ABSTRACT Among the multi-trait models selected to study several traits and environments jointly, the Bayesian framework has been a preferred tool when constructing a more complex and biologically realistic model. In most cases, non-informative prior distributions are adopted in studies using the Bayesian approach. However, the Bayesian approach presents more accurate estimates when informative prior distributions are used. The present study was developed to evaluate the efficiency and applicability of multi-trait multi-environment (MTME) models within a Bayesian framework utilizing a strategy for eliciting informative prior distribution using previous data on rice. The study involved data pertaining to rice (Oryza sativa L.) genotypes in three environments and five crop seasons (2010/2011 until 2014/2015) for the following traits: grain yield (GY), flowering in days (FLOR) and plant height (PH). Variance components, genetic and non-genetic parameters were estimated using the Bayesian method. In general, the informative prior distribution in Bayesian MTME models provided higher estimates of individual narrow-sense heritability and variance components, as well as minor lengths for the highest probability density interval (HPD), compared to their respective non-informative prior distribution analyses. More informative prior distributions make it possible to detect genetic correlations between traits, which cannot be achieved with non-informative prior distributions. Therefore, this mechanism presented to update knowledge for an elicitation of an informative prior distribution can be efficiently applied in rice breeding programs.

ABSTRACT: Quantile Random Forest (QRF) is a non-parametric methodology that combines the advantages of Random Forest (RF) and Quantile Regression (QR). Specifically, this approach can explore non-linear functions, determining the probability distribution of a response variable and extracting information from different quantiles instead of just predicting the mean. This evaluated the performance of the QRF in the genomic prediction for complex traits (epistasis and dominance). In addition, compare the accuracies obtained with those derived from the G-BLUP. The simulation created an F2 population with 1,000 individuals and genotyped for 4,010 SNP markers. Besides, twelve traits were simulated from a model considering additive and non-additive effects, QTL (Quantitative trait loci) numbers ranging from eight to 120, and heritability of 0.3, 0.5, or 0.8. For training and validation, the 5-fold cross-validation approach was used. For each fold, the accuracies of all the proposed models were calculated: QRF in five different quantiles and three G-BLUP models (additive effect, additive and epistatic effects, additive and dominant effects). Finally, the predictive performance of these methodologies was compared. In all scenarios, the QRF accuracies were equal to or greater than the methodologies evaluated and proved to be an alternative tool to predict genetic values in complex traits.

RESUMO: Quantile Random Forest (QRF) é uma metodologia não paramétrica, que combina as vantagens do Random Forest (RF) e da Regressão Quantílica (QR). Especificamente, essa abordagem pode explorar funções não lineares, determinando a distribuição de probabilidade de uma variável resposta e extraindo informações de diferentes quantis em vez de apenas prever a média. O objetivo deste trabalho foi avaliar o desempenho do QRF em predizer o valor genético genômico para características com arquitetura genética não aditiva (epistasia e dominância). Adicionalmente, as acurácias obtidas foram comparadas com aquelas advindas do G-BLUP. A simulação criou uma população F2 com 1.000 indivíduos genotipados para 4.010 marcadores SNP. Além disso, doze características foram simuladas a partir de um modelo considerando efeitos aditivos e não aditivos, com número de QTL (Quantitative trait loci) variando de oito a 120 e herdabilidade de 0,3, 0,5 ou 0,8. Para treinamento e validação foi usada a abordagem da validação cruzada 5-fold. Para cada um dos folds foram calculadas as acurácias de todos os modelos propostos: QRF em cinco quantis diferentes e três modelos do G-BLUP (com efeito aditivo, aditivo e epistático, aditivo e dominante). Por fim, o desempenho preditivo dessas metodologias foi comparado. Em todos os cenários, as acurácias do QRF foram iguais ou superiores às metodologias avaliadas e mostrou ser uma ferramenta alternativa para predizer valores genéticos em características complexas.

