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

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

ABSTRACT. 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 Multitrait Multi trait multienvironment multi environment (MTME structure adaptability so 21 3 environments age (DBH PP (PP measured criterion (HMRPGV accuracy addition genotypebyenvironment genotype complex productivity Thus 2

Abstract This study aimed to apply selection indexes in situations in which F2 populations and their parents are evaluated simultaneously in field trials to predict population genotypic values and selecting the best populations. Fifteen F2 soybean populations were evaluated for number of days to flowering and to maturity and grain yield. The data was analyzed using restricted maximum likelihood/best linear unbiased prediction (REML/BLUP) to obtain genotypic effects, variance components and accuracies. Four selection methods were compared: genotypic values of the F2 populations (gF2), combined index with the mean genotypic value of parents and F2 population (Ia) and two indexes that add (to gF2 and to Ia) and consider genetic variability within populations (Ib and Ic). The index Ia presented a result similar to that obtained with the gF2 selection method. Selection indexes (Ib and Ic) based on several sources of information were more efficient than selection based on gF2 values only. F yield likelihoodbest likelihood REML/BLUP REMLBLUP REML BLUP (REML/BLUP effects accuracies compared gF2, gF , (gF2) (Ia Ib Ic. Ic . method only (gF2 (gF

Abstract Genetic selection efficiency is measured by accuracy. Model selection relies on hypothesis testing with effectiveness given by statistical significance (p-value). Estimates of selection accuracy are based on variance parameters and precision. Model selection considers the amount of genetic variability and significance of effects. Questions arise as to which one to use: accuracy or p-value? We show there is a link between the two and both may be used. We derive equations for accuracy in multi-environment trials and determine numbers of repetitions and environments to reach accuracy. We propose a new methodology for accuracy classification based on p-values. This enables a better understanding of the level of accuracy being accepted when certain p-value is used. Accuracy of 90% is associated with p-value of 2%. Use of p-values up to 20% (accuracies above 50%) are acceptable to verify significance of genetic effects. Sample sizes for desired p-values are found via accuracy values.

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 Fisher’s infinitesimal model is traditionally used in quantitative genetics and genomic selection, and it attributes most genetic variance to additive variance. Recently, the dominance maximization model was proposed and it prioritizes the dominance variance based on alternative parameterizations. In this model, the additive effects at the locus level are introduced into the model after the dominance variance is maximized. In this study, the new parameterizations of additive and dominance effects on quantitative genetics and genomic selection were evaluated and compared with the parameterizations traditionally applied using the genomic best linear unbiased prediction method. As the parametric relative magnitude of the additive and dominance effects vary with allelic frequencies of populations, we considered different minor allele frequencies to compare the relative magnitudes. We also proposed and evaluated two indices that combine the additive and dominance variances estimated by both models. The dominance maximization model, along with the two indices, offers alternatives to improve the estimates of additive and dominance variances and their respective proportions and can be successfully used in genetic evaluation.

RESUMO A técnica de enxertia de topo pode possibilitar o florescimento precoce e, consequentemente, acelerar a autopolinização no melhoramento de Eucalyptus, reduzindo o período de cada geração. O objetivo deste estudo é estabelecer uma metodologia para enxertia de topo, aplicando o regulador de crescimento paclobutrazol em genótipos de Eucalyptus autopolinizados, para induzir o florescimento precoce e acelerar estratégias que envolvam a produção de linhagens. Foram realizados 448 enxertos de topo de sete genótipos (três híbridos de Eucalyptus urophylla × Eucalyptus grandis, um de Eucalyptus urophylla e três de Eucalyptus grandis) em dois períodos do ano: julho e outubro. As amostras de enxertia de topo foram avaliadas quanto à indução floral e o desenvolvimento do enxerto em intervalos de três meses. Foi realizado um teste t com nível de significância de 5% para o erro tipo I para comparar a relevância da aplicação de paclobutrazol e um modelo fixo também foi usado para analisar a significância entre os tratamentos. A floração mais rápida foi observada após três meses de aplicação da metodologia de enxertia. Após dois anos, as enxertias de topo realizadas em outubro apresentaram maior produção de botões florais e frutos. A enxertia de topo afetou a indução de flores de Eucalyptus autopolinizadas devido a ter produzido botões florais suficientes para realizar o próximo ciclo de autopolinização em alguns genótipos. A eficácia das enxertias de topo autopolinizadas variou com o genótipo utilizado como copa. O paclobutrazol melhorou a floração das amostras de enxerto de topo. A metodologia estabelecida neste trabalho permite acelerar as estratégias de autopolinização em Eucalyptus, que é uma cultura industrial globalmente importante.

