ABSTRACT: This study assessed distributions associated with Bayesian nonlinear modeling error in the description of total plant dry matteraccumulation (TDMA) of Allium sativumas a function of days after planting (DAP). According to the DIC criterion, Logistic and Gompertzmodels that use student’s t distribution error exhibited the highest DIC with logistic error distribution. In general, the difference of DIC in all the scenarios was not more than 5.The Bayes factor (BF) criterion showed no difference in the Logistic and Gompertzmodel fit when four distributions are used for the errors, where BF values do not exceed 2. Posterior distributions and the usual estimators of Logistic and Gompertz model parameters were similar even forvaried error distribution. In summary, there was no difference in the use of 4 distributions associated with the modeling error of garlic plant growth by the Bayes factor, whereby the results showed that alternating between error distributions significantly changes the number of Markov Chain Monte Carlo (MCMC) iterations. ABSTRACT TDMA (TDMA DAP. DAP . (DAP) students student s general 5The The 5 (BF errors 2 summary MCMC (MCMC iterations (DAP

RESUMO: O objetivo deste trabalho foi avaliar algumas distribuições associadas ao erro na modelagem não linear bayesiana na descrição do acúmulo de matéria seca total da planta (MSTP) de Allium sativum em função dos dias após o plantio (DAP). Pelo critério DIC os modelos Logístico e Gompertz que utilizam a distribuição do erro t de Student apresentaram a melhor qualidade de ajuste, sendo que o modelo Logístico apresentou o maior DIC com a distribuição de erro Logística. No geral, a diferença de DIC em todos os cenários não apresentou valores superiores a cinco. Pelo critério do Fator de Bayes (FB), não houve diferença no ajuste do modelo Logístico e Gompertz quando se utilizam as quatro distribuições para os erros, sendo que os valores de FB não superaram 2. As distribuições a posteriori e os estimadores usuais dos parâmetros dos modelos Logístico e Gompertz apresentaram semelhanças mesmo variando a distribuição do erro. Em suma não houve diferença na utilização das quatro distribuições associadas ao erro na modelagem do crescimento planta de alho pelo fator de Bayes, sendo que os resultados mostram que alternar entre as distribuições dos erros altera de forma significativa o número de iterações de MCMC. RESUMO MSTP (MSTP DAP. DAP . (DAP) Logística geral cinco FB, , (FB) 2 MCMC (DAP (FB

ABSTRACT. This study evaluated the efficiency of genome-wide selection (GWS) based on regularized quantile regression (RQR) to obtain genomic growth curves based on genomic estimated breeding values (GEBV) of individuals with different probability distributions. The data were simulated and composed of 2,025 individuals from two generations and 435 markers randomly distributed across five chromosomes. The simulated phenotypes presented symmetrical, skewed, positive, and negative distributions. Data were analyzed using RQR considering nine quantiles (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9) and traditional methods of genomic selection (specifically, RR-BLUP, BLASSO, BayesA, and BayesB). In general, RQR-based estimation of the GEBV was efficient-at least for a quantile model, the results obtained were more accurate than those obtained by the other evaluated methodologies. Specifically, in the symmetrical-distribution scenario, the highest accuracy values were obtained for the parameters with the models RQR0.4, RQR0.3, and RQR0.4. For positive skewness, the models RQR0.2, RQR0.3, and RQR0.1 presented higher accuracy values, whereas for negative skewness, the best model was RQR0.9. Finally, the GEBV vectors obtained by RQR facilitated the construction of genomic growth curves at different levels of interest (quantiles), illustrating the weight-age relationship. ABSTRACT genomewide genome wide GWS (GWS (RQR (GEBV distributions 2025 2 025 2,02 43 chromosomes symmetrical skewed 0.1, 01 0 1 (0.1 02 0.2 03 3 0.3 04 4 0.4 05 5 0.5 06 6 0.6 07 7 0.7 08 8 0.8 0.9 09 9 specifically, specifically (specifically RRBLUP, RRBLUP RR BLUP, BLUP RR-BLUP BLASSO BayesA BayesB. BayesB . BayesB) general RQRbased efficientat efficient methodologies Specifically symmetricaldistribution distribution scenario RQR04 RQR0 RQR0.4 RQR03 RQR0.3 skewness RQR02 RQR0.2 RQR01 RQR0. RQR09 RQR0.9 Finally quantiles, , (quantiles) weightage weight age relationship 202 2,0 0.1 (0. 0. (quantiles 20 2, (0 (