ABSTRACT. The study of traits in crops enables breeders to guide strategies for selecting and accelerating the progress of genetic breeding. Although the simultaneous evaluation of characteristics in the plant breeding programme provides large quantities of information, identifying which phenotypic characteristic is the most important is a challenge facing breeders. Thus, this work aims to quantify the best approaches for prediction and establish a network of better predictive power in flood-irrigated rice via methodologies based on regression, artificial intelligence, and machine learning. Multiple regression, computational intelligence, and machine learning were used to predict the importance of the characteristics. Computational intelligence and machine learning were notable for their ability to extract nonlinear information from model inputs. Predicting the relative contribution of auxiliary characteristics in rice through computational intelligence and machine learning proved to be efficient in determining the relative importance of variables in flood-irrigated rice. The characteristics indicated to assist in decision making are flowering, number of grains filled by panicles and length of panicles for this study. The network with only one hidden layer with 15 neurons was observed to be efficient in determining the relative importance of variables in flooded rice.

ABSTRACT. The genotype by environment interaction is the main factor that influences the response of evaluated genotypes in trials of value for cultivation and use. Adaptability and stability analyses are fundamental to understanding the performance of genotypes in a growing region. Some of these methodologies incorporate previous information for recommending an extra group of genotypes denominated as specific ideotypes under certain cultivation conditions. Based on this strategy, the centroid method and its modifications have been widely used due to the simplicity of classification of the evaluated genotypes. However, these methodologies present problems in identifying adaptability patterns of some genotypes. Artificial intelligence techniques, such as fuzzy C-means, can be an alternative to reduce these difficulties, since they use, in addition to distance information between genotypes, memberships (measures quantifying how much an observation belongs to a particular class) to increase discriminatory power. Therefore, our aim was to propose and evaluate the phenotypic adaptability method by fuzzy clustering to assist cultivar recommendations. The adaptation of the fuzzy C-Means method to classify the genotypes was implemented in BioFuzzy software. The grain yield data of black common bean genotypes were used to evaluate the potential of the method. The results obtained by this method were compared with those obtained by the centroid method. The phenotypic adaptability method by fuzzy clustering was effective in identifying the adaptability patterns of common bean genotypes. Moreover, the discriminatory power was higher than that observed with the centroid method. ABSTRACT use region conditions strategy However techniques Cmeans, Cmeans C means, means C-means difficulties measures class Therefore recommendations CMeans Means software Moreover

ABSTRACT: The principal component regression (PCR) and the independent component regression (ICR) are dimensionality reduction methods and extremely important in genomic prediction. These methods require the choice of the number of components to be inserted into the model. For PCR, there are formal criteria; however, for ICR, the adopted criterion chooses the number of independent components (ICs) associated to greater accuracy and requires high computational time. In this study, seven criteria based on the number of principal components (PCs) and methods of variable selection to guide this choice in ICR are proposed and evaluated in simulated and real data. For both datasets, the most efficient criterion and that drastically reduced computational time determined that the number of ICs should be equal to the number of PCs to reach a higher accuracy value. In addition, the criteria did not recover the simulated heritability and generated biased genomic values.

ABSTRACT The development of water quality indices (WQIs), duly modified and using a small number of parameters, may be of great economic use. The purpose of this work was to develop a WQI with a reduced number of parameters (WQIred), in relation to what is used in the Brazilian state of Minas Gerais (WQIIGAM), in the basin of the Doce River. Four different scenarios were analysed, with the absence of the following parameters for the calculation of the WQIred: BOD, E. coli and phosphate; BOD and E. coli; BOD, E. coli and total solids (TS); BOD, E. coli, phosphate and TS. The redistribution of the weight attributed to the eliminated parameters was done according to the following methods: (i) in weighted form, through optimisation of the correlation between the WQIred and the WQIIGAM; (ii) based on the cluster analysis. The best scenario found was that of the WQIred considering only DO, pH, temperature variation, nitrates and turbidity, with the weights being redistributed based on cluster analysis. This scenario maintained satisfactory performance, with a minimum difference being observed between WQIIGAM and WQIred, in terms of management purpose. The WQIred as proposed makes it possible to establish a monitoring control system operating in real time in the Doce river basin, as all the parameters considered can be obtained with the use of multiparameter probes.

