ABSTRACT A large set of variables is assessed for progeny selection in a plant-breeding program and other agronomic fields. The meta-analysis of the coefficient of variation (CVe) produces information for researchers and breeders on the experimental quality of trials. This analysis can also be applied in the decision-making process of the experimental plan regarding the experimental design, the number of repetitions, and the treatments and plants/progenies to be measured. In this study, we evaluated the dataset distribution and the descriptive statistics of CVe through the Frequentist and Bayesian approaches, aiming to establish the credibility and confidence intervals. We submitted CVe data of ten wheat (Triticum aestivum L.) traits reported in 1,068 articles published to the Bayesian and Frequentist analyses. Sample data were analyzed via Gamma and normal models. We selected the model with the lowest Akaike Information Criterion (AIC) value, and then we tested three link functions. In the Bayesian analysis, uniform distributions were used as non-informative priors for the Gamma distribution parameters with three ranges of q~U (a,b,). Thus, the prior probability density function was given by: p θ = 1 β - α , θ ∈ α , β . The Bayesian and Frequentist approaches with the Gamma model presented similar results for CVe; however, the range Bayesian credible intervals was narrower than the Frequentist confidence intervals. Gamma distribution fitted the CVe data better than the normal distribution. The credible and confidence intervals of CVe were successfully applied to wheat traits and could be used as experimental accuracy measurements in other experiments.

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.

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 Methods for genetic improvement of semi–perennial species, such as passion fruit, often involve large areas, unbalanced data, and lack of observations. Some strategies can be applied to solve these problems. In this work, different models and approaches were tested to improve the precision of estimates of genetic evaluation models for several characteristics of the passion fruit. A randomized block design (RBD) model was compared to a posteriori correction, adding two factors to the model (post–hoc blocking Row–Col). These models were also combined with the frequentist and Bayesian approaches to identify which combination yields the most accurate results. These approaches are part of a strategic plan in a perennial plant breeding program to select promising genitors of passion to compose the next selection cycle. For Bayesian, we tested two priors, defining different values for the distribution parameters of effect variances of the model. We also performed a cross–validation test to choose a priori values and compare the frequentist and Bayesian approaches using the root mean square error (RMSE) and the correlation between the predicted and observed values, called Predictive capacity of the model (PC). The model with the post–hoc blocking Row–Col design captured the spatial variability for productivity and number of fruits, directly affecting the experimental precision. Both approaches applied to the models showed a similar performance, with predictive capacity and selective efficiency leading to the selection of the same individuals.

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 We aimed to estimate genetic parameters for growth, reproductive, and carcass traits in Tabapuã cattle. Phenotypic data were collected between 1990 and 2019 in 1,218 farms, and the pedigree file had 340,868 animals. The traits evaluated were body weight at 120 (W120), 210 (W210), 365 (W365), and 550 (W550) days of age; age at first calving (AFC), scrotal circumference at 365 days of age (SC365), ribeye area (REA), backfat thickness (BF), and rump fat thickness (RF). The (co)variance components were estimated using the restricted maximum likelihood method, considering single and two-traits animal models. For all traits, the models considered fixed, direct additive genetic, and residual random effects. In addition, for W120 and W210, the maternal additive genetic and maternal permanent environmental effects were also included. Heritabilities for W120, W210, W365, W550, SC365, REA, BF, and RF were of moderate magnitude (0.15, 0.16, 0.23, 0.19, 0.22, 0.36, 0.31, and 0.27, respectively). Low heritability was observed for AFC (0.07). The genetic correlations between growth traits were higher than 0.90, while AFC and SC365 presented negative moderate correlation (−0.66). The REA showed low genetic correlations with BF (0.07) and RF (0.07), whereas BF and RF were highly correlated (0.77). Considering the heritability estimates, selection for AFC would result in limited genetic gain, while for the other traits, it would be satisfactory. Based on the high genetic correlations between growth traits, selection of Tabapuã animals can be performed at younger ages. Additionally, animals can be indirectly selected for AFC through SC365, and only one fat thickness trait may be used in the selection process considering the high genetic correlation and similar heritability values for BF and RF.

ABSTRACT We aimed to reduce the dimensionality of quantitative traits in pigs applying factor analysis. Quantitative variables were collected, and the factor analysis extracted five factors with biological meaning related to performance, carcass quality, carcass yield, meat quality, and initial pH. These factors were posteriorly used as dependent variable to evaluate the effects of genetic groups (Piau, Duroc, and Pietrain crossbreds), nutritional plans (low, medium and high lysine levels) and sex. An interaction effect between genetic group and sex was observed in performance, in which Duroc crossbred showed the greatest scores. The Pietrain genetic group showed greater values of carcass quality compared with Duroc and Piau, while Piau crossbred pigs had greater values for meat quality compared with Pietrain and Duroc. A greater carcass yield was observed in Pietrain crossbred compared with Duroc pigs. Pigs fed under low lysine level had the lowest performance values. Carcass yield was affected by nutritional plans, in which the medium lysine level showed the greatest values. Meat quality was improved by the nutritional plan with high lysine level compared with the low lysine level. Initial pH showed increased means when using nutritional plans with low and medium lysine levels in diet composition. With regard to sex effects, a greater carcass quality was found for gilts compared with barrows. The reduction of the data dimensionality allowed the joint evaluation of genetic group, nutritional plan, and sex based on new latent variables that represented the original dataset under easier framework based on factors’ biological interpretation.

