Maize hybrid stability in environments under water restriction using mixed models and factor analysis.

In several crops, the water deficit is perhaps the main limiting factor in the search for high yields. The objective of this study was to evaluate the phenotypic stability of maize hybrids in environments with and without water restriction using the analytical factor (AF) approach. We evaluated 171 maize hybrids in 14 environments, divided into environments with (A1, A2, A3, A4, A5, A6, and A7) and without (A8, A9, A10, A11, A12, A13, and A14) water restriction, over a period of 7 years. Each year, 36 hybrids were evaluated. A square lattice design (6 x 6) was used, with common treatments between years. The characteristics of grain yield (GY), male flowering (MF) and female flowering (FF), plant height (PH), and ear height (EH) were evaluated. Phenotypic adaptability and stability of the hybrids were also verified. Hybrids G66, G99, G86, and G26 were the most stable and showed potential for use in environments with and without water restriction. The AF models showed to be useful for evaluating hybrids over many years, allowing selection of better hybrids with adaptability, specific and general stability, and correlation of hybrids with their production components, in addition to allowing identification of mega-environments that permit stability in the response of the adapted hybrids.

Assessing non-additive effects in GBLUP model.

Understanding non-additive effects in the expression of quantitative traits is very important in genotype selection, especially in species where the commercial products are clones or hybrids. The use of molecular markers has allowed the study of non-additive genetic effects on a genomic level, in addition to a better understanding of its importance in quantitative traits. Thus, the purpose of this study was to evaluate the behavior of the GBLUP model in different genetic models and relationship matrices and their influence on the estimates of genetic parameters. We used real data of the circumference at breast height in Eucalyptus spp and simulated data from a population of F2. Three commonly reported kinship structures in the literature were adopted. The simulation results showed that the inclusion of epistatic kinship improved prediction estimates of genomic breeding values. However, the non-additive effects were not accurately recovered. The Fisher information matrix for real dataset showed high collinearity in estimates of additive, dominant, and epistatic variance, causing no gain in the prediction of the unobserved data and convergence problems. Estimates presented differences of genetic parameters and correlations considering the different kinship structures. Our results show that the inclusion of non-additive effects can improve the predictive ability or even the prediction of additive effects. However, the high distortions observed in the variance estimates when the Hardy-Weinberg equilibrium assumption is violated due to the presence of selection or inbreeding can converge at zero gains in models that consider epistasis in genomic kinship.

White mold resistance-associated quantitative trait loci in the Jalo x Small White common bean population.

We aimed to identify simple sequence repeat (SSR) markers linked to quantitative trait loci (QTLs) associated with white mold resistance in a segregating population derived from a cross between common bean cultivars Jalo and Small White, in the Southern State of Minas Gerais. Parents were crossed to obtain the F2 generation of 190 plants. From these, F2:3 and F2:4 progenies were obtained for phenotypic evaluation. DNA was extracted from F2 plants and parents for genotyping with SSR primers. For phenotypic assessment by the straw test, we used 190 F2:3 progenies and six lines in a triple-lattice design of 14 x 14 m. Nine trials were conducted for phenotyping by the oxalic acid method to evaluate 177 F2:4 progenies, in addition to the two parents and two common treatments represented by the Jalo and Corujinha lines. The experimental design for the oxalic acid method was completely randomized with three replicates. Adjusted means of evaluations related to F2:3 and F2:4 were used to identify QTLs by using the moving away method from the marker under Bayesian analysis. The markers GATS91, BM197, and X60000 stood out with high heritability and with effects on disease reduction by the straw test; therefore, these markers are promising for selection. The markers BM183, BM189, and SSR-IAC143 were associated with the QTLs identified by oxalic acid, providing greater effects in white mold resistance with high heritability. Based on the oxalic acid and straw test methods, the most prominent marker was PVBR189.

Bayesian GGE biplot models applied to maize multi-environments trials.