Resumo O objetivo deste trabalho foi avaliar um procedimento para elicitação de distribuição a priori informativa, comparada à distribuição a priori não informativa, em tamanho amostral reduzido, com uso de 14 caracteres de três genótipos de linhaça (Linum usitatissimum), em sete épocas de semeadura. Os valores dos hiperparâmetros regulam a informatividade da distribuição a priori; portanto, para cada época, foram calculados os hiperparâmetros a serem utilizados na próxima época. As duas distribuições a priori, não informativa e informativa, foram comparadas pelo comprimento dos intervalos de credibilidade e pela variância da distribuição a posteriori. Em geral, quando a distribuição a priori informativa é adotada, os parâmetros genéticos apresentam menor comprimento do intervalo de credibilidade e estimativas mais precisas. O mecanismo de elicitação a priori informativa com uso de informações prévias de programas de melhoramento é eficiente para estimativa de parâmetros genéticos, incluindo herdabilidade e variância genética, mesmo quando o tamanho da amostra é pequeno. Na avaliação genética, o uso da distribuição a priori informativa é melhor do que o da distribuição não informativa para tamanho amostral pequeno. Em geral, os resultados das distribuições a priori informativas indicam que os valores genéticos da primeira época de semeadura são maiores para os seguintes caracteres: comprimento do ciclo, altura da planta, e número de cápsulas não granuladas e de ramos produtivos.

Abstract The objective of this work was to evaluate a procedure for the elicitation of informative prior distribution, compared with non-informative prior distribution, in a small sample size, using 14 traits of three linseed (Linum usitatissimum) genotypes in seven sowing seasons. The values of the hyperparameters regulate the informativeness of the prior distribution; therefore, for each season, the hyperparameters to be used in the next season were calculated. The two prior distributions, non-informative and informative, were compared by the length of the credible interval and variance of the posterior distribution. In general, when the informative prior distribution is adopted, the genetic parameters present a shorter length of the credible interval and more precise estimates. The mechanism for informative prior elicitation using previous information from breeding programs is efficient for the estimation of genetic parameters, including heritability and genetic variance, even when the sample size is small. In genetic evaluation, the use of informative prior distribution is better than that of non-informative distribution for a small sample size. In general, the results of the informative prior distributions are indicative that the genetic values of the first sowing season are greater for the following traits: cycle length, plant height, and number of non-grained capsules and of productive branches.

ABSTRACT: The development of efficient methods for genome–wide association studies (GWAS) between quantitative trait loci (QTL) and genetic values is extremely important to animal and plant breeding programs. Bayesian approaches that aim to select regions of single nucleotide polymorphisms (SNPs) proved to be efficient, indicating genes with important effects. Among the selection criteria for SNPs or regions, selection criterion by percentage of variance can be explained by genomic regions (%var), selection of tag SNPs, and selection based on the window posterior probability of association (WPPA). To also detect potentially associated regions, we proposed measuring posterior probability of the interval PPint), which aims to select regions based on the markers of greatest effects. Therefore, the objective of this work was to evaluate these approaches, in terms of efficiency in selecting and identifying markers or regions located within or close to genes associated with traits. This study also aimed to compare these methodologies with single–marker analyses. To accomplish this, simulated data were used in six scenarios, with SNPs allocated in non–overlapping genomic regions. Considering traits with oligogenic inheritance, WPPA criterion followed by %var and PPint criteria were shown to be superior, presenting higher values of detection power, capturing higher percentages of genetic variance and larger areas. For traits with polygenic inheritance, PPint and WPPA criteria were considered superior. Single–marker analyses identified SNPs associated only in oligogenic inheritance scenarios and was lower than the other criteria.

