ABSTRACT. Multi-trait multi-environment (MTME) models were fitted to eucalyptus breeding trials data to assess residual variance structure, genetic stability and adaptability. To do so, 215 eucalyptus clones were evaluated in a randomized complete block design with 30 replicates and one plant per plot in four environments. At 36 months of age, tree diameter at breast height (DBH) and pilodyn penetration (PP) were measured. Two MTME models were fitted, for which residuals were considered homoscedastic and heteroscedastic, with the best MTME model selected using Bayesian information criterion. The harmonic mean of the relative performance of the genotypic values (HMRPGV) was used to determine stability and adaptability. Of the two models, the heteroscedastic MTME model had better fit and provided greater accuracy. In addition, genotype-by-environment interaction was complex, and there was low genetic correlation between DBH and PP. Rank correlation between the clones selected by the MTME models was high for DBH but low for PP. The HMRPGV facilitated clone selection through simultaneous evaluation of stability, adaptability, and productivity. Thus, our results suggest that heteroscedastic MTME model / HMRPGV can be efficiently applied in the genetic evaluation and selection of eucalyptus clones.

Abstract The objective of this work was to estimate the genetic parameters and to evaluate the genotypic diversity of 12 'Tahiti' acid lime (Citrus latifolia) genotypes grafted onto two rootstocks. The experiment was carried out from July 2017 to January 2019, in the municipality of São Mateus, in the state of Espírito Santo, Brazil. Vegetative (stem diameter, canopy projection diameter, and plant height), productive (yield and fruit number), and fruit quality (fruit diameter, soluble solids content, and juice yield) traits were determined. A mixed model was used to estimate heritability and repeatability coefficients, as well as to predict clonal values. Scion diversity was determined through the standardized mean difference of Euclidean distances, and genotypes were clustered by modified Tocher. Clustering quality and trait importance were evaluated using the principal component analysis (PCA). Genotypic variance was observed, which is indicative of the possibility of selection of superior genotypes. The Tocher method showed the presence of three clusters, which is in alignment with the PCA results. The multivariate analyses allows of the selection and the recommendation of superior 'Tahiti' acid lime genotypes.

Resumo O objetivo deste trabalho foi estimar os parâmetros genéticos e avaliar a diversidade genética de 12 genótipos de lima ácida 'Tahiti' (Citrus latifolia) enxertados em dois porta-enxertos. O experimento foi conduzido de julho de 2017 a janeiro de 2019, no município de São Mateus, no estado de Espírito Santo, Brasil. Foram mensuradas características vegetativas (diâmetro de caule, diâmetro de projeção de copa e altura de planta), produtivas (rendimento e número de frutos) e de qualidade de frutos (diâmetros de fruto, teor de sólidos solúveis e rendimento de suco). Utilizou-se modelo misto para estimar os coeficientes de herdabilidade e repetibilidade, bem como predizer os valores genéticos. A diversidade entre os enxertos foi obtida por meio da diferença da distância euclidiana média padronizada, e os genótipos foram agrupados pelo método de Tocher modificado. A qualidade do agrupamento e a importância dos caracteres foi avaliada pela análise de componentes principais (ACP). Observou-se variabilidade genética, o que indica a possibilidade de seleção de genótipos superiores. O método de Tocher mostrou a presença de três grupos de genótipos, o que foi congruente com os resultados da ACP. O uso de técnicas multivariadas permite a seleção e a recomendação de genótipos superiores de lima ácida 'Tahiti'.

RESUMO: Embora a produtividade seja uma característica fundamental em programas de melhoramento da lima ácida Tahiti, outras características se destacam por proporcionar uma seleção mais eficiente ou mesmo influenciar na expressão de atributos produtivos. A aplicação de inferência Bayesiana, pode tornar o processo de identificação de indivíduos superiores e o estudo das correlações entre as características ainda mais acurado. Objetivou-se, por meio deste estudo, estimar valores genéticos em genótipos de lima ácida Tahiti através de inferência Bayesiana e estimar coeficientes de correlação e de trilha entre características vegetativas, produtivas e de qualidade de frutos. Vinte e quatro genótipos de lima ácida foram avaliados durante dois anos para peso e número de frutos, volume de copa, diâmetro de caule, teor de sólidos solúveis dos frutos, espessura de casca e rendimento de suco. Os valores genéticos foram estimados por meio de inferência Bayesiana e modelos com diferentes estruturas residuais foram testados via critério de informação de deviance. Coeficiente de correlação de Pearson e de análise de trilha foram determinados, removendo o efeito de multicolinearidade. A estimação de valores genéticos via inferência Bayesiana apresentou alta acurácia seletiva. As correlações obtidas entre caracteres de diferentes grupos podem ser úteis em estratégias de seleção para melhoramento da lima ácida Tahiti. A inferência Bayesiana demonstrou ser uma ferramenta importante e deve ser considerada em programas de melhoramento de culturas perenes.

ABSTRACT: Although the fruit yield has a core importance in Tahiti acid lime breeding programs, other traits stand out among the quality fruit and vegetative traits as ones that still need to be improved in selection of superior genotypes. Appling efficient tools aiming selection, such as the Bayesian inference, becomes an alternative in perennial crops. This study applied Bayesian inference in the genetic evaluation of Tahiti acid lime genotypes and estimated the interrelation between vegetative, productive and fruit quality traits. Twenty-four acid lime genotypes were evaluated for number of fruits, fruit yield, canopy volume, stem diameter, soluble solids content, shell thickness, and juice yield traits. The genotypic values were estimated through Bayesian inference and models with different residual structure were tested via deviance information criterion. Pearson’s correlation and the path analysis were estimated, removing the multicollinearity effect. The Bayesian inference estimates genotypic values with high selective accuracy. The correlations obtained between traits from different groups can be useful in selection strategies for improvement of Tahiti acid lime. The Bayesian inference demonstrated to be an important tool and should be considered in perennial breeding programs.

RESUMO: Compreender a diversidade genética e contornar os problemas causados pela interação genótipos por ambientes é uma etapa importante em programas de melhoramento. Este estudo teve como objetivo estimar a diversidade genética e aplicar a metodologia de biplot genótipo + genótipo por ambiente (GGE biplot) em doze genótipos de algodão avaliados quanto ao rendimento da fibra, comprimento da fibra, resistência da fibra e micronaire. A estimativa dos componentes de variância e dos parâmetros genéticos foi feita através do método da máxima verossimilhança restrita e a predição dos valores genotípicos por meio da melhor predição linear não enviesada. Os métodos de Tocher modificado e análise de componentes principais (PCA) foram utilizados para quantificar a diversidade genética entre os genótipos. O método GGE biplot foi conduzido para encontrar os melhores genótipos em relação à adaptabilidade e estabilidade. As técnicas de Tocher e PCA permitiram a formação de clusters de genótipos semelhantes com base em uma estrutura multivariada. O GGE biplot indicou que os genótipos IMACV 690 e IMA08 WS foram altamente adaptáveis e estáveis para as principais características do algodão. O cruzamento dentre os genótipos IMACV 690 e IMA08 WS é o mais recomendado para aumentar o desempenho das principais características na cultura do algodão.

ABSTRACT: Understanding the genetic diversity and overcoming genotype-by-environment interaction issues is an essential step in breeding programs that aims to improve the performance of desirable traits. This study estimated genetic diversity and applied genotype + genotype-by-environment (GGE) biplot analyses in cotton genotypes. Twelve genotypes were evaluated for fiber yield, fiber length, fiber strength, and micronaire. Estimation of variance components and genetic parameters was made through restricted maximum likelihood and the prediction of genotypic values was made through best linear unbiased prediction. The modified Tocher and principal component analysis (PCA) methods, were used to quantify genetic diversity among genotypes. GGE biplot was performed to find the best genotypes regarding adaptability and stability. The Tocher technique and PCA allowed for the formation of clusters of similar genotypes based on a multivariate framework. The GGE biplot indicated that the genotypes IMACV 690 and IMA08 WS were highly adaptable and stable for the main traits in cotton. The cross between the genotype IMACV 690 and IMA08 WS is the most recommended to increase the performance of the main traits in cotton crops.

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.

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.

Resumo O objetivo deste trabalho foi avaliar a variabilidade genética e as associações de características produtivas do feijão-bóer, para indicação dessa cultura ao programa de melhoramento em Moçambique. Foram avaliadas 11 características do feijão-bóer, em delineamento de três blocos ao acaso, nos ambientes de Namapa (I) e Montepuez (II), em 2017/2018. Para avaliação das características, utilizaram-se análises de variância, parâmetros genéticos, correlações, rede de correlação e análise de trilha. Em ambos os ambientes, há alta variabilidade genética e fenotípica para ramos primários, ramos secundários, vagens por planta, número de sementes por vagem, largura e comprimento da vagem e produtividade, bem como alta herdabilidade para todas as características, exceto para altura da planta. Os ramos primários e secundários apresentam alta correlação com a produtividade e efeito direto positivo sobre ela. No entanto, altura de planta e vagens por planta apresentam alta variabilidade fenotípica e correlação positiva com a produtividade no ambiente I. Vagens por planta, peso de 100 sementes e ramos primários apresentam altos efeitos positivos diretos no ambiente I, e ramos secundários e número de sementes por vagem, no ambiente II. Os ramos primários e secundários apresentam alta variabilidade e associações com a produtividade em ambos os ambientes e são indicados para o programa de melhoramento do feijão-bóer em Moçambique.

Abstract The objective of this work was to evaluate the genetic variability and associations of yield traits of pigeon pea, for indication of this crop for the breeding program in Mozambique. Eleven pigeon pea traits were evaluated in a experimental design with three randomized complete blocks, in the environments of Namapa (I) and Montepuez (II), in 2017/2018. To evaluate the traits, analyses of variance, genetic parameters, correlations, correlation network, and path analysis were used. In both environments, there is a high genetic and phenotypic variability for primary branches, secondary branches, pods per plant, number of seed per pod, pod width, pod length, and yield, as well as a high heritability for all traits except for plant height. The primary and secondary branches have a high correlation with yield and a positive direct effect on it. However, plant height and pods per plant show a high phenotypic variability and a positive correlation with yield in environment I. Pods per plant, weight of 100 seed, and primary branches show high direct positive effects in environment I, and secondary branches and number of seed per pod, in environment II. The primary and secondary branches show high variability and associations with yield in both environments and are indicated for the pigeon pea breeding program in Mozambique.

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.

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 Combining longitudinal data and statistical models from perennial crops enabled us to estimate the optimum number of measures (harvests), implying accurate discrimination of superior genotypes in those crops. Herein, the goal of this study was to determine the optimum number of harvests based on yield traits and recommend a superior graft/rootstock combination (GRC) for Citrus latifolia Tanaka. Twenty-four GRCs of 'Tahiti' acid lime were evaluated from July 2017 to August 2018 for fruit yield per plant (FYP), number of fruits per plant (NFP), and longitudinal (LFD) and transversal fruit diameter (TFD). The experimental design was a randomized complete block with 4 replications. The experimental unit consisted of three individuals, totalling 244 individuals. The GRCs were composed of (i) two hybrids that were used as rootstock, citrumelo ‘Swingle’ (Citrus paradisi x Poncirus trifoliata) and cintrandarin ‘Riverside’ (Citrus sunki x Poncirus trifoliata); and (ii) 12 different C. latifolia genotypes that were used as grafts: Bello Fruit, Eledio, Iconha, Itarana, Santa Rosa, Bearss lime, CNPMF 01, CNPMF 02, CNPMF 2001, CNPMF 5059, BRS Passos, and Persian 58. Mixed models were employed to estimate the variance components. The optimum number of harvests was determined based on selective efficiency values above 0.9. The estimated repeatability coefficients presented values of 0.14 (LFD), 0.16 (TFD), 0.36 (FYP), and 0.38 (NFD). Based on the results, four harvests were able to choose genotypes based on FYP and NFP, whereas LFD and TFD were considered inefficient traits for recommending superior GRCs.

Abstract In this manuscript we discuss the purpose and scope of biometry and its interactions, complementation, and even overlap with several other areas of genetics. We emphasize that biometry is an area of genetics that enables researchers to analyze, process, and interpret biological phenomena from data, usually obtained from experimental tests, in an improved way to guide strategies and decision making for optimization of resources. We also highlight the importance of the biometry professional in the context of breeding and the need for continual training, due to new demands for and challenges from inclusion of different types of information for processing and analysis paradigms to better interpret these paradigms.

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 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.

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.

ABSTRACT Tree breeders are prioritizing the increase of the interspecific diversity in the breeding programs due to the pronounced environmental changes, and expansion of the forest frontier to less productive areas. In this scenario, there is a growing interest for species of the genus Corymbia due to their good growth, resistance to biotic and abiotic factors, and industrial properties. Also, Corymbia spp. can cross with each other, generating interspecific hybrids. However, there are great difficulties on defining the best crosses. Thus, the objectives of this study were to evaluate the genetic variability of 64 progenies of Corymbia maculata and 64 progenies of Corymbia torelliana and to use the GGE biplot method to point the most appropriated crosses to broad and specific environments in order to generate stable and productive interspecific hybrids of C. maculata and C. torelliana. The GGE biplot was an efficient method for evaluating the genetic variability between progenies, for visualizing the genotype by environment interaction pattern and for identifying the best crosses in order to generate interspecific hybrids of the species. By adopting a selection intensity of 10%, the recommended progenies to generate interspecific hybrids for the Aracruz municipality (ARA) were 10, 40, 49, 64, 20, 9 and 47 of C. maculata and 24, 56, 41, 64, 43, 31 and 12 of C. torelliana. For Três Lagoas municipality (TLA), the recommended progenies were 11, 17, 1, 48, 7, 63 and 21 of C. maculata and 42, 46, 61, 44, 10, 63 and 28 of C. torelliana.