ABSTRACT The top grafting technique can make early flowering possible and consequently accelerate self-pollination in Eucalyptus breeding, reducing the period of each generation. This study aims to establish a methodology to top graft by applying the growth regulator paclobutrazol in self-pollinated Eucalyptus genotypes to induce early flowering and accelerate inbred line strategies. A total of 448 top grafts of seven genotypes (three Eucalyptus urophylla × Eucalyptus grandis hybrids, one Eucalyptus urophylla, and three Eucalyptus grandis) were performed in two periods of the year: July and October. The top grafting samples were evaluated concerning flower induction and graft development at three-month intervals. A t-test was performed with a 5% significance level for type I error to compare the relevance of paclobutrazol application. A fixed model was also used to analyze the significance of the treatments. The fastest blooming occurred after three months of applying the graft methodology. After two years, the top graftings performed in October presented higher flower bud and fruit production. The top grafting affected the induction of self-pollinated Eucalyptus flowers with enough flower buds produced to follow the next cycle of self-pollination in some genotypes. The effectiveness of self-pollinated top graftings varied with the genotype used as the scion. The paclobutrazol improved the flowering of the top grafting samples. The methodology established in this work allows accelerating self-pollination strategies in the globally important industrial crop Eucalyptus.

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

ABSTRACT: The genotype × environment (G×E) interaction plays an essential role in phenotypic expression and can lead to difficulties in genetic selection. Thus, the present study aimed to estimate genetic parameters and to compare different selection strategies in the context of mixed models for soybean breeding. For this, data referring to the evaluation of 30 genotypes in 10 environments, regarding the grain yield trait, were used. The variance components were estimated through restricted maximum likelihood (REML) and genotypic values were predicted through best linear unbiased prediction (BLUP). Significant effects of genotypes and G×E interaction were detected by the likelihood ratio test (LRT). Low genotypic correlation was obtained across environments, indicating complex G×E interaction. The selective accuracy was very high, indicating high reliability. Our results showed that the most productive soybean genotypes have high adaptability and stability.

Abstract The aims of this study were to estimate genetic parameters, predict genotypic values, and analyze the genotypic divergence in S0 and S1 peach trees evaluated in a subtropical environment by the mixed model methodology. For this, twenty-two clones were evaluated for plant and fruit traits. Genotypic variance among clones was significant. The individual broad-sense heritabilities ranged from 0.11 to 0.84, and the individual repeatability coefficients ranged from 0.15 to 0.89. The genotypic coefficients of variation were higher than 10% for most of the traits. Clustering based on plant and fruit traits led to the formation of two and five mutually exclusive groups, respectively. Multivariate analysis of principal components indicated that some traits could be excluded from genetic evaluation. Considering the yield trait and the selection of five clones, predicted gain from selection was 70%, which shows the possibility of considerable genetic progress from clonal selection in peach trees.

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

Resumo: O objetivo deste trabalho foi selecionar genótipos superiores de laranjeira-doce (Citrus sinensis) com maior potencial produtivo com base em dados de oito safras, com uso da metodologia “residual or restricted maximum likelihood/best linear unbiased prediction” (REML/BLUP). O experimento foi realizado de 2002 a 2008 e em 2010, no município de Rio Branco, no estado do Acre, Brasil. Análises de deviance foram realizadas para testar a significância dos componentes da variância de acordo com os efeitos aleatórios do modelo utilizado, e os parâmetros foram estimados a partir das variâncias genotípicas e fenotípicas individuais. Foi adotada uma intensidade de seleção de 20% em relação à seleção genotípica, ou seja, apenas os melhores 11 dos 55 genótipos testados foram selecionados. As estimativas dos parâmetros genéticos mostram a existência de variabilidade genética e o potencial de seleção dos genótipos de laranjeira-doce estudados. A correlação genotípica entre as safras é de baixa magnitude, exceto para a variável massa média dos frutos, e, como reflexo, há uma mudança na ordenação dos genótipos. Os genótipos 5, 48, 19, 14 e 47 se destacam como os mais produtivos e, portanto, são os mais adequados para fins de seleção. Os genótipos 14 e 47 apresentam desempenho superior para o conjunto de caracteres avaliados.

