ability for megatrait 2 (tassel size) of 90 crosses conducted in Frederico Westphalen (a), Pato Branco (b) and Campos Novos (c).
Simultaneous selection for the three environments aiming at reducing the tassel size would not be efficient because there were no common combinations across the sites. It is noticed that the combinations 1×5, 6×8, 4×8, 4×7 and 5×10 are favorable in at least two environments. Souza et al. (2015)SOUZA VQ, BARETTA D, NARDINO M, CARVALHO IR, FOLLMANN DN, KONFLANZ VA & SCHMIDT D. 2015. Variance components and association between corn hybrids morphoagronomic characters. Científica 43: 246253. studying variance components and canonical correlations with simple maize hybrids, reported the presence of genetic variation, making possible the selection of hibrids with smaller tassel size. The same authors also proved the negative and significant effects on the canonical pairs of the tassels on the grain yield of the simple hybrids studied.
Experimental results with diallel analyzes for tasselrelated traits are scarce in the literature, but they are of great importance in maize breeding programs. One of the main changes introduced by breeding programs in the current single hybrids was the reduction of tassel size; that is, tassel length, tassel mass and also reduction on number of primary and secondary branches of the tassel (Duvick & Cassmann 1999). These modifications resulted in a reduction of the apical dominance, and consequently, in a more vigorous development of the ear, even under conditions of biotic and abiotic stress.
Specific combining ability for megatrait grain yield
Estimates of SCA considering the ten negative estimates of increasing order of s_{ij} (Figure 4) indicated the best combinations for increasing grain yield as follows: 5×9, 8×10, 2×9, 1×10, 3×6, 4×10, 7×9, 1×2, 7×8 and 3×5 for FW (Figure 4a); 1×8, 6×9, 3×4, 2×4, 5×8, 1×10, 5×9, 4×6, 4×7 and 1×2 for PB (Figure 4b); 1×4, 8×9, 2×8, 3×7, 6×9, 4×9, 4×6, 5×8, 1×8 and 1×10 for CN (Figure 4c). The combinations that presented at least one parent with high GCA were 5×9, 8×10, 2×9, 1×10, 4×10, 7×9, 1×2 and 3×5 for FW; 1×8, 6×9, 3×4, 5×8, 4×6 and 1×2 for PB; and 1×4, 2×8, 6×9, 4×6, 5×8, 1×8 and 1×10 for CN.
Specific combining ability for megatrait 3 (grain yield) of 90 crosses conducted in Frederico Westphalen (a), Pato Branco (b) and Campos Novos (c).
The selection for the three simultaneously environments aiming at increasing grain yield indicated only the 1×10 cross in common to all three sites. On the other hand, the combinations 5×9, 1×2, 1×8, 6×9, 5×8, 4×6 and 1×2 are favorable for at least two environments. An improvement program that has combinations of hybrids with high levels of grain yield is important from the point of view of the recommendation and commercialization of cultivars.
Reciprocal specific combining ability for megatrait plant stature
Estimates of reciprocal specific combining ability (RSCA, r_{ji}) indicate which line is the most promising as female or male parent for the set of traits of agronomic interest. Thus, the correct choice of male or female parent may vary by combination. Silva et al. (2006)SILVA SDA, SERENO MJCM, SILVA CFL & BARBOSA NETO JF. 2006. Capacidade combinatória de genótipos de milho para tolerância ao encharcamento do solo. Ciênc Rural 36: 391396. point out that the correct choice of the female parent is a decisive aspect in the performance of the hybrid when there is a pronounced maternal effect, being decisive for the final manifestation of the trait(s).
Estimates of RSCA considering the ten negative estimates of increasing order indicated the following combinations for reduction of MT1 (Figure 5): 2×3, 8×10, 3×9, 5×6, 2×4, 6×7, 1×3, 4×9, 1×2 and 1×8 for FW (Figure 5a); 6×8, 1×5, 1×2, 7×8, 8×9, 7×9, 3×9, 2×5, 1×4 and 1×6 for PB (Figure 5b) and 1×6, 1×4, 6×10, 3×5, 2×7, 1×7, 3×9, 2×3, 3×4 and 1×3 for CN (Figure 5c). In recent decades, plant breeding has achieved gains in yield by combining selection techniques in other important agronomic traits, such as reduction in plant stature. The gains are obtained indirectly, since the smaller stature of the plant reduces the percentage of lodging and breakage, besides providing a greater density of plants without showing great losses due to intraspecific competition (Pfann et al. 2009PFANN AZ, FARIA MV, ANDRADE AA, NASCIMENTO IR, FARIA CMDR & BRINGHENTTI RM. 2009. Capacidade combinatória entre híbridos simples de milho em dialelo circulante. Ciênc Rural 39: 635641.).
