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.

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.

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.