ABSTRACT. This paper aimed to evaluate the effectiveness of subset selection of markers for genome-enabled prediction of genetic values using radial basis function neural networks (RBFNN). To this end, an F1 population derived from the hybridization of divergent parents with 500 individuals genotyped with 1000 SNP-type markers was simulated. Phenotypic traits were determined by adopting three different gene action models - additive, additive-dominant, and epistatic, representing two dominance situations: partial and complete with quantitative traits having a heritability (h2) of 30 and 60%; traits were controlled by 50 loci, considering two alleles per locus. Twelve different scenarios were represented in the simulation. The stepwise regression was used before the prediction methods. The reliability and the root mean square error were used for estimation using a fivefold cross-validation scheme. Overall, dimensionality reduction improved the reliability values for all scenarios, specifically with h2 =30 the reliability value from 0.03 to 0.59 using RBFNN and from 0.10 to 0.57 with RR-BLUP in the scenario with additive effects. In the additive dominant scenario, the reliability values changed from 0.12 to 0.59 using RBFNN and from 0.12 to 0.58 with RR-BLUP, and in the epistasis scenarios, the reliability values changed from 0.07 to 0.50 using RBFNN and from 0.06 to 0.47 with RR-BLUP. The results showed that the use of stepwise regression before the use of these techniques led to an improvement in the accuracy of prediction of the genetic value and, mainly, to a large reduction of the root mean square error in addition to facilitating processing and analysis time due to a reduction in dimensionality.

RESUMO: Padrões empíricos de desequilíbrio de ligação (LD) podem ser utilizados para aumentar o poder estatístico do mapeamento genético. Este trabalho foi realizado com o objetivo de verificar a eficácia da análise de fatores (AF) aplicada a conjuntos de dados de marcadores moleculares do tipo SNP, visando identificar grupos de ligação e blocos de haplótipos. O conjunto de dados SNPs utilizado foi oriundo de um processo de simulação de uma população F2, contendo 2000 marcas com informações de 500 indivíduos. A estimação das cargas fatoriais (loadings) da AF foi feita de duas formas, considerando a matriz de distâncias entre os marcadores (A) e considerando a matriz de correlação (R). O número de fatores (k) a ser utilizado foi estabelecido com base no gráfico scree-plot e com base na proporção da variância total explicada. Os resultados indicam que as matrizes A e R conduzem a resultados similares. Com base no scree-plot considerou-se k igual a 10 e os fatores interpretados como sendo representativos dos grupos de ligação. O segundo critério conduziu a um número de fatores igual a 50, e os fatores interpretados como sendo representativos dos blocos de haplótipos. Isto mostra o potencial da técnica que permite obter resultados aplicáveis a qualquer tipo de população, corroborando a interpretação de estudos genômicos. O trabalho demonstrou que a AF foi capaz de identificar padrões de associação entre marcadores, identificando subgrupos de marcadores que refletem grupos de ligação fatorial e também grupos de desequilíbrio de ligação.

ABSTRACT: Empirical patterns of linkage disequilibrium (LD) can be used to increase the statistical power of genetic mapping. This study was carried out with the objective of verifying the efficacy of factor analysis (AF) applied to data sets of molecular markers of the SNP type, in order to identify linkage groups and haplotypes blocks. The SNPs data set used was derived from a simulation process of an F2 population, containing 2000 marks with information of 500 individuals. The estimation of the factorial loadings of FA was made in two ways, considering the matrix of distances between the markers (A) and considering the correlation matrix (R). The number of factors (k) to be used was established based on the graph scree-plot and based on the proportion of the total variance explained. Results indicated that matrices A and R lead to similar results. Based on the scree-plot we considered k equal to 10 and the factors interpreted as being representative of the bonding groups. The second criterion led to a number of factors equal to 50, and the factors interpreted as being representative of the haplotypes blocks. This showed the potential of the technique, making it possible to obtain results applicable to any type of population, helping or corroborating the interpretation of genomic studies. The study demonstrated that AF was able to identify patterns of association between markers, identifying subgroups of markers that reflect factor binding groups and also linkage disequilibrium groups.

Abstract: The aim of this study was to obtain estimates of genetic parameters via meta-analysis and mixed models to evaluate the potential of the germplasm from Embrapa Pecuaria Sudeste for integration in breeding programs. Data on the dry matter yield of 77 accessions evaluated in 24 harvests were used. Descriptive analysis was performed for mixed model and meta-analytical estimates. The variances for each parameter were estimated. For the meta-analysis, variances were used as weighting measures, and the fixed and random models were tested. A diagonal structure was considered for the residual variance matrix. Mean dry matter yield ranged from 1019.5 to 2684 kg ha-1. The phenotypic, permanent environmental, and genotypic variances oscillated widely throughout the harvests, as well as heritability. Meta-analytical estimates proved to be an accurate and complementary approach to the mixed model analysis. Both mixed model and meta-analytical estimates indicated the breeding potential of the alfalfa germplasm.

ABSTRACT Genomic selection (GS) emphasizes the simultaneous prediction of the genetic effects of thousands of scattered markers over the genome. Several statistical methodologies have been used in GS for the prediction of genetic merit. In general, such methodologies require certain assumptions about the data, such as the normality of the distribution of phenotypic values. To circumvent the non-normality of phenotypic values, the literature suggests the use of Bayesian Generalized Linear Regression (GBLASSO). Another alternative is the models based on machine learning, represented by methodologies such as Artificial Neural Networks (ANN), Decision Trees (DT) and related possible refinements such as Bagging, Random Forest and Boosting. This study aimed to use DT and its refinements for predicting resistance to orange rust in Arabica coffee. Additionally, DT and its refinements were used to identify the importance of markers related to the characteristic of interest. The results were compared with those from GBLASSO and ANN. Data on coffee rust resistance of 245 Arabica coffee plants genotyped for 137 markers were used. The DT refinements presented equal or inferior values of Apparent Error Rate compared to those obtained by DT, GBLASSO, and ANN. Moreover, DT refinements were able to identify important markers for the characteristic of interest. Out of 14 of the most important markers analyzed in each methodology, 9.3 markers on average were in regions of quantitative trait loci (QTLs) related to resistance to disease listed in the literature.

Resumen El desarrollo de máquinas eficientes para la cosecha de café requiere un conocimiento sólido sobre el comportamiento dinámico de la planta. La transmisibilidad de la vibración es un parámetro del comportamiento dinámico que puede ayudar a comprender este proceso. El objetivo de este estudio fue evaluar la transmisibilidad de vibración promedio en muestras de rama de pedúnculo de fruta de café que contienen frutas inmaduras y maduras. Los experimentos se realizaron utilizando plantas de café Arábica "Catuaí Vermelho". Las muestras se sometieron a tres niveles de frecuencia de vibración, 20, 30 y 40 Hz, inducido a la rama con impacto de varillas rígidas de fibra de vidrio que se mueven a una amplitud constante de 2 mm. Los datos sobre la aceleración se recopilaron utilizando un acelerómetro fijado a la rama. La frecuencia de 20 Hz presentó la máxima transmisibilidad. Las muestras que contenían frutas maduras también presentaron una alta transmisibilidad en comparación con las que contenían frutas inmaduras.

Abstract The development of efficient machines for coffee harvesting requires solid knowledge about the dynamic behavior of the plant. Vibration transmissibility is a parameter on dynamic behavior that may help understand this process. The aim of this study was to evaluate the average vibration transmissibility in coffee fruit-peduncle-branch samples containing unripe and ripe fruits. The experiments were performed using Arabica coffee plants of the cultivar Catuaí Vermelho. The samples were submitted to three vibration frequency levels, 20, 30 and 40 Hz, induced to the branch with impact of rigid fiberglass rods moving at a constant amplitude 2 mm. Data on acceleration were collected using an accelerometer fixed to the branch. The frequency of 20 Hz presented the highest transmissibility. Samples containing ripe fruits also presented high transmissibility when compared to those containing unripe fruits.