Reciprocal specific combining ability for megatrait 1 (plant stature) of 90 crosses conducted in Frederico Westphalen (a), Pato Branco (b) and Campos Novos (c).
The specific reciprocal crosses that present at least one parent with high GCA in FW are 8×10, 5×6, 2×4, 6×7, 4×9 and 1×8; in PB, 6×8, 1×5, 7×8, 7×9, 2×5, 1×4 and 1×6; and in CN, 1×4, 6×10, 3×5, 2×7, 1×7, 3×9 and 3×4. Acording to Cruz et al. (2012)CRUZ CD, REGAZZI AJ & CARNEIRO PCS. 2012. Modelos biométricos aplicados ao melhoramento genético. 4th ed., UFV, Viçosa, MG., the most promissing crosses are those with these features, that is, with promissing SCA and at least one parente with promissing GCA.
The simultaneous selection of crosses for the three environments, considering the reciprocal effects, revealed only the 3×9 crosses in common to all environments, but the GCA of these two lines does not have constant magnitude across the sites. On the other hand, the simultaneous selection of crosses for two environments has the combinations 2×3, 1×3 and 1×2 as promising for reducing MT1. However, it is worth mentioning that the lines involved in these crosses are more likely to reduce three variables simultaneously, plant stature, ear height, and plant/ear height ratio.
Reciprocal specific combining ability for megatrait tassel size
Estimates of RSCA considering the ten negative estimates of increasing order indicated the best combinations for reducing MT2 (Figure 6), as follows: 4×8, 2×9, 5×9, 1×6, 3×10, 1×10, 6×10, 3×7, 5×10 and 3×8 for FW (Figure 6a); 8×10, 2×7, 3×5, 3×7, 5×6, 3×6, 4×6, 2×9, 3×8 and 1×8 for PB (Figure 6b); 7×10, 3×8, 2×5, 4×5, 2×6, 1×7, 7×8, 2×3, 1×9 and 3×6 for CN (Figure 6c). The crosses 1×6, 6×10, 3×7, 2×9, 3×10, 3×7 and 3×8 in FW, 8×10, 2×7, 2×9, 3×5 and 5×6, in PB and 2×6, 3×6, 2×5, 4×5, 7×10, 1×7, and 7×8 in CN have a parent with high estimates of GCA and are favorable for reduction of tassel size. A recent study focused on tasselrelated traits provided relevant information to maize breeding, revealing the direct and indirect negative effects of the distance from the last node to the first branching of the tassel with grain yield (Nardino et al. 2016aNARDINO M, SOUZA VQ, BARETTA D, KONFLANZ VA, CARVALHO IR, FOLLMANN DN & CARON BO. 2016a. Association of secondary traits with yield in maize F1’s. Ciênc Rural 46: 776782.). In the same way, Nardino et al. (2016b)NARDINO M, SOUZA VQ, BARETTA D, KONFLANZ VA, FOLLMANN DN, CARVALHO IR, FERRARI M, CARON BO & SCHMIDT D. 2016b. Partial diallel analysis among maize lines for characteristics related to the tassel and the productivity. African J Agric Res 11: 974982. in a diallel analysis study with F1’s, indicated that there were crosses within the study group that would allow the reduction of the tassel size.
Reciprocal specific combining ability for megatrait 2 (tassel size) of 90 crosses conducted in Frederico Westphalen (a), Pato Branco (b) and Campos Novos (c).
Simultaneous selection of specific crosses favorable to the three environments can be achieved by the 3×8 crossing, whereas the 2×9, 3×7, 3×6 and 2×9 crossings are common to at least two sites. The few combinations found simultaneously are possibly due to the presence of SCA×E interaction. Thus, it is suggested to identify specific combinations for each site individually.