Abstract: The objective of this work was to select superior sweet orange (Citrus sinensis) genotypes with higher yield potential based on data from eight harvests, using the residual or restricted maximum likelihood/best linear unbiased prediction (REML/BLUP) methodology. The experiment was carried out from 2002 to 2008 and in 2010 in the municipality of Rio Branco, in the state of Acre, Brazil. Analyzes of deviance were performed to test the significance of the components of variance according to the random effects of the used model, and parameters were estimated from individual genotypic and phenotypic variances. A selection intensity of 20% was adopted regarding genotypic selection, i.e., only the best 11 of the 55 genotypes tested were selected. The estimates of the genetic parameters show the existence of genetic variability and the selection potential of the studied sweet orange genotypes. The genotypic correlation between harvests is of low magnitude, except for the variable average fruit mass, and, as a reflex, there is a change in the ordering of the genotypes. Genotypes 5, 48, 19, 14, and 47 stand out as being the most productive, and, therefore, are the most suitable for selection purposes. Genotypes 14 and 47 show superior performance for the character set evaluated.

ABSTRACT An accurate, efficient and informative statistical method for analyses of genotype × environment (G × E) interactions is a key requirement for progress in any breeding program. Thus, the objective of this study was to quantify individual variation in reaction norms using random regression models fitted through Legendre polynomials in eucalyptus (Eucalyptus spp.) breeding. To this end, a data set with 215 eucalyptus clones of different species and hybrids evaluated in four environments for diameter at breast height (DBH) and Pilodyn penetration (PP) was used. Variance components were estimated by restricted maximum likelihood, and genetic values were predicted by best linear unbiased prediction. The best-fitted model for DBH and PP was indicated by the Akaike information criterion, and the significance of the genotype effects was tested using the likelihood ratio test. Genetic variability between eucalyptus clones and very high accuracies ( r g ^ g ≥ 0 . 90) were detected for both traits. Reaction norms and eigenfunctions generated genetic insights into G × E interactions. This is the first study that quantified individual variation in reaction norms using random regression models fitted through Legendre polynomials in eucalyptus breeding and demonstrated the great potential of this technique.

ABSTRACT Jatropha curcas L. is a perennial plant with great potential for biodiesel production. Thus, the aim of this study was to select J. curcas genotypes for bioenergy purpose considering multitrait, multiharvest and effective population size. To this end, a data set with 70 J. curcas families, obtained through controlled crosses, evaluated in a randomized block design, with six replications, three plants per plot, spaced at 4 × 2 m was used. The following traits were evaluated: plant height in the 2014 and 2015 crop seasons; canopy projection in the row (2015 crop season); canopy projection between rows (2015 crop season); and grain yield (2015, 2016, and 2017 harvests). The mixed model methodology was used to estimate the variance components and to predict the genetic values. Superior genotypes were selected through Multitrait index based on factor analysis and genotype-ideotype distance (FAI-BLUP index), considering the effective population size. According to this index, 98% of all additive genetic variability were summarized in three factors. By adopting the selection intensity that allows maintaining the effective population size equal to 30 (i.e., selection of 214 individuals), the predicted gains were 15.56, 21.75, 4.16, and 5.37% for the traits grain yield in the 2015 and 2016 harvests, canopy projection in the row, and canopy projection between rows in the 2015 crop season, respectively. Thus, the results suggest that the FAI-BLUP index can be successfully used in J. curcas breeding.

Resumo Mais de 95% da produção brasileira de castanha-da-amazônia é oriunda da coleta extrativista sendo poucos os plantios para produção comercial. Buscando contribuir com informações básicas para o melhoramento genético da castanheira, este estudo teve por objetivos: estimar os coeficientes de repetibilidade para o número de frutos (NFP); determinar o número adequado de medições para uma eficiente seleção de matrizes; e, selecionar castanheiras promissoras em dois castanhais nativos, no Estado do Acre. O estudo foi realizado em parcelas permanentes no Filipinas (Resex Chico Mendes, Epitaciolândia-AC) e Cachoeira (PAE Chico Mendes, Xapuri-AC). O número de frutos por planta (NFP) foi avaliado em 140 castanheiras no Filipinas, no período de 2002 a 2014 (13 anos), enquanto no Cachoeira foram 175 castanheiras de 2009 a 2014 (seis anos). As análises genético-estatísticas foram feitas com base na metodologia de modelos mistos, utilizando-se o software Selegen-REML/BLUP, Modelo 63. Foram selecionadas 20 matrizes, sendo 08 no Filipinas e 12 no Cachoeira. Em ambos os castanhais, a variância fenotípica permanente (Vfp) representou a maior porcentagem da variância fenotípica individual (Vf). O coeficiente de repetibilidade foi considerado moderado para o Cachoeira e alto para o Filipinas. Considerando um coeficiente de determinação de 90%, seriam necessários sete anos de avaliação do NFP para o Cachoeira e seis anos para o Filipinas. O banco de dados existentes para a produção de frutos das castanheiras é suficiente para se realizar a seleção de matrizes com alta produção de frutos. Com base nos valores estimados espera-se que a nova população apresente uma produção média de 465,3 frutos.arv-1, indicando um ganho na produção de frutos cerca de 2,4 vezes para o Cachoeira e 4,2 para o Filipinas.

