Multiple-trait model tends to be the best alternative for the analysis of repeated measures, since they consider the genetic and residual correlations between measures and improve the selective accuracy. Thus, the objective of this study was to propose a multiple-trait Bayesian model for repeated measures analysis in Jatropha curcas breeding for bioenergy. To this end, the grain yield trait of 730 individuals of 73 half-sib families was evaluated over six harvests. The Markov Chain Monte Carlo algorithm was used to estimate genetic parameters and genetic values. Genetic correlation between pairs of measures were estimated and four selective intensities (27.4%, 20.5%, 13.7%, and 6.9%) were used to compute the selection gains. The full model was selected based on deviance information criterion. Genetic correlations of low (ρg ≤ 0.33), moderate (0.34 ≤ ρg ≤ 0.66), and high magnitude (ρg ≥ 0.67) were observed between pairs of harvests. Bayesian analyses provide robust inference of genetic parameters and genetic values, with high selective accuracies. In summary, the multiple-trait Bayesian model allowed the reliable selection of superior Jatropha curcas progenies. Therefore, we recommend this model to genetic evaluation of Jatropha curcas genotypes, and its generalization, in other perennials.

In multi-environment trials (MET), large networks are assessed for results improvement. However, genotype by environment interaction plays an important role in the selection of the most adaptable and stable genotypes in MET framework. In this study, we tested different residual variances and measure the selection gain of cotton genotypes accounting for adaptability and stability, simultaneously. Twelve genotypes of cotton were bred in 10 environments, and fiber length (FL), fiber strength (FS), micronaire (MIC), and fiber yield (FY) were determined. Model selection for different residual variance structures (homogeneous and heterogeneous) was tested using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The variance components were estimated through restricted maximum likelihood and genotypic values were predicted through best linear unbiased prediction. The harmonic mean of relative performance of genetic values (HMRPGV) were applied for simultaneous selection for adaptability, stability, and yield. According to BIC heterogeneous residual variance was the best model fit for FY, whereas homogeneous residual variance was the best model fit for FL, FS, and MIC traits. The selective accuracy was high, indicating reliability of the prediction. The HMRPGV was capable to select for stability, adaptability and yield simultaneously, with remarkable selection gain for each trait.

Reaction norms fitted through random regression models (RRM) have been widely used in animal and plant breeding for analyses of genotype × environment (G × E) interaction. However, in annual crops, they remain unexplored. Thus, this study aimed to evaluate the applicability and efficiency of RRM fitted through Legendre polynomials as a tool to recommend cotton (Gossypium hirsutum L.) genotypes. To this end, a data set with 12 genotypes of cotton evaluated in 10 environments for fiber length (FL) and fiber fineness was used. The restricted maximum likelihood/best linear unbiased prediction (REML/BLUP) procedure was used to estimate the variance components and to predict the genetic values. Results showed that there was genetic variability among cotton genotypes and that the reaction norms over the environmental gradient illustrated the G × E interaction. Very high selective accuracies (̂> 0.90) were found for both traits in all environments, which indicates high reliability in the genotype's recommendation. The areas under the reaction norms were calculated for the recommendation of genotypes for unfavorable, favorable, and overall environments. Regarding genotypes recommendation, areas under reaction norms allow recommending genotypes for unfavorable and favorable environments, as well as for overall recommendation, for both traits. This study is the first considering reaction norms fitted through RRM for the recommendation of cotton genotypes and demonstrated the potential of this technique in cotton breeding, besides its great potential to deal with G × E interactions.

The genotype × environment (G×E) interaction plays an essential role in phenotypic expression and can lead to difficulties in genetic selection. Thus, the present study aimed to estimate genetic parameters and to compare different selection strategies in the context of mixed models for soybean breeding. For this, data referring to the evaluation of 30 genotypes in 10 environments, regarding the grain yield trait, were used. The variance components were estimated through restricted maximum likelihood (REML) and genotypic values were predicted through best linear unbiased prediction (BLUP). Significant effects of genotypes and G×E interaction were detected by the likelihood ratio test (LRT). Low genotypic correlation was obtained across environments, indicating complex G×E interaction. The selective accuracy was very high, indicating high reliability. Our results showed that the most productive soybean genotypes have high adaptability and stability.

