Abstract The objective of this work was to compare the use of noninformative and informative priors in Bayesian models, as well as to evaluate the viability of including informative priors in the estimation of variance components and genetic values in soybean breeding programs. The used phenotypic data refer to the evaluation of 80 soybean genotypes in ten environments over three years. For each evaluated crop year, informative and noninformative priors were used, and the parameters were estimated using the Gibbs sampler algorithm. Parameter estimates from the previous crop year were used as prior information for the next evaluated crop year. The goodness-of-fit was calculated using the deviance information criterion (DIC). Selective accuracy showed the highest values for the models chosen through DIC for both crop years. However, the intervals of the highest posterior density are narrower for all models that adopted informative priors. Adding information into Bayesian inference does not always result in a better model fitting. programs 8 years algorithm goodnessoffit goodness fit DIC. . (DIC) However fitting (DIC

Resumo O objetivo deste trabalho foi comparar o uso de a priori não informativas e informativas em modelos bayesianos, bem como avaliar a viabilidade da inclusão de a priori informativas na estimativa dos componentes de variância e dos valores genotípicos em programas de melhoramento de soja. Os dados fenotípicos utilizados referem-se à avaliação de 80 genótipos de soja, em dez ambientes, ao longo de três anos. Para cada safra avaliada, foram utilizadas a priori informativas e não informativas, e os parâmetros foram estimados com uso do algoritmo de amostragem de Gibbs. As estimativas dos parâmetros da safra anterior foram utilizadas como informação prévia para a próxima safra avaliada. A qualidade do ajuste foi calculada com uso do critério de informação de desvio (DIC). A acurácia seletiva apresentou maiores valores nos modelos escolhidos por meio do DIC, para ambas as safras. No entanto, os intervalos de maior densidade a posteriori são menores para todos os modelos que adotaram a priori informativas. Adicionar informações à inferência bayesiana nem sempre resulta em melhor ajuste ao modelo. bayesianos soja referemse referem se 8 ambientes anos avaliada Gibbs DIC. DIC . (DIC) safras entanto modelo (DIC

Abstract Species of the genus Cynodon are among the most cultivated forage crops in the world due to their high yield and nutritional quality, and its use in cattle feeding has been associated with gains in animal weight and increased milk production. The objective of this study was to model covariance structures in Cynodon spp. clones and study the changes in ranking of the selected genotypes, since it is believed that affects the ranking of genotypes. A total of 202 genotypes were evaluated in an experiment conducted in an augmented block design with four replications and four harvests. The genotypes were assessed for plant height, green weight, percentage of dry matter, and plant vigor. Nineteen repeated measures models with different covariance structures were tested. The best-fitted model adopts the CORH covariance structure for the genetic effects. Correct modeling of the covariance structure affected the ranking of genotypes in all variables evaluated. quality production spp 20 harvests height matter vigor tested bestfitted best fitted effects 2

ABSTRACT An accurate and efficient statistical method for genetic evaluation is a key requirement for progress in any breeding program. Thus, the present study aimed to evaluate the performance of Frequentist and Bayesian inferences for repeated measures analysis in Jatropha curcas breeding. To this end, 730 individuals from 73 half-sib families were evaluated for grain yield trait, over six crop years. Frequentist and Bayesian analyses were made considering repeatability models with different residual variance structures. Variance components were estimated through restricted maximum likelihood (REML) and Markov Chain Monte Carlo (MCMC). Genetic values were predicted through best linear unbiased prediction (BLUP) and estimated through MCMC. Variance components and genetic and non-genetic parameters estimated by the Frequentist inference presented values similar to those estimated by the Bayesian inference. The selective accuracy presented high magnitude (0.84) by the Frequentist and Bayesian inferences, indicating high reliability. Confidence and highest posterior density (HPD) intervals were similar for the genetic parameters, however the HPD intervals range was slightly short. This study highlighted the importance of testing the residual variance structure and pointed out that the Frequentist and Bayesian inferences presented similar results when using non-informative prior. Then, both inferences can be efficiently applied in Jatropha curcas breeding.

ABSTRACT Forest plantations are strong allies in preserving natural resources, providing social and economic benefits. The plantations carried out in the coming years will be vital to meet the growing demand for forest products. To ensure the continuity of genetic progress and the good results achieved with the improvement of forest species, statistical methods that accurately selects superior genotypes are desirable. Multi-trait multi-environment trials are preferred over single-trait single-environment trials, since they can exploit the covariance between traits and environments, increasing the analysis’s prediction power. The Bayesian multi-trait multi-environments approach (BMTME) combines the cited advantages with the parsimony of Bayesian statistics promoting a more informative data analysis. Thus, the aims of this study were to estimate genetic parameters, evaluate genetic variability, and select eucalyptus clones through BMTME models. To this end, a data set with 215 eucalyptus clones evaluated in four environments for diameter at breast height and Pilodyn penetration was used. The Markov Chain Monte Carlo algorithm was applied to estimate the variance components and genetic parameters and to predict the genotypic values. The Smith-Hazel index was used to simultaneously achieve gains with selection for both traits. The BMTME approach provided high accuracies, being a good strategy to the evaluation of multiple environmental trials of Eucalyptus for breeding purposes.