Reciprocal specific combining ability for megatrait grain yield
Estimates of RSCA considering the ten positive estimates of increasing order showed the following combinations for increasing MT3 (Figure 7): 2×8, 2×10, 8×10, 5×7, 3×4, 5×6, 1×8, 6×7, 4×6 and 2×7 for FW (Figure 7a); 5×10, 4×8, 4×9, 3×9, 7×9, 4×7, 6×10, 1×2, 1×6 and 4×5 for PB (Figure 7b); and 2×9, 2×10, 1×9, 5×7, 3×8, 2×5, 5×9, 5×8, 7×10 and 5×10 for CN (Figure 7c). The crosses 2×8, 2×10, 8×10, 5×7, 3×4, 5×6, 4×6 and 2×7 for FW, 4×8, 3×9, 6×10, 1×2 and 1×6 for PB and 2×9, 2×10, 1×9, 5×7, 3×8, 2×5, 5×9, 5×8 and 5×10 for CN, have one parent with high GCA.
Reciprocal specific combining ability for megatrait 3 (grain yield) of 90 crosses conducted inFrederico Westphalen (a), Pato Branco (b) and Campos Novos (c).
Simultaneous selection of specific crosses favorable to the three environments was not achieved. Based on the effects of r_{ji}, the promising and common combinations for two of the three sites are 2×10, 5×7 and 5×10. This finding reinforces the importance in regionalizing recommendation of single maize hybrids, focusing on the exploration and commercialization in the regions near to the sites when the F_{1}’s were evaluated. This regionalization becomes important due to the specific edaphoclimatic conditions of the sites.
CONCLUSIONS
The diallel analyzes based on megatraits present an important evolution in statistical procedures used in evaluating plant breeding trials, since the simultaneous selection of lines with favorable estimates is based on several traits. In this way, we believe that the proposed method fills an important gap in evaluating diallel trials, being an important statistical tool for breeders.
In our example, three MTs were established. The first, formed by plant staturerelated traits, the second by tassel sizerelated traits, and the third by grain yieldrelated traits. Individual and joint diallel analysis using the established MTs allowed identifying the best hybrid combinations for achieving F_{1}’s with lower plant stature, tassel size, and higher grain yield.
ACKNOWLEGMENTS
The authors thank to Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERG) for project financing and the granting of the first author’s post doctoral fellowship.
REFERENCES
 AGUIAR CG DE, SCAPIM CA, PINTO RJB, DO AMARAL JÚNIOR AT, SILVÉRIO L & ANDRADE CAB. 2004. Análise dialélica de linhagens de milho na safrinha. Ciênc Rural 34: 17311737.
 ALLARD RW. 1999. Principles of plant breeding. 2ª ed. New York: J Wiley & Sons, 254 p.
 BARETTA D, NARDINO M, CARVALHO IR, DANIELOWSKI R, LUCHE HS, DE OLIVEIRA VF, DE SOUZA VQ, DE OLIVEIRA AC & DA MAIA LC. 2016. Characterization of Dissimilarity among Varieties in Brazilian Maize Germplasm. Aust J Crop Sci 10: 112.
 BENIN G, SILVA GO, PAGLIOSA ES, LEMES C, SIGNORINI A, BECHE E & CAPELIN MA. 2009. Capacidade de combinação em genótipos de trigo estimada por meio de análise multivariada. Pesq Agropec Bras 44: 11451151.
 COELHO AM, FRANÇA GE, PITTA GVE, ALVES VMC & HERNANI LC. 2002. Cultivo do milho: nutrição e adubação. Sete Lagoas: Embrapa, 12 p. (Comunicado Técnico, 44).
 CRUZ CD. 2013. GENES  a software package for analysis in experimental statistics and quantitative genetics. Acta Sci Agron 35: 271276.
 CRUZ CD & CARNEIRO PCS. 2003. Modelos biométricos aplicados ao melhoramento genético. 2nd ed., UFV, Viçosa, MG.
 CRUZ CD, REGAZZI AJ & CARNEIRO PCS. 2012. Modelos biométricos aplicados ao melhoramento genético. 4th ed., UFV, Viçosa, MG.