Resumo: O objetivo deste trabalho foi avaliar o potencial da inteligência computacional e de variáveis canônicas para estudos de diversidade genética entre genótipos de sorgo (Sorghum bicolor) biomassa. Os experimentos foram realizados no campo experimental da Embrapa Milho e Sorgo, nos municípios de Nova Porteirinha e Sete Lagoas, no estado de Minas Gerais, Brasil. Foram avaliadas as seguintes características: dias para a floração, altura das plantas, produção de biomassa fresca, biomassa seca total e produção de biomassa seca. O estudo da diversidade genética foi realizado por meio da análise de variáveis canônicas. Para o reconhecimento do padrão de organização da diversidade genética, utilizou-se o mapa auto-organizável de Kohonen. O uso de variáveis canônicas e o mapa auto-organizável foram eficientes no estudo de diversidade genética. A utilização de inteligência computacional com mapa auto-organizável é promissora e eficiente para estudos de diversidade genética entre genótipos de sorgo biomassa.

Abstract: The objective of this work was to evaluate the potential of computational intelligence and canonical variables for studies on the genetic diversity between biomass sorghum (Sorghum bicolor) genotypes. The experiments were carried out in the experimental field of Embrapa Milho e Sorgo, in the municipalities of Nova Porteirinha and Sete Lagoas, in the state of Minas Gerais, Brazil. The following traits were evaluated: days to flowering, plant height, fresh biomass yield, total dry biomass, and dry biomass yield. The study of genetic diversity was performed through the analysis of canonical variables. For the recognition of the organization pattern of genetic diversity, Kohonen’s self-organizing map was used. The use of canonical variables and a self-organizing map were efficient for the study of genetic diversity. The application of computational intelligence using a self-organized map is promising and efficient for studies on the genetic diversity between biomass sorghum genotypes.

Resumo: O objetivo deste trabalho foi avaliar o método gráfico de rede de similaridade na classificação de genótipos de arroz (Orzya sativa) irrigado quanto a sua adaptabilidade e estabilidade. Duas medidas estatísticas foram utilizadas para representar a proximidade de comportamento (baseada na correlação de Pearson) ou de valores (baseada na distância de Gower) entre pares de genótipos ou entre genótipo e ambiente. Foram avaliados dados de produtividade de 18 genótipos de arroz irrigado em três locais de Minas Gerais, nas safras de 2012/2013, 2013/2014, 2014/2015 e 2015/2016, em delineamento em blocos ao acaso. Os genótipos foram previamente avaliados quanto à adaptabilidade e à estabilidade pelos métodos de Eberhart & Russell e centroide. As representações gráficas fornecidas pelas redes de similaridade facilitaram o reconhecimento do padrão de interação genótipo x ambiente, o que permitiu superar as dificuldades de interpretação devido à discordância entre os resultados obtidos com os métodos de Eberhart & Russell e centroide. As redes de similaridade facilitam os estudos de interação genótipo x ambiente.

Abstract: The objective of this work was to evaluate the similarity network graphic methodology for the classification of flood-irrigated rice (Orzya sativa) genotypes regarding their adaptability and stability. Two statistical measures were used to represent the proximity of the behavior (based on Pearson’s correlation) or values (based on Gower’s distance) between pairs of genotypes or between genotype and environment. Productivity data of 18 genotypes were evaluated in three locations in the state of Minas Gerais, Brazil, in the harvests of 2012/2013, 2013/2014, 2014/2015, and 2015/2016, in a randomized complete block design. The genotypes were previously assessed for adaptability and stability by the Eberhart & Russell and centroid methods. The graphical representations provided by the similarity networks allowed to better identify the pattern of the genotype x environment interaction, overcoming the interpretation difficulties due to the disagreements between the results obtained by the Eberhart & Russell and centroid methods. The similarity networks improve genotype x environment interaction studies.