The additive main effects and multiplicative interaction (AMMI) and the genotype main effects and genotype x environment interaction (GGE) models stand out among the linear-bilinear models used in genotype x environment interaction studies. Despite the advantages of their use to describe genotype x environment (AMMI) or genotype and genotype x environment (GGE) interactions, these methods have known limitations that are inherent to fixed effects models, including difficulty in treating variance heterogeneity and missing data. Traditional biplots include no measure of uncertainty regarding the principal components. The present study aimed to apply the Bayesian approach to GGE biplot models and assess the implications for selecting stable and adapted genotypes. Our results demonstrated that the Bayesian approach applied to GGE models with non-informative priors was consistent with the traditional GGE biplot analysis, although the credible region incorporated into the biplot enabled distinguishing, based on probability, the performance of genotypes, and their relationships with the environments in the biplot. Those regions also enabled the identification of groups of genotypes and environments with similar effects in terms of adaptability and stability. The relative position of genotypes and environments in biplots is highly affected by the experimental accuracy. Thus, incorporation of uncertainty in biplots is a key tool for breeders to make decisions regarding stability selection and adaptability and the definition of mega-environments.

Genomic breeding value prediction for simple maize hybrid yield using total effects of associated markers, under different imbalance levels and environments.

The main objective of a maize breeding program is to generate hybrid combinations that are more productive than those pre-existing in the market. However, the number of parents, and consequently the number of crosses, increases so rapidly that the phenotypic evaluation of all the possible combinations becomes economically and technically infeasible. In this context, predicting the performance of the most promising genotypes may increase the genetic gains with increased selection intensity and reduced breeding cycles. Thus, the present study aimed to use the total effects of associated markers method to predict genomic breeding values (GBVs) via cross-validation and by using different imbalance levels (10, 30, 50, and 70%). A set of 51 genotyped strains was used with 79 microsatellite markers and 273 hybrids that were generated by a partial diallel. A total of 186 and 272 hybrids were analyzed in the experiments within the southern and central regions of Brazil, respectively. The GBVs were, thus, predicted for each location in both the regions, and for training in one region and validation in another region. The correlation between the predicted and observed GBVs ranged from 0.48 to 0.91, depending on the imbalance level and the region analyzed. Overall, the results obtained in the present study were promising, particularly considering that a small number of markers were used and that the training and predictions occurred in the very distinct regions of southern and central Brazil.

Factor analysis using mixed models of multi-environment trials with different levels of unbalancing.

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 multi-environment 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 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.

A new method of QTL identification for undersaturated maps.

In many species, low levels of polymorphism prevent the assembly of linkage maps that are used to identify genetic markers related to the expression of quantitative trait loci (QTLs). This study compared two methods of locating QTLs in association studies that do not require a previous estimation of linkage maps. Method I (MI) was a Bayesian multiple marker regression and Method II (MII) combined multiple QTL mapping and "moving away from markers". In this method, markers are not directly regressed to the phenotype, but are used as pivots to search for QTLs along the genome. To compare methods, we simulated 300 individuals from an F2 progeny with two levels of marker loss (20 and 80%). A total of 165 markers and seven QTLs were spread along 11 chromosomes (roughly emulating the genetic structure of the common bean, Phaseolus vulgaris). A real data example with 186 progenies of a F2:4 generation of the species was analyzed using 59 markers (17 simple sequence repeats, 31 amplified fragment length polymorphisms, and 11 sequence-related amplified polymorphisms). MII was more precise than MI for both levels of marker loss. For real data, MII detected 17 candidate positions for QTLs, whereas MI did not detect any. MII is a powerful method that requires further studies with actual data and other designs such as crossover, and genome-wide studies.

Indirect selection for resistance to ear rot and leaf diseases in maize lines using biplots.