RESUMO: Diante da importância de descrever o acúmulo de matéria seca total em acessos de alho e a vantagem dos Modelos Não Lineares Mistos (MNLM) nesse processo, o presente trabalho teve como objetivo comparar quatro equações não lineares (Gompertz, Logístico, Richards e von Bertalanffy) no ajuste do acúmulo de matéria seca total por planta de 30 acessos de alho. O objetivo também foi identificar os melhores acessos de acordo com cada parâmetro de crescimento, estimando os efeitos aleatórios em torno da média através do melhor entre os modelos. A análise foi realizada com o uso do software R. O melhor modelo foi o Logístico segundo os critérios utilizados para comparação (AIC, BIC, R a j . 2, EQM e EAM), apresentando estimativas mais próximas dos valores reais observados. De acordo com os efeitos aleatórios estimados por este modelo, que representam desvios da média, os acessos que apresentaram maior peso assintótico foram 4505, 4826 e 4500, enquanto os acessos 4826, 4837 e 4491 demoraram mais para atingir o ponto de inflexão da curva. A abordagem NLME utilizou apenas um ajuste por equação para obter informações sobre todos os indivíduos da amostra, ajustando eficientemente a matéria seca total acumulada e identificando os melhores acessos de acordo com os efeitos aleatórios estimados de seus parâmetros. RESUMO MNLM (MNLM processo Gompertz, Gompertz (Gompertz Bertalanffy 3 crescimento modelos AIC, AIC (AIC BIC 2 EAM, EAM , EAM) observados 4505 482 4500 483 449 curva amostra parâmetros 450 48 44 45 4

ABSTRACT: Given the importance of describing the accumulation of total dry matter in garlic accessions and the advantage of Nonlinear Mixed Effect Models (NLME) in this process, the present work research compared four nonlinear equations (Gompertz, Logistic, Richards, and von Bertalanffy) in the fit of accumulation of total dry matter per plant of 30 garlic accessions. The objective was also to identify the best accessions according to each growth parameter by estimating the random effects around the mean through the best among the models. The analysis was carried out using the R software. The best model was the Logistic according to the criteria used for comparison (AIC, BIC, R a j . 2, MSE and MAE), presenting estimates closer to the actual observed values. According to the random effects estimated by this model, which represent deviations from the mean, the accessions that showed the highest asymptotic weight were 4505, 4826 and 4500, while accessions 4826, 4837 and 4491 took longer to reach the inflection point of the curve. The NLME approach used one fit per equation to obtain information on all individuals in the sample, efficiently adjusting the accumulated total dry matter and identifying the best accessions according to the estimated random effects of its parameters. ABSTRACT (NLME process Gompertz, Gompertz (Gompertz Richards Bertalanffy 3 models software AIC, AIC (AIC BIC 2 MAE, MAE , MAE) values 4505 482 4500 483 449 curve sample parameters 450 48 44 45 4

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 Thus floodirrigated flood irrigated regression inputs flowering 1

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. ABSTRACT (QRF nonparametric non parametric RF (RF QR. QR . (QR) Specifically nonlinear linear functions mean epistasis dominance. dominance dominance) addition GBLUP. GBLUP G BLUP. BLUP F 1000 1 000 1,00 4010 4 010 4,01 markers Besides nonadditive effects Quantitative loci 120 03 0 3 0.3 05 5 0.5 08 8 0.8 validation 5fold fold crossvalidation cross used calculated effect effects. effects) Finally compared scenarios (QR 100 00 1,0 401 01 4,0 12 0. 10 1, 40 4,

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. RESUMO (QRF paramétrica RF (RF QR. QR . (QR) Especificamente lineares média epistasia dominância. dominância dominância) Adicionalmente GBLUP. GBLUP G BLUP. BLUP F 1000 1 000 1.00 4010 4 010 4.01 SNP disso Quantitative loci 12 03 0 3 0,3 05 5 0, 08 8 0,8 5fold. 5fold fold fold. 5-fold propostos epistático dominante. dominante dominante) fim comparado cenários complexas (QR 100 00 1.0 401 01 4.0 10 1. 40 4.

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 Although maize is one of the main crops in the Northeast region, yield is still considered low when compared to other regions. One of the main solutions to increasing yield is the selection of cultivars adapted to the conditions of the Northeast region. Thus, the present study aims to use the Bayesian segmented regression model to evaluate the adaptability and stability of maize. The experiment was set up in a randomized block design with two repetitions, where 25 maize hybrids were evaluated in different states. Initially, the analysis of variance was performed. Then, the Bayesian approach of the segmented regression method was used to select the hybrids regarding adaptability and stability. There was a difference between the genotypes indicated using the a priori distribution and those indicated by the minimally informative a priori distribution. Hybrids 20A55HX, 2B433HX, 2B512HX, and P2830H were considered ideal for the Northeast region. region regions Thus repetitions 2 states Initially performed Then 20A55HX AHX A HX 2B433HX BHX B 2B512HX PH P H

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.

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 Bayesian approaches applied in association studies select regions of single-nucleotide polymorphisms, indicating genes with important effects. The Bayesian methods differ in terms of the distribution assumed for the marker effects. Here, we used the window posterior probability of association to detect potential regions. The present study evaluated the efficiency of these methods in identifying regions located close to genes. Data were simulated in six scenarios. Considering the lack of dominance, BayesA was more efficient in the scenario with three QTLs. For scenarios with 10 or 100 QTLs, BayesCπ and BayesDπ were more efficient according to the false positive rate and detection power. Considering the presence of dominance, all methods were similar in the scenario with three QTLs, except in terms of accuracy. BayesDπ was superior in the scenario with 10 QTLs, while BRR was more efficient in the scenario with 100 QTLs.

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: 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.

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.

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.