Resumo -O objetivo deste trabalho foi selecionar, sob a perspectiva bayesiana, genótipos de feijão-caupi (Vigna unguiculata) que reúnam alta adaptabilidade e estabilidade fenotípicas, no Estado do Mato Grosso do Sul. Foram utilizados dados de quatro experimentos, conduzidos em delineamento de blocos ao acaso, em que a produtividade de grãos de 20 genótipos de feijão-caupi semiprostrado foi avaliada. Para representar as distribuições a priori pouco informativas, utilizaram-se distribuições de probabilidade com grande variância; e, para representar distribuições a priori informativas, adotou-se o conceito de metanálise, com uso de informações de trabalhos anteriores. A comparação entre as distribuições a priori foi realizada por meio do fator de Bayes. A abordagem bayesiana proporciona maior acurácia na seleção de genótipos de feijão-caupi semiprostrado, com elevadas adaptabilidade e estabilidade fenotípicas avaliadas por meio da metodologia de Eberhart & Russell. Com base nas prioris informativas, os genótipos MNC99-507G-4, TE97-309G-24, MNC99-542F-7 e BR 17-Gurguéia são classificados como de alta adaptabilidade a ambientes favoráveis. Já os genótipos TE96-290-12G, MNC99-510F-16, MNC99-508G-1, MNC99-541F-21, MNC99-542F-5 e MNC99-547F-2 apresentam alta adaptabilidade a ambientes desfavoráveis.Termos para indexação: Vigna unguiculata, fator de Bayes, interação genótipo x ambiente, metanálise, priori informativa. Bayesian perspective in the selection of cowpea genotypes in trials of value for cultivation and useAbstract -The objective of this work was to select, under the Bayesian perspective, cowpea (Vigna unguiculata) genotypes that meet high phenotypic adaptability and stability, in the state of Mato Grosso do Sul, Brazil. Data from four experiments, conducted in a randomized complete block design, were used, in which grain yield of 20 semiprostrate cowpea genotypes was evaluated. To represent non-informative prior distributions, probability distributions with high variance were used; and, to represent informative prior distributions, a metanalysis concept was adopted using information from previous studies. The comparison between the prior distributions was done using the Bayes factor. The Bayesian approach provides greater accuracy in the selection of semiprostrate cowpea genotypes, with high phenotypic adaptability and stability assessed by the Eberhart & Russell methodology. Based on the informative priors, the MNC99-507G-4, TE97-309G-24, MNC99-542F-7, and BR 17-Gurguéia genotypes are classified as with high adaptability to favorable environments. The TE96-290-12G, MNC99-510F-16, MNC99-508G-1, MNC99-541F-21, MNC99-542F-5, and MNC99-547F-2 genotypes have high adaptability to unfavorable environments.Index terms: Vigna unguiculata, Bayes factor, genotype x environment interaction, metanalysis, informative prior. IntroduçãoO feijão-caupi [Vigna unguiculata (L.) Walp.] é uma das fontes alimentares mais importantes para regiões tropicais e subtropicais do planeta. Atualmente, o Brasil é o terceiro maior produtor m...

Resumo -O objetivo deste trabalho foi verificar a concordância entre as redes neurais artificiais (RNAs) e o método de Eberhart & Russel na identificação de genótipos de feijão-caupi (Vigna unguiculata) com alta adaptabilidade e estabilidade fenotípicas. Utilizou-se o delineamento experimental de blocos ao acaso com quatro repetições. Os tratamentos consistiram de 18 linhagens experimentais e duas cultivares de feijão-caupi. Foram conduzidos quatro ensaios de valor de cultivo e uso nos municípios de Aquidauana, Chapadão do Sul e Dourados, no estado do Mato Grosso do Sul. Os dados de produtividade de grãos foram submetidos às análises de variância individual e conjunta. Em seguida, os dados foram submetidos às análises de adaptabilidade e estabilidade por meio dos métodos de Eberhart & Russell e de RNAs. Houve elevada concordância entre os métodos avaliados quanto à discriminação da adaptabilidade fenotípica dos genótipos de feijão-caupi semiprostrado, o que indica que as RNAs podem ser utilizadas em programas de melhoramento genético. Em ambos os métodos avaliados, os genótipos BRS Xiquexique, TE97-304G-12 e MNC99-542F-5 são recomendados para ambientes desfavoráveis, gerais e favoráveis, respectivamente, por apresentarem produtividade de grãos acima da média geral dos ambientes e alta estabilidade fenotípica.Termos para indexação: Vigna unguiculata, inteligência artificial, interação genótipos x ambientes.Artificial neural networks to identify semi-prostrate cowpea genotypes with high phenotypic adaptability and stabilityAbstract -The objective of this work was to verify the agreement between artificial neural networks (ANNs) and the Eberhart & Russel method in identifying cowpea (Vigna unguiculata) genotypes with high phenotypic adaptability and stability. The experimental design was in a randomized complete block with four replicates. The treatments consisted of 18 experimental lines and two cowpea cultivars. Four value for cultivation and use trials were conducted in the municipalities of Aquidauana, Chapadão do Sul, and Dourados, in the state of Mato Grosso do Sul, Brazil. Grain yield data were subjected to individual and joint variance analyses. Then, the data were subjected to adaptability and stability analyses through the methods of Eberhart & Russell and ANNs. There was a high agreement between the methods evaluated for discrimination of the phenotypic adaptability of semi-prostrate cowpea genotypes, indicating that ANNs can be used in breeding programs. In both evaluated methods, the BRS Xiquexique, TE97-304G-12, and MNC99-542F-5 genotypes are recommended for harsh, general, and favorable environments, respectively, for having grain yield above the overall average of environments and high phenotypic stability.Index terms: Vigna unguiculata, artificial intelligence, genotypes x environments interaction. IntroduçãoO feijão-caupi [Vigna unguiculata (L.) Walp.] é atualmente cultivado em três regiões do Brasil, o que torna importante investigar a magnitude da interação genótipos x ambientes para a escolha d...