Leaf disease and ear rot have caused reductions in maize yield in Brazil and other producer countries. Therefore, the aims of this study were to analyze the association between husked ear yield and the severity of maize white spot, gray leaf spot, helminthosporium, and ear rot caused by Fusarium verticillioides and Diplodia maydis using biplots in a mixed-model approach. The responses of 238 lines introduced to Brazil and four controls were evaluated using an incomplete block design with three replicates in two locations: Lavras and Uberlândia, Minas Gerais, Brazil. Two experiments were conducted in each location, one with F. verticillioides and the other with D. maydis. The mixed models elucidated the relationship between yield, leaf disease, and ear disease. Significant genotype x environment and genotype x pathogen interactions were observed. In conclusion, husked ear yield is more associated with ear rot than with the leaf diseases evaluated, justifying the indirect selection for resistance to kernel rot in maize-F. verticillioides and maize-D. maydis pathosystems by yield evaluation.

Identification of QTLs of resistance to white mold in common bean from multiple markers by using Bayesian analysis.

In this study, we identified simple sequence repeat, ampli-fied fragment length polymorphism, and sequence-related amplified poly-morphism markers linked to quantitative trait loci (QTLs) for resistance to white mold disease in common bean progenies derived from a cross between lines CNFC 9506 and RP-2, evaluated using the oxalic acid test and using Bayesian analysis. DNA was extracted from 186 F2 plants and their parental lines for molecular analysis. Fifteen experiments were car-ried out for phenotypic analysis, which included 186 F2:4 progenies, the F1 generation, the F2 generation, and the lines CNFC 9506, RP-2, and G122 as common treatments. A completely randomized experimental design with 3 replications was used in controlled environments. The adjusted means for the F2:4 generation were to identify QTLs by Bayesian shrink-age analysis. Significant differences were observed among the progenies for the reaction to white mold. The moving away method under the Bayes-ian approach was effective for identifying QTLs when it was not possible to obtain a genetic map because of low marker density. Using the Wald test, 25 markers identified QTLs for resistance to white mold, as well as 16 simple sequence repeats, 7 amplified fragment length polymorphisms, and 2 sequence-related amplified polymorphisms. The markers BM184, BM211, and PV-gaat001 showed low distances from QTLs related white mold resistance. In addition, these markers showed, signal effects with increasing resistance to white mold and high heritability in the analysis with oxalic acid, and thus, are promising for marker-assisted selection.

Genome-wide prediction of maize single-cross performance, considering non-additive genetic effects.

The prediction of single-cross hybrids in maize is a promising technique for optimizing the use of financial resources in a breeding program. This study aimed to evaluate Genomic Best Linear Unbiased Predictors models for hybrid prediction and compare them with the Bayesian Ridge Regression, Bayes A, Bayesian LASSO, Bayes C, Bayes B, and Reproducing Kernel Hilbert Spaces Regression models, with inclusion or absence of non-additive effects under three heritability scenarios. Data from a maize germplasm bank belonging to USDA were used to determine the effects of molecular markers, which were considered to be parametric, to build 400 single-cross hybrids between two line groups via simulation. The following parameters were used to compare the models: predictive ability, estimation of variance components, heritability of genetic effects present in all situations, and the sum of squares of the predicted errors. The models responded positively when dominance effects were included in non-additive models, with all models tending to show an increase in the values of heritability parameters under all scenarios. Differences occur between models depending on the heritability range considered. Estimates of additive and dominant effects were better than estimates of epistatic effects. Estimates increased in accuracy for all models when non-additive effects for maize cob weight were considered.

Production and identification of doubled haploids in tropical maize.

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 F2 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 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.

Bayesian inference to study genetic control of resistance to gray leaf spot in maize.

Gray leaf spot (GLS) is a major maize disease in Brazil that significantly affects grain production. We used Bayesian inference to investigate the nature and magnitude of gene effects related to GLS resistance by evaluation of contrasting lines and segregating populations. The experiment was arranged in a randomized block design with three replications and the mean values were analyzed using a Bayesian shrinkage approach. Additive-dominant and epistatic effects and their variances were adjusted in an over-parametrized model. Bayesian shrinkage analysis showed to be an excellent approach to handle complex models in the study of genetic control in GLS, since this approach allows to handle overparametrized models (main and epistatic effects) without using model-selection methods. Genetic control of GLS resistance was predominantly additive, with insignificant influence of dominance and epistasis effects.