Cowpea is a legume of great importance in the Brazilian nutrition, mainly in the Northeast region. Despite the low yield of Brazilian cowpea, the species presents a genetic potential to be explored. Thus, this work aimed to characterize the genetic diversity of cowpea genotypes by agronomic traits and select genotypes for possible crosses by multivariate analysis. Four value for cultivation and use tests were carried out with cowpea genotypes in 2005 and 2006, in the municipalities of Aquidauana, Chapadão do Sul, and Dourados, in the state of Mato Grosso do Sul. The experimental design was a complete randomized block with 20 genotypes and four replications. The evaluated traits were value for cultivation, plant lodging, pod length, grain weight of five pods, number of grains per pod, pod weight, severity of powdery mildew, and grain yield. To estimate the genetic diversity among the genotypes, the optimization methods of Tocher and UPGMA were used. The generalized distance of Mahalanobis was used as a dissimilarity measure. The clustering methods revealed genetic variability among the cowpea genotypes evaluated. The methods used formed a different number of groups for each environment. Genotypes TE97-309G-24, MNC99-542F-5, BRS Paraguaçu, BRS Paraguaçu, BR 17-Gurguéia, and CNC x 409-11F-P2 can be used to obtain promising combinations and high genetic variability.

The present study aimed to evaluate the applicability and efficiency of the FAI-BLUP index in the genetic selection of maize hybrids, using 84 maize hybrids that were evaluated for cycle, morphology, and yield traits in four environments. Models accounting for homogeneous and heterogeneous residual variances were tested, and variance components were estimated using the residual maximum likelihood. Genotypic values were predicted by best linear unbiased prediction, and factor analysis was applied to group the traits. The FAI-BLUP index was used for the selection of maize hybrids based on ideotype design. Three factors explained more than 70% of genotypic variability, with selective accuracies varying from low (0.46) to high (0.99). Predicted genetic gains were positive for traits related to yield and negative for traits related to cycle and morphology, as is desirable in maize crop.

Random regression models (RRM) are a powerful tool to evaluate genotypic plasticity over time. However, to date, RRM remains unexplored for the analysis of repeated measures in Jatropha curcas breeding. Thus, the present work aimed to apply the random regression technique and study its possibilities for the analysis of repeated measures in Jatropha curcas breeding. To this end, the grain yield (GY) trait of 730 individuals of 73 half-sib families was evaluated over six years. Variance components were estimated by restricted maximum likelihood, genetic values were predicted by best linear unbiased prediction and RRM were fitted through Legendre polynomials. The best RRM was selected by Bayesian information criterion. According to the likelihood ratio test, there was genetic variability among the Jatropha curcas progenies; also, the plot and permanent environmental effects were statistically significant. The variance components and heritability estimates increased over time. Non-uniform trajectories were estimated for each progeny throughout the measures, and the area under the trajectories distinguished the progenies with higher performance. High accuracies were found for GY in all harvests, which indicates the high reliability of the results. Moderate to strong genetic correlation was observed across pairs of harvests. The genetic trajectories indicated the existence of genotype × measurement interaction, once the trajectories crossed, which implies a different ranking in each year. Our results suggest that RRM can be efficiently applied for genetic selection in Jatropha curcas breeding programs.

An efficient and informative statistical method to analyze genotype-by-environment interaction (GxE) is needed in maize breeding programs. Thus, the objective of this study was to compare the effectiveness of multiple-trait models (MTM), random regression models (RRM), and compound symmetry models (CSM) in the analysis of multi-environment trials (MET) in maize breeding. For this, a data set with 84 maize hybrids evaluated across four environments for the trait grain yield (GY) was used. Variance components were estimated by restricted maximum likelihood (REML), and genetic values were predicted by best linear unbiased prediction (BLUP). The best fit MTM, RRM, and CSM were identified by the Akaike information criterion (AIC), and the significance of the genetic effects were tested using the likelihood ratio test (LRT). Genetic gains were predicted considering four selection intensities (5, 10, 15, and 20 hybrids). The selected MTM, RRM, and CSM models fit heterogeneous residuals. Moreover, for RRM the genetic effects were modeled by Legendre polynomials of order two. Genetic variability between maize hybrids were assessed for GY. In general, estimates of broad-sense heritability, selective accuracy, and predicted selection gains were slightly higher when obtained using MTM and RRM. Thus, considering the criterion of parsimony and the possibility of predicting genetic values of hybrids for untested environments, RRM is a preferential approach for analyzing MET in maize breeding.