Gene expression time series (GETS) analysis aims to characterize sets of genes according to their longitudinal patterns of expression. Due to the large number of genes evaluated in GETS analysis, an useful strategy to summarize biological functional processes and regulatory mechanisms is through clustering of genes that present similar expression pattern over time. Traditional cluster methods usually ignore the challenges in GETS, such as the lack of data normality and small number of temporal observations. Independent Component Analysis (ICA) is a statistical procedure that uses a transformation to convert raw time series data into sets of values of independent variables, which can be used for cluster analysis to identify sets of genes with similar temporal expression patterns. ICA allows clustering small series of distribution-free data while accounting for the dependence between subsequent time-points. Using temporal simulated and real (four libraries of two pig breeds at 21, 40, 70 and 90 days of gestation) RNA-seq data set we present a methodology (ICAclust) that jointly considers independent components analysis (ICA) and a hierarchical method for clustering GETS. We compare ICAclust results with those obtained for K-means clustering. ICAclust presented, on average, an absolute gain of 5.15% over the best K-means scenario. Considering the worst scenario for K-means, the gain was of 84.85%, when compared with the best ICAclust result. For the real data set, genes were grouped into six distinct clusters with 89, 51, 153, 67, 40, and 58 genes each, respectively. In general, it can be observed that the 6 clusters presented very distinct expression patterns. Overall, the proposed two-step clustering method (ICAclust) performed well compared to K-means, a traditional method used for cluster analysis of temporal gene expression data. In ICAclust, genes with similar expression pattern over time were clustered together.

Resumo -O objetivo deste trabalho foi desenvolver e validar uma metodologia de análise da adaptabilidade e da estabilidade fenotípica baseada em regressão quantílica (RQ). Para tanto, foram simulados valores fenotípicos com distribuição simétrica e com distribuição assimétrica à direita e à esquerda, com ou sem a presença de "outliers". A metodologia proposta foi aplicada a um conjunto de dados provenientes de um experimento com 92 genótipos de alfafa (Medicago sativa), avaliados em 20 ambientes, e comparada às metodologias de Eberhart & Russell e de regressão não paramétrica. A metodologia da RQ proporcionou resultados iguais ou superiores aos obtidos com as metodologias alternativas avaliadas. No entanto, a ocorrência de resultados discordantes entre as metodologias evidencia a importância de se avaliar a simetria na distribuição dos valores fenotípicos. Para distribuições simétricas, na presença de "outliers", deve-se utilizar a RQ com valor de quantil estimado (t) em 0,50; na ausência de "outliers", pode-se utilizar tanto a metodologia de Eberhart & Russell quanto a RQ (t = 0,50). Para distribuições assimétricas, indica-se o uso da RQ com t = 0,25, para assimetria à direita, e com t = 0,75, para assimetria à esquerda, independentemente da presença de "outliers".Termos para indexação: Medicago sativa, distribuição assimétrica, interação genótipo x ambiente, melhoramento vegetal, outliers, regressão não paramétrica. Methodology for analysis of adaptability and stability using quantile regressionAbstract -The objective of this work was to develop and validate a methodology for analyzing phenotypic adaptability and stability based on quantile regression (QR). For this, phenotypic values were simulated with symmetrical distribution and with asymmetrical distribution to the right and to the left, with or without outliers. The proposed methodology was applied to a data set from an experiment with 92 alfalfa (Medicago sativa) genotypes, evaluated in 20 environments, and compared with the methodologies of Eberhart & Russell and nonparametric regression. The QR methodology provided equal or superior results, compared to the evaluated alternative methodologies. However, the occurrence of disagreeing results between methodologies evidences the importance of evaluating symmetry in the distribution of phenotypic values. For symmetric distributions with outliers, QR should be used with estimated quantile value (t) of 0.50; in the absence of outliers, both the methodology of Eberhart & Russel and QR (t = 0.50) may be used. For asymmetric distributions, the use of RQ with t = 0.25 is suggested for asymmetry to the right, and with t = 0.75 for asymmetry to the left, regardless of the presence of outliers.