 DRUMOND ESC, PIRES AV, BONAFÉ CM, MOREIRA J, VELOSO RC, ROCHA GMF, BALLOTIN LMV & ALCÂNTARA DC. 2014. Rendimento de carcaça de codornas de corte em cruzamentos dialélicos. Ciênc Rural 44: 129134.
 DUVICK DN & CASSMAN KG. 1999. Post–Green Revolution Trends in Yield Potential of Temperate Maize in the NorthCentral United States. Crop Sci 39: 16221630.
 FEHER K, LISEC J, RÖMISCHMARGL L, SELBIG J, GIERL A, PIEPHO HP, NIKOLOSKI Z & WILLMITZER L. 2014. Deducing Hybrid Performance from Parental Metabolic Profiles of Young Primary Roots of Maize by Using a Multivariate Diallel Approach, Lukens L (Eds). PLoS One 9:e85435.
 FERREIRA FM, NEVES LG, BRUCKNER CH, VIANA AP, CRUZ CD & BARELLI MAA. 2010. Formação de supercaracteres para seleção de famílias de maracujazeiro amarelo. Acta Sci Agron 32: 247254.
 FREITAS ILJ, AMARAL JUNIOR AT, VIANA AP, PENA GF, CABRAL PS, VITTORAZZI C & SILVA TRC. 2013. Ganho genético avaliado com índices de seleção e com REML/Blup em milhopipoca. Pesq Agropec Bras 48: 14641471.
 GRANATE MJ, CRUZ CD, CECON PR & PACHECO CAP. 2008. A análise de fatores na predição de ganhos por seleção em milho (Zea mays L.). Acta Sci Agron 23: 12711279.
 GRIFFING B. 1956. Concept of general and specific combining ability in relation to diallel crossing systems. Aust J Biol Sci 9: 463493.
 HALLAUER AR, CARENA MJ & MIRANDA FILHO JB. 2010. Quantitative genetics in maize breeding. Springer New York, New York, NY.
 HU G, GU W, YANG R & WANG B. 2017. Multivariate diallel crossanalyses for body weight of rainbow trout, Oncorhynchus mykiss, in China. J World Aquac Soc 48: 240247.
 JOHNSON R & WICHERN D. 2002. Applied multivariate statistical analysis. 5th ed., Upper Saddle River, NJ. Prentice Hall, Englewood Cliffs.
 KOSTETZER V, MOREIRA RMP & FERREIRA JM. 2009. Cruzamento dialélico parcial entre variedades locais do Paraná e variedades sintéticas de milho. Pesq Agropec Bras 44: 11521159.
 LEDO CAS, FERREIRA DF & RAMALHO MAP. 2003. Análise de variância multivariada para os cruzamentos dialélicos. Ciênc Agrotec 27: 12141221.
 LOCATELLI AB, FEDERIZZI LC & NASPOLINI FILHO V. 2002. Capacidade combinatória de nove linhagens endogâmicas de milho (Zea mays L.) em dois ambientes. Ciênc Rural 32: 365370.
 MARDIA KV, KENT JT & BIBBY JM. 1979. Multivariate analysis. London: Academic Press, 521 p.
 MUTIMAAMBA C, MACROBERT J, CAIRNS JE, MAGOROKOSHO CE, NDHLELA T, MUKUNGURUTSE C, MINNAARONTONG A & LABUSCHAGNE MT. 2017. Diallel analysis of acid soil tolerant and susceptible maize inbred lines for grain yield under acid and nonacid soil conditions. Euphytica 213: 88.
 NARDINO M, SOUZA VQ, BARETTA D, KONFLANZ VA, CARVALHO IR, FOLLMANN DN & CARON BO. 2016a. Association of secondary traits with yield in maize F1’s. Ciênc Rural 46: 776782.
 NARDINO M, SOUZA VQ, BARETTA D, KONFLANZ VA, FOLLMANN DN, CARVALHO IR, FERRARI M, CARON BO & SCHMIDT D. 2016b. Partial diallel analysis among maize lines for characteristics related to the tassel and the productivity. African J Agric Res 11: 974982.
 NASCIMENTO IR, MALUF WR, GOLÇALVES LD, FARIA MV, DE RESENDE JTV & NOGUEIRA DW. 2010. Capacidade combinatória de linhagens de pimentão a partir de análise dialélica multivariada. Acta Sci Agron 32: 235240.
 OGUT F, MALTECCA C, WHETTEN R, MCKEAND S & ISIK F. 2014. Genetic analysis of diallel progeny test data using factor analytic linear mixed models. For Sci 60: 119127.
 OLIBONI R, FARIA MV, NEUMANN M, RESENDE JTV, BATTISTELLI GM, TEGONI RG & OLIBONI DF. 2013. Análise dialélica na avaliação do potencial de híbridos de milho para a geração de populaçõesbase para obtenção de linhagens. Semina Ciênc Agrár 34: 718.
 OLIVEIRA GH, BUZINARO R, REVOLTI LT, GIORGENON CH, CHARNAI K, RESENDE D & MORO GV. 2016. An accurate prediction of maize crosses using diallel analysis and best linear unbiased predictor (BLUP). Chil J Agric Res 76: 294299.
 PAIXÃO SL, CAVALCANTE M, FERREIRA PV, DA SILVA MADALENA JÁ & PEREIRA RG. 2008. Divergência genética e avaliação de populações de milho em diferentes ambientes no estado de Alagoas. RC 21: 191195.
 PFANN AZ, FARIA MV, ANDRADE AA, NASCIMENTO IR, FARIA CMDR & BRINGHENTTI RM. 2009. Capacidade combinatória entre híbridos simples de milho em dialelo circulante. Ciênc Rural 39: 635641.
 RAMALHO MAP, ABREU A, SANTOS JB & NUNES JAR. 2012. Aplicações da genética quantitativa no melhoramento de plantas autógamas. UFV, Viçosa, MG.
 ROCHA F, STINGHEN JC, GEMELI MS, COIMBRA JLM & GUIDOLIN AF. 2014. Análise dialélica como ferramenta na seleção de genitores em feijão. Rev Ciênc Agron 45: 7481.
 SANGOI L, GUIDOLIN AF, COIMBRA JLM & DA SILVA PRF. 2006. Resposta de híbridos de milho cultivados em diferentes épocas à população de plantas e ao despendoamento. Ciênc Rural 36: 13671373.
 SAS Institute Inc. 2010. SAS/STAT 9.22 User’s Guide. SAS Institute Inc., Cary, NC.
 SILVA GO, PEREIRA A, SOUZA VQ, CARVALHO FIF & VIEIRA EA. 2008. Capacidade de combinação multivariada para caracteres de tubérculo em gerações iniciais de seleção em batata. Ciênc Rural 38: 321325.
 SILVA SDA, SERENO MJCM, SILVA CFL & BARBOSA NETO JF. 2006. Capacidade combinatória de genótipos de milho para tolerância ao encharcamento do solo. Ciênc Rural 36: 391396.
 SOUZA VQ, BARETTA D, NARDINO M, CARVALHO IR, FOLLMANN DN, KONFLANZ VA & SCHMIDT D. 2015. Variance components and association between corn hybrids morphoagronomic characters. Científica 43: 246253.
 SOUZA NETO IL, PINTO RJB, SCAPIM CA, JOBIM CC, FIGUEIREDO AST & BIGNOTTO LS. 2015. Análise dialélica e depressão endogâmica de híbridos forrageiros de milho para características agronômicas e de qualidade bromatológica. Bragantia 74: 4249.
 VIVAS M, SILVEIRA SF, DA PEREIRA MG, CARDOSO DL & FERREGUETTI GA. 2013. Análise dialélica em mamoeiro para resistência a manchadephoma. Ciênc Rural 43: 945950.
 ZHANG YD, FAN X, YAO W, PIEPHO HP & KANG MS. 2016. Diallel analysis of four maize traits and a modified heterosis hypothesis. Crop Sci 56: 11151126.
SUPPLEMENTARY MATERIAL
Table SI
Publication Dates

Publication in this collection
01 June 2020 
Date of issue
2020
History

Received
28 Aug 2018 
Accepted
11 Dec 2018