ABSTRACT. In cotton crops, the cotton seed yield significantly contributes with the success of any cultivar. However, other traits are considered when an ideotype is pointed out in the selection, such as the fiber quality traits. The aim of this study was to applied genotype by yield*trait (GYT) biplot to a multi-environment trial data of cotton genotypes and selected the best genotypes. For this end, thirteen genotypes from nineteen trials were assessed. Seven traits were evaluated [cotton seed yield (SY), fiber percentage (FP), fiber length (FL), fiber uniformity (FU), short fiber index (SFI), fiber strength (FS), and elongation (EL)] and residual error variances structures [identity variance (IDV) and diagonal (Diag)] were tested by bayesian information criterion. After, the REML/BLUP approach was applied to predict the genetic values of each trait and the selective accuracy were measured from the prediction. Then, the GYT-biplot were applied to the data. For SP and SFI traits, the model with Diag residual variance was indicated, whereas for SY FL, FU, FS, and EL traits the model with IDV residual variance demonstrated the best fit to the data. Values of accuracy were higher than 0.9 for all traits analyzed. In the GYT-biplot acute angles were find for all traits relations, which means high correlation between the yield*traits combination. Besides that, the correlation still can be seen in the GYT-biplot, as shown by the magnitudes of the angles between the pairs Yield*FU-Yield*FS and Yield*FS-Yield*EL. Also, the GYT-biplot indicates the genotype G4 with the best performance for Yield*FS, Yield*SFI, Yield*FU, Yield*FL, and Yield*FP combined. The genotypes G4, G1, G13, G8, and G9 represent those genotypes with yield advantage over the other cultivars. Then, the genotype G4 combines all desirable characteristics and demonstrate have large potential in the cotton breeding. The GYT approach were valuable and were highly recommended in cotton breeding programs for selection purpose in a multivariate scenario.

RESUMO: A interação genótipo × ambiente (G × E) desempenha um papel essencial na expressão fenotípica e pode provocar dificuldades na seleção genética. Assim, o presente estudo teve como objetivo estimar parâmetros genéticos e comparar diferentes estratégias de seleção no contexto de modelos mistos para melhoramento da soja. Para isso, foram utilizados dados referentes à avaliação de 30 genótipos em dez ambientes, referentes à característica produtividade de grãos. Os componentes de variância foram estimados pela máxima verossimilhança restrita (REML) e os valores genotípicos foram preditos pela melhor previsão imparcial linear (BLUP). Efeitos significativos dos genótipos e interação G × E foram detectados pelo teste da razão de verossimilhança (LRT). Correlação genotípica baixa foi obtida entre os ambientes indicando interação G × E do tipo complexa. A acurácia seletiva foi muito alta, indicando alta confiabilidade. Os resultados mostraram que os genótipos de soja mais produtivos apresentam alta adaptabilidade e estabilidade.

ABSTRACT: 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.

Abstract The genotype × environment (G×E) interaction plays an essential role in phenotypic expression and can lead to difficulties in genotypes recommendation. Thus, the objectives of this study were: i) propose the Multi-Environment Index Based on Factor Analysis and Ideotype-Design/Markov Chain Monte Carlo (FAI/MCMC index), and ii) apply it for soybean genotypes recommendation. To this end, a data set with 30 soybean genotypes evaluated in 10 environments for grain yield trait was used. Variance components, genetic parameters and genetic values were estimated through MCMC algorithm. Environmental stratification was conducted by factor analyses and the selection of soybean genotypes was performed using the FAI/MCMC index. The results indicated the existence of genotypic variability and G×E interaction. The environments were grouped into three factors. The predicted genetic gains from indirect selection was 4.81%. Thus, our results suggest that the FAI/MCMC index can be successfully used in soybean breeding.

RESUMO: Em ensaios multi-ambientes, grandes redes experimentais são utilizadas para a avaliação de genótipos, tentando contornar o efeito que a interação genótipo por ambiente desempenha na seleção genotípica. Neste estudo, objetivamos testar diferentes estruturas de variância residual e medir o ganho de seleção de genótipos de algodão, baseados em produtividade, adaptabilidade e estabilidade, simultaneamente. Doze genótipos de algodão foram plantados em 10 ambientes, sendo determinados o comprimento da fibra (CF), a resistência da fibra (RF), a micronaire (MIC) e produtividade de fibras (PF). A seleção do modelo para diferentes estruturas de variância residual (homogênea e heterogênea) foi testada usando o Critério de Informação de Akaike (AIC) e o Critério de Informação Bayesiano (BIC). Os componentes de variância foram estimados através de máxima verossimilhança restrita e os valores genotípicos foram preditos através da melhor predição linear não viesada. A média harmônica do desempenho relativo dos valores genéticos (HMRPGV) foram aplicadas para seleção simultânea para adaptabilidade, estabilidade e produtividade. De acordo com o BIC, a estrutura residual heterogênea apresentou o melhor ajuste para a característica PF, enquanto a estrutura residual homogênea apresentou o melhor ajuste para as características CF, RF e MIC. A acurácia seletiva foi alta, indicando confiabilidade da predição. O método HMRPGV foi capaz de selecionar para estabilidade, adaptabilidade e produtividade, simultaneamente, com notável ganho de seleção para cada característica.

ABSTRACT: 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.

Abstract: 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.