Prediction of maize double-cross hybrids using the best linear unbiased prediction with microsatellite marker information.

We examined the usefulness of the best linear unbiased prediction associated with molecular markers for prediction of untested maize double-cross hybrids. Ten single-cross hybrids from different commercial backgrounds were crossed using a complete diallel design. These 10 single-cross hybrids were genotyped with 20 microsatellite markers. The best linear unbiased prediction associated with microsatellite information gave relatively good prediction ability of the double-cross hybrid performance, with correlations between observed phenotypic values and genotypic prediction values varying from 0.27 to 0.54. Taking into account the predictions of specific combing ability, the correlation between observed and predicted specific combining ability varied from 0.50 to 0.88. Based on these results, we infer that it is feasible to predict maize double-cross hybrids with different unbalance degrees without including any prior information about parental inbreed lines or single-cross hybrid performance.

Prediction of maize hybrid performance using similarity in state and similarity by descent information.

We evaluated the efficiency of the best linear unbiased predictor (BLUP) and the influence of the use of similarity in state (SIS) and similarity by descent (SBD) in the prediction of untested maize hybrids. Nine inbred lines of maize were crossed using a randomized complete diallel method. These materials were genotyped with 48 microsatellite markers (SSR) associated with the QTL regions for grain yield. Estimates of four coefficients of SIS and four coefficients of SBD were used to construct the additive genetic and dominance matrices, which were later used in combination with the BLUP for predicting genotypic values and specific combining ability (SCA) in unanalyzed hybrids under simulated unbalance. The values of correlations between the genotypic values predicted and the means observed, depending on the degree of unbalance, ranged from 0.48 to 0.99 for SIS and 0.40 to 0.99 using information from SBD. The results obtained for the SCA ranged from 0.26 to 0.98 using the SIS and 0.001 to 0.990 using the SBD information. It was also observed that the predictions using SBD showed less biased than SIS predictions demonstrating that the predictions obtained by these coefficients (SBD) were closer to the observed value, but were less efficient in the ranking of genotypes. Although the SIS showed a bias due to overestimation of relatedness, this type of coefficient may be used where low values are detected in the SBD in the group of parents because of its greater efficiency in ranking the candidates hybrids.

Prediction of maize single-cross performance by mixed linear models with microsatellite marker information.

We evaluated the potential of the best linear unbiased predictor (BLUP) along with the relationship coefficient for predicting the performance of untested maize single-cross hybrids. Ninety S(0:2) progenies arising from three single-cross hybrids were used. The 90 progenies were genotyped with 25 microsatellite markers, with nine markers linked to quantitative trait loci for grain yield. Based on genetic similarities, 17 partial inbred lines were selected and crossed in a partial diallel design. Similarity and relationship coefficients were used to construct the additive and dominance genetic matrices; along with BLUP, they provided predictions for untested single-crosses. Five degrees of imbalance were simulated (5, 10, 20, 30, and 40 hybrids). The correlation values between the predicted genotypic values and the observed phenotypic means varied from 0.55 to 0.70, depending on the degree of imbalance. A similar result was observed for the specific combining ability predictions; they varied from 0.61 to 0.70. It was also found that the relationship coefficient based on BLUP provided more accurate predictions than similarity-in-state predictions. We conclude that BLUP methodology is a viable alternative for the prediction of untested crosses in early progenies.

Genotypic stability and adaptability in tropical maize based on AMMI and GGE biplot analysis.

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 single-cross hybrids, a complete diallel was done, resulting in 45 double-cross 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.

Potential use of molecular markers for prediction of genotypic values in hybrid maize performance.

We evaluated the potential of genetic distances estimated by microsatellite markers for the prediction of the performance of single-cross maize hybrids. We also examined the potential of molecular markers for the prediction of genotypic values and the applicability of the Monte Carlo method for a correlation of genetic distances and grain yield. Ninety S(0:2) progenies derived from three single-cross hybrids were analyzed. All 90 progenies were genotyped with 25 microsatellite markers, including nine markers linked to quantitative trait loci for grain yield. The genetic similarity datasets were used for constructing additive genetic and dominance matrices that were subsequently used to obtain the best linear unbiased prediction of specific combining ability and general combining ability. The genetic similarities were also correlated with grain yield, specific combining ability and heterosis of the hybrids. Genetic distances had moderate predictive ability for grain yield (0.546), specific combining ability (0.567) and heterosis (0.661). The Monte Carlo simulation was found to be a viable alternative for a correlation of genetic distances and grain yield. The accuracy of genotypic values using molecular data information was slightly higher than if no such information was incorporated. The estimation of the relationship using molecular markers proved to be a promising method for predicting genetic values using mixed linear models, especially when information about pedigree is unavailable.

Potential of maize single-cross hybrids for extraction of inbred lines using the mean components and mixed models with microsatellite marker information.

The present study examined the importance of mean (m+a' and d) components in the performance of single-cross hybrids for the formation of new populations and determined the contribution of the mixed model (best linear unbiased predictor of random effects, BLUP) method associated with molecular markers for the choice of crosses to obtain interpopulation hybrids. Ten single-cross commercial hybrids of different companies were used for this purpose, producing all possible double-cross hybrids through a complete diallel. The hybrids were evaluated in 15 locations in the agricultural year 2005/2006, using randomized complete block design with three repetitions. In three of these locations, estimates of m+a' and d were obtained. DNA was extracted from the single-cross hybrids and 20 SSR primers were used, nine of which were linked to QTL for yield. There was no correlation between m+a' of the single-cross hybrids with general combining ability (r = -0.15) inferring that populations with lines with high means do not always produce good hybrids. Also, it was observed that the correlation between the genetic distances with specific combining ability varied from 0.31 to 0.80 in the inter-group hybrids, while in the intra-group hybrids these estimates were low and non-significant. The heritability value obtained by BLUP was high and greater than that obtained by ordinary least squares (h(2) = 0.95 and 0.86), confirming the greater selection accuracy by the BLUP method. There were no differences between the accuracy values obtained with microsatellite information and without this information, inferring that there was no advantage of progenitor information on balanced data. It can be concluded that the estimate m+a' should not be used as a deciding parameter about the potential for extracting lines from a given population. The heritability and accuracy values obtained by BLUP allow the inference that it is possible to predict success in the choice of progenitors to obtain interpopulation hybrids.

Comparison of maize similarity and dissimilarity genetic coefficients based on microsatellite markers.

The present study compared different similarity and dissimilarity coefficients and their influence in maize inbred line clustering. Ninety maize S0:1 inbred lines were used and genotyped with 25 microsatellite markers (simple sequence repeat). The simple matching, Rogers and Tanimoto, Russel and Rao, Hamann, Jaccard, Sorensen-Dice, 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 (rs = 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.

Genetic distance estimates among single cross hybrids and correlation with specific combining ability and yield in corn double cross hybrids.

The objective of the present study was to correlate the genetic distances (GD) of single cross hybrids with yield, heterosis and specific combining ability (SCA) in the double cross hybrid synthesis. For this, 10 single cross commercial hybrids were used from different companies, and all the possible double hybrids were synthesized by a complete dialell. The hybrids were assessed in 15 locations in the 2005/2006 agricultural season, using the randomized complete block design with three repetitions. DNA was extracted from the single cross hybrids and 20 simple sequence repeat primers were used, nine of which were linked to the quantitative trait loci. It was ascertained that the single hybrids were superior in general to the double cross hybrids and that yield was highly correlated with heterosis and SCA (r = 0.75 and 0.82, respectively). There was no significant correlation between yield and GD (r = 0.25), but this index was at the limit of significance. There was a medium correlation between GD and heterosis (r = 0.40) and GD and SCA (r = 0.38). The intergroup hybrids placed by genetic grouping were generally more productive than intragroup hybrids, and the hybrids with GD greater than 0.84 had the maximum heterosis and SCA. It was concluded that the markers were efficient in placing hybrids in different heterosis groups and were also useful in eliminating the most negative heterosis and SCA.