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 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.

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.

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.

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.

ABSTRACT An accurate and efficient statistical method for genetic evaluation is a key requirement for progress in any breeding program. Thus, the present study aimed to evaluate the performance of Frequentist and Bayesian inferences for repeated measures analysis in Jatropha curcas breeding. To this end, 730 individuals from 73 half-sib families were evaluated for grain yield trait, over six crop years. Frequentist and Bayesian analyses were made considering repeatability models with different residual variance structures. Variance components were estimated through restricted maximum likelihood (REML) and Markov Chain Monte Carlo (MCMC). Genetic values were predicted through best linear unbiased prediction (BLUP) and estimated through MCMC. Variance components and genetic and non-genetic parameters estimated by the Frequentist inference presented values similar to those estimated by the Bayesian inference. The selective accuracy presented high magnitude (0.84) by the Frequentist and Bayesian inferences, indicating high reliability. Confidence and highest posterior density (HPD) intervals were similar for the genetic parameters, however the HPD intervals range was slightly short. This study highlighted the importance of testing the residual variance structure and pointed out that the Frequentist and Bayesian inferences presented similar results when using non-informative prior. Then, both inferences can be efficiently applied in Jatropha curcas breeding.

ABSTRACT Forest plantations are strong allies in preserving natural resources, providing social and economic benefits. The plantations carried out in the coming years will be vital to meet the growing demand for forest products. To ensure the continuity of genetic progress and the good results achieved with the improvement of forest species, statistical methods that accurately selects superior genotypes are desirable. Multi-trait multi-environment trials are preferred over single-trait single-environment trials, since they can exploit the covariance between traits and environments, increasing the analysis’s prediction power. The Bayesian multi-trait multi-environments approach (BMTME) combines the cited advantages with the parsimony of Bayesian statistics promoting a more informative data analysis. Thus, the aims of this study were to estimate genetic parameters, evaluate genetic variability, and select eucalyptus clones through BMTME models. To this end, a data set with 215 eucalyptus clones evaluated in four environments for diameter at breast height and Pilodyn penetration was used. The Markov Chain Monte Carlo algorithm was applied to estimate the variance components and genetic parameters and to predict the genotypic values. The Smith-Hazel index was used to simultaneously achieve gains with selection for both traits. The BMTME approach provided high accuracies, being a good strategy to the evaluation of multiple environmental trials of Eucalyptus for breeding purposes.

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 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.

Resumo: O objetivo deste trabalho foi selecionar progênies e indivíduos de cupuaçuzeiro (Theobroma grandiflorum) com base em características agronômicas e, indiretamente, identificar aqueles adaptados a um ambiente de sistema agroflorestal (SAF) na Amazônia brasileira. Para tanto, 25 progênies de irmãos completos foram plantadas e testadas em consórcio com pimenta-do-reino (Piper nigrum), banana (Musa spp.) e bacuri (Platonia insignis). O experimento foi realizado em delineamento de blocos ao acaso, com cinco repetições e três plantas por parcela, de 2005 a 2019. Para as análises estatísticas, foram utilizadas as médias fenotípicas de produção e incidência da vassoura de bruxa avaliadas durante 11 safras. Progênies e indivíduos superiores foram identificados pela metodologia de modelos mistos (REML/BLUP), o que resultou na seleção de dez plantas de cinco famílias com características agronômicas superiores. As progênies de cupuaçu 6, 36, 37, 49 e 52 são as que melhor se adaptam ao ambiente de um SAF multiespécies na região amazônica, em razão de suas características agronômicas em condições competitivas. Dez matrizes apresentam potencial agronômico e adaptação indireta ao SAF e podem ser utilizadas como cultivares clonais de cupuaçu nesse ambiente.

Abstract: The objective of this work was to select cupuaçu (Theobroma grandiflorum) tree progenies and individuals based on their agronomic traits, and, indirectly, to identify those adapted to an agroforestry system (AFS) environment in the Brazilian Amazon. For this purpose, 25 full-sib progenies were planted and tested in consortium with black pepper (Piper nigrum), banana (Musa spp.), and bacuri (Platonia insignis) trees. The experiment was carried out in a randomized complete block design, with five replicates and three plants per plot, from 2005 to 2019. For the statistical analyses, the phenotypic averages for production and incidence of witches’ broom disease, evaluated during 11 harvests, were used. Superior progenies and individuals were identified using the mixed model methodology (REML/BLUP), which led to the selection of ten plants from five families with superior agronomic traits. Cupuaçu tree progenies 6, 36, 37, 49, and 52 are the ones that best adapt to the environment of a multispecies AFS in the Amazon region because of their agronomic traits under competitive conditions. Ten matrices show agronomic potential and indirect adaptation to the AFS and can be used as clonal cupuaçu cultivars in this environment.

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.

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

ABSTRACT 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.