BackgroundGenomic growth curves are generally defined only in terms of population mean; an alternative approach that has not yet been exploited in genomic analyses of growth curves is the Quantile Regression (QR). This methodology allows for the estimation of marker effects at different levels of the variable of interest. We aimed to propose and evaluate a regularized quantile regression for SNP marker effect estimation of pig growth curves, as well as to identify the chromosome regions of the most relevant markers and to estimate the genetic individual weight trajectory over time (genomic growth curve) under different quantiles (levels).ResultsThe regularized quantile regression (RQR) enabled the discovery, at different levels of interest (quantiles), of the most relevant markers allowing for the identification of QTL regions. We found the same relevant markers simultaneously affecting different growth curve parameters (mature weight and maturity rate): two (ALGA0096701 and ALGA0029483) for RQR(0.2), one (ALGA0096701) for RQR(0.5), and one (ALGA0003761) for RQR(0.8). Three average genomic growth curves were obtained and the behavior was explained by the curve in quantile 0.2, which differed from the others.ConclusionsRQR allowed for the construction of genomic growth curves, which is the key to identifying and selecting the most desirable animals for breeding purposes. Furthermore, the proposed model enabled us to find, at different levels of interest (quantiles), the most relevant markers for each trait (growth curve parameter estimates) and their respective chromosomal positions (identification of new QTL regions for growth curves in pigs). These markers can be exploited under the context of marker assisted selection while aiming to change the shape of pig growth curves.

ABSTRACT. Genomic selection (GS) is a variant of marker-assisted selection, in which genetic markers covering the whole genome predict individual genetic merits for breeding. GS increases the accuracy of breeding values (BV) prediction. Although a variety of statistical models have been proposed to estimate BV in GS, few methodologies have examined statistical challenges based on non-normal phenotypic distributions, e.g., skewed distributions. Traditional GS models estimate changes in the phenotype distribution mean, i.e., the function is defined for the expected value of trait-conditional on markers, E(Y|X). We proposed an approach based on regularized quantile regression (RQR) for GS to improve the estimation of marker effects and the consequent genomic estimated BV (GEBV). The RQR model is based on conditional quantiles, Q t (Y|X), enabling models that fit all portions of a trait probability distribution. This allows RQR to choose one quantile function that "best" represents the relationship between the dependent and independent variables. Data were simulated for 1000 individuals. The genome included 1500 markers; most had a small effect and only a few markers with a sizable effect were simulated. We evaluated three scenarios according to symmetrical, positively, and negatively skewed distributions. Analyses were performed using Bayesian LASSO (BLASSO) and RQR considering three quantiles (0.25, 0.50, and 0.75). The use of RQR to estimate GEBV was efficient; the RQR method achieved better results than BLASSO, at least for one quantile model fit for all evaluated scenarios. The gains in relation to BLASSO were 86.28 and 55.70% for positively and negatively skewed distributions, respectively.

ABSTRACT. This study aimed to verify that a Bayesian approach could be used for the selection of upright cowpea genotypes with high adaptability and phenotypic stability, and the study also evaluated the efficiency of using informative and minimally informative a priori distributions. Six trials were conducted in randomized blocks, and the grain yield of 17 upright cowpea genotypes was assessed. To represent the minimally informative a priori distributions, a probability distribution with high variance was used, and a meta-analysis concept was adopted to represent the informative a priori distributions. Bayes factors were used to conduct comparisons between the a priori distributions. The Bayesian approach was effective for selection of upright cowpea genotypes with high adaptability and phenotypic stability using the Eberhart and Russell method. Bayes factors indicated that the use of informative a priori distributions provided more accurate results than minimally informative a priori distributions.

ABSTRACT. Artificial neural networks have been used for various purposes in plant breeding, including use in the investigation of genotype x environment interactions. The aim of this study was to use artificial neural networks in the selection of common bean genotypes with high phenotypic adaptability and stability, and to verify their consistency with the Eberhart and Russell method. Six trials were conducted using 13 genotypes of common bean between 2002 and 2006 in the municipalities of Aquidauana and Dourados. The experimental design was a randomized block with three replicates. Grain yield data were submitted to individual and joint variance analyses. The data were then submitted to analysis of adaptability and stability through the Eberhart and Russell and artificial neural network methods. There was high concordance between the methodologies evaluated for discrimination of phenotypic adaptability of common bean genotypes, indicating that artificial neural networks can be used in breeding programs. Based on both approaches, the genotypes Aporé, Rudá, and CNFv 8025 are recommended for use in unfavorable, general and favorable environments, respectively by the grain yield above the overall average of environments and high phenotypic stability.