RESUMO: Objetivou-se, neste estudo, comparar modelos não lineares ajustados às curvas de crescimento de codornas para determinar qual modelo que melhor descreve o crescimento de codornas e verificar a similaridade dos modelos analisando as estimativas dos parâmetros. Para as análises foram utilizados os dados peso e idade de codornas européias de corte (Coturnix coturnix coturnix) proveniente de três linhagens, em um esquema fatorial 2x4, instalado em um delineamento inteiramente casualizado, com dois níveis de energia metabolizável e quatro níveis de proteína bruta, com seis repetições. Os modelos não lineares utilizados foram: Brody, Von Bertalanffy, Richards, Logístico e Gompertz. Para a escolha do melhor modelo utilizou-se o Coeficiente de Determinação Ajustado, o Percentual de Convergência, o Quadrado Médio do Resíduo, o Teste de Durbin-Watson, o Critério de informação Akaike e o Critério de informação Bayesiano como avaliadores da qualidade do ajuste. Utilizou-se a análise de agrupamento para verificar, baseado nas estimativas médias dos parâmetros, a similaridades entre os modelos. Entre os modelos estudados, o Richard foi o mais adequado para descrever as curvas de crescimento. Os modelos Logístico e Richards foram considerados similares nas análises sem distinção de linhagem, bem como nas análises das Linhagem 1, 2 e 3.

ABSTRACT: The objective of this study was to compare non-linear models fitted to the growth curves of quail to determine which model best describes their growth and check the similarity between models by analyzing parameter estimates.Weight and age data of meat-type European quail (Coturnix coturnix coturnix) of three lines were used, from an experiment in a 2 × 4 factorial arrangement in a completely randomized design, consisting of two metabolizable energy levels, four crude protein levels and six replicates. The non-linear Brody, Von Bertalanffy, Richards, Logistic and Gompertz models were used. To choose the best model, the Adjusted Coefficient of Determination, Convergence Rate, Residual Mean Square, Durbin-Watson Test, Akaike Information Criterion and Bayesian Information Criterion were applied as goodness-of-fit indicators. Cluster analysis was performed to check the similarity between models based on the mean parameter estimates. Among the studied models, Richards’ was the most suitable to describe the growth curves. The Logistic and Richards models were considered similar in the analysis with no distinction of lines as well as in the analyses of Lines 1, 2 and 3.

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 The improvement of superior wheat cultivars depends on the identification of promising segregating populations to derive superior lines. A lattice model (8×8) involving 56 F2 populations and eight parents was conducted in the 2020 cropping season, and grain yield per plant was evaluated for every F2 population, with further analysis of the population potential by Jinks and Pooni method via REML/BLUP. A total of 5,410 F2 plants were evaluated in this study. The results showed that the use of genetic variance associated with the individual genotypic value (BLUP) was superior compared with the use of variance and traditional phenotypic values. The F2 populations, CD 1303/BRS 254, CD 1303/Tbio Duque, CD 1303/Tbio Ponteiro, BRS 264/Tbio Aton, Tbio Ponteiro/Tbio Aton, and Tbio Sossego/CD 1303 had the highest likelihood of deriving superior lines.

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.

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.

RESUMO: Sarcomas de tecidos moles (STM) caninos compreendem um grupo heterogêneo de neoplasias malignas, que apresentam alterações histopatológicas similares, baixa a moderada taxa de recorrência e baixo potencial metastático. Em medicina humana, a expressão de receptor para estrógeno (RE) e receptor para progesterona (RP) nos sarcomas tem sido estudada, visando a busca por fatores prognósticos e novos alvos para tratamentos. Na medicina veterinária, ainda não foram realizados estudos similares. O objetivo deste trabalho foi investigar por imuno-histoquímica a expressão de RE e RP em uma série de 80 sarcomas cutâneos e subcutâneos de cães, com características histopatológicas de tumor de bainha de nervo periférico e tumor de parede perivascular. Todos os casos foram positivos para RP e negativos para RE. Tumores de alto grau de malignidade (grau III) exibiram maior expressão deste receptor que os tumores de baixo grau (grau I). Tumores com atividade mitótica maior que 9 figuras mitóticas/10 campos de grande aumento também exibiram maior expressão do RP. Em adição, houve correlação positiva entre o índice de proliferação celular (Ki67) e a expressão de RP. Assim, é possível que a progesterona desempenhe maior papel que o estrógeno na patogênese desses tumores. Futuros trabalhos poderão explorar o potencial dos moduladores seletivos de RP como agente terapêutico em STM caninos, bem como avaliar a expressão de RP como preditiva de prognóstico.

ABSTRACT: Canine soft tissue sarcomas (STS) comprise a heterogeneous group of malignancies that share similar histopathological features, a low to moderate recurrence rate and low metastatic potential. In human medicine, the expression of estrogen receptors (ER) and progesterone receptors (PR) in sarcomas has been studied to search for prognostic factors and new treatment targets. Similar studies have yet to be conducted in veterinary medicine. The objective of this study was therefore to investigate by immunohistochemistry (IHC) the ER and PR expression in a series of 80 cutaneous and subcutaneous sarcomas in dogs with histopathological features of peripheral nerve sheath tumor (PNST) and perivascular wall tumor (PWT). All cases were positive for PR and negative for ER. Tumors of high malignancy grade (grade III) exhibited higher PR expression than low-grade tumors (grade I). Tumors with mitotic activity greater than 9 mitotic figures/10 high power fields also exhibited higher PR expression. In addition, there was a positive correlation between cell proliferation (Ki67) and PR expression. Therefore, it is possible that progesterone plays a greater role than estrogen in the pathogