ABSTRACT. The production of maize doubled haploid (DH) lines is a technique commonly used by private companies, but not by Brazilian public institutions. Research on this technique is essential to develop and improve the production of DH lines grown under tropical conditions. We assessed the ability of a gynogenetic haploid inducer system to induce haploids in a tropical environment, assessed the induction rate of haploids identified using the R-navajo morphological marker, checked for interference from the generation of hybrid donors on haploid induction, measured the ability of flow cytometry, and simple sequence repeat marker techniques to identify doubled haploids. Seeds from the inducer Krasnodar Embryo Marker Synthetic (KEMS) line were sown in Ponta Grossa, PR, and Cravinhos, SP, and the plants were crossed to produce six hybrids and their F 2 generations. The seeds were separated according to the R-navajo morphological marker indicator of haploidy (purple endosperm and white embryo) and germinated in a controlled environment. Chromosomal duplication was performed in seedlings selected as putative haploids. We performed subsequent confirmation of ploidy and the success of duplication using flow cytometry and SSR 4231©FUNPEC-RP www.funpecrp.com.br Genetics and Molecular Research 12 (4): 4230-4242 (2013) Production of doubled haploid lines in tropical maize marker techniques. We concluded that DH lines can be obtained from hybrids crossed with the inducer KEMS line. The generation of inbred hybrids did not affect the induction rate or chromosomal duplication in haploids. The use of flow cytometry and SSR markers was effective in verifying chromosomal duplication in haploids.

ABStRACt. The present study compared different similarity and dissimilarity coefficients and their influence in maize inbred line clustering. Ninety maize S 0:1 inbred lines were used and genotyped with 25 microsatellite markers (simple sequence repeat). The simple matching, Rogers and Tanimoto, Russel and Rao, Hamann, Jaccard, SorensenDice, Ochiai, and Roger's modified distance coefficients were compared by consensus index, projection efficiency in a two-dimensional space and by Spearman's correlation. Changes were found in high genetic similarity groupings with different coefficients using the consensus index. Russel and Rao and Jaccard coefficients had the greatest stress values with 75.67 and 40.16%, respectively, indicating that these coefficients should not be used. Genotype ranking changed, mainly in the comparison of the Roger's modified distance in relation to some coefficients (r s = 0.75). Russel and Rao's and Jaccard's coefficients should be avoided for their low accuracy. Moreover, genotype clustering by different similarly coefficients, without a close consideration of these coefficients could affect the research results.

ABSTRACT.This study aimed to analyze the robustness of mixed models for the study of genotype-environment interactions (G x E). Simulated unbalancing of real data was used to determine if the method could predict missing genotypes and select stable genotypes. Data from multienvironment trials containing 55 maize hybrids, collected during the 2005-2006 harvest season, were used in this study. Analyses were performed in two steps: the variance components were estimated by restricted maximum likelihood, using the expectation-maximization (EM) algorithm, and factor analysis (FA) was used to calculate the factor scores and relative position of each genotype in the biplot. Random unbalancing of the data was performed by removing 10, 30, and 50% of the plots; the scores were then re-estimated using the FA model. It was observed that 10, 30, and 50% unbalancing exhibited mean correlation values of 0.7, 0.6, and 0.56, respectively. Overall, the genotypes classified as stable in the biplot had smaller prediction error sum of squares (PRESS) value and prediction 14263 Factor analysis using mixed models ©FUNPEC-RP www.funpecrp.com.br Genetics and Molecular Research 14 (4): 14262-14278 (2015) amplitude of ellipses. Therefore, our results revealed the applicability of the PRESS statistic to evaluate the performance of stable genotypes in the biplot. This result was confirmed by the sizes of the prediction ellipses, which were smaller for the stable genotypes. Therefore, mixed models can confidently be used to evaluate stability in plant breeding programs, even with highly unbalanced data.

New proposals for models and applications of prediction processes with data on molecular markers may help reduce the financial costs of and identify superior genotypes in maize breeding programs. Studies evaluating Genomic Best Linear Unbiased Prediction (GBLUP) models including dominance effects have not been performed in the univariate and multivariate context in the data analysis of this crop. A single cross hybrid construction procedure was performed in this study using phenotypic data and actual molecular markers of 4,091 maize lines from the public database Panzea. A total of 400 simple hybrids resulting from this process were analyzed using the univariate and multivariate GBLUP model considering only additive effects additive plus dominance effects. Historic heritability scenarios of five traits and other genetic architecture settings were used to compare models, evaluating the predictive ability and estimation of variance components. Marginal differences were detected between the multivariate and univariate models. The main explanation for the small discrepancy between models is the low- to moderate-magnitude correlations between the traits studied and moderate heritabilities. These conditions do not favor the advantages of multivariate analysis. The inclusion of dominance effects in the models was an efficient strategy to improve the predictive ability and estimation quality of variance components.

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ABSTRACT. We evaluated the phenotypic and genotypic stability and adaptability of hybrids using the additive main effect and multiplicative interaction (AMMI) and genotype x genotype-environment interaction (GGE) biplot models. Starting with 10 singlecross hybrids, a complete diallel was done, resulting in 45 doublecross hybrids that were appraised in 15 locations in Southeast, Center-West and Northeast Brazil. In most cases, when the effects were considered as random (only G effects or G and GE simultaneously) in AMMI and GGE analysis, the distances between predicted values and observed values were smaller than for AMMI and GGE biplot phenotypic means; the best linear unbiased predictors of G and GE generally showed more accurate predictions in AMMI and GGE analysis. We found the GGE biplot method to be superior to the AMMI 1 graph, due to more retention of GE and G + GE in the graph analysis. However, based on cross-validation results, the GGE biplot was less accurate than the AMMI 1 graph, inferring that the quantity of GE or G + GE retained in the graph analysis alone is not a good parameter for choice of stabilities and adaptabilities when comparing AMMI and GGE analyses.

The additive main effects and multiplicative interaction (AMMI) model is frequently applied in plant breeding for studying the genotype × environment (G × E) interaction. One of the main difficulties related to this method of analysis is the incorporation of inference to the bilinear terms that compose the biplot representation. This study aimed to incorporate credible intervals for the genotypic and environmental scores in the AMMI model by using an informative prior for the genotype effect. This approach differs from the Bayesian methods that have been presented so far, which assume the same restrictions as the fixed effects model. The method was exemplified by using data from a study with 55 maize hybrids in nine different environments for which variable being studied was the yield of unhusked ears. Our results demonstrated that the credible intervals allowed for the identification of genotypes and environments that did not contribute to the G × E interaction. In addition, it facilitated recognition of homogeneous subgroups of genotypes and environments (with respect to the effect of the interaction) and the adaptability of genotypes to specific environments of great interest to breeders. The posterior distributions of singular vectors were bimodal but with the same density peaks in absolute value. This reflects the arbitrary choice of signs of the main component that was used in different mathematical algorithms. Although our data set was based on unrelated single cross hybrids, the choice of genotypes as random effects enabled the Bayesian AMMI to accommodate the additive and nonadditive relationship matrices. Additionally, the flexibility of the analysis facilitated working with unbalanced data and the incorporation of heterogeneity of variances.

Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI) model, are widely applicable to genotype-by-environment interaction (GEI) studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05) in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct posterior distribution retaining more GEI pattern in the first components and discarding noise without Gaussian assumption as requested in F-based tests or deal with parametric problems as observed in traditional AMMI shrinkage method.