Abstract More than 95% of Brazil nut production in Brazil comes from the extractive collection, with few plantations for commercial production. To contribute with Brazil nut tree genetic improvement, this study aimed to estimate number of fruits (NFP) repeatability coefficients; determine the appropriate number of measurements for efficient selection; and select Brazil nut promising trees from two Brazil nut stands in the state of Acre. The study was carried out in permanent plots in Filipinas (Resex Chico Mendes, Epitaciolândia-AC) and Cachoeira (PAE Chico Mendes, Xapuri-AC). The number of fruits per plant (NFP) was estimated at 140 Brazil nut trees from 2002 to 2014 (13 years), while in Cachoeira there were 175 Brazil nut trees from 2009 to 2014 (six years). Genetic-statistical analyzes were performed based on the mixed model methodology, using the Selegen-REML/BLUP Model 63. Twenty matrices were selected, 08 in Filipinas and 12 in Cachoeira. In both Brazil nuts stands, the permanent phenotypic variance (Vfp) represented the largest percentage of the individual phenotypic variance (Vf). The repeatability coefficient was considered moderate for Cachoeira and high for Filipinas. Considering a 90% coefficient of determination, it would take seven years of NFP assessment for Cachoeira and six years for Filipinas. The existing database for the Brazil nut production is sufficient to make selection for matrices with high fruit production. Based on the estimated values we expect the new population to have an average yield of 465.3 fruits.arv-1, indicating a gain in fruit production of about 2.4 times for Cachoeira and 4.2 for Filipinas.

Resumo Este trabalho teve como objetivos estimar parâmetros genéticos de procedências e progênies de polinização livre de taxi-branco e selecionar genótipos superiores quanto ao crescimento inicial em campo. O experimento foi instalado em 2015, no Campo experimental Serra da Prata, pertencente à Embrapa Roraima e localizado no Município de Mucajaí - RR. O delineamento experimental utilizado foi em blocos ao acaso, com 28 progênies provenientes de três procedências e 20 repetições, sendo cada parcela experimental constituída por uma planta. Foram avaliados aos 6, 12 e 18 meses após o plantio, a porcentagem de sobrevivência, a altura da planta (ALT) e o diâmetro do caule a 10 cm do solo (DC) ou o diâmetro à altura do peito (DAP). As análises genético-estatísticas foram realizadas por meio do procedimento REML/BLUP, com análise de deviance, obtenção das estimativas dos parâmetros genéticos e predição dos valores genéticos nas diferentes idades. A sobrevivência geral variou de 50,68% a 62,10% aos 18 e aos 6 meses, respectivamente. As únicas diferenças significativas observadas foram entre progênies, para ALT e DC, aos seis meses. Com exceção do DAP avaliado aos 18 meses, as demais estimativas de herdabilidade em nível individual no sentido restrito foram moderadas, sendo estas inferiores às estimativas da herdabilidade da média de progênies. Os ganhos com a seleção de progênies e indivíduos foram de baixos a moderados e variaram entre as idades avaliadas, sendo decrescentes com o aumento da idade das plantas.

Abstract This study aimed to estimate the genetic parameters of open-pollinated Tachigali vulgaris provenances and progenies and select superior genotypes for initial growth in the field. The experiment was conducted in Campo experimental Serra da Prata which belongs to Embrapa Roraima and is located in the municipality of Mucajaí - RR. The experimental design used was randomized blocks with 28 progenies from three provenances and 20 repetitions. Each experimental plot consisted of a single plant. At 6, 12 and 18 months after planting, the survival rate (%), the height of the plant (ALT; m), the diameter of the stem 10 cm above ground (DC; mm) or the diameter at breast height (DAP: m) were evaluated. The genetic-statistical analyses were performed using the REML/BLUP procedure, with analysis of deviance, estimation of genetic parameters and prediction of genetic values at the different stages. The overall survival rate varied from 50.68% to 62.10% at 18 months and 6 months, respectively. The only significant differences were between progenies, for ALT and DC, at six months after planting. Except for the evaluated DAP at 18 months after planting, the other estimations of individual narrow sense heritability were moderated, being lower than the estimates of progenies average heritability. The gains with the selection of progenies and plants were from low to moderate and varied between each evaluated stage, decreasing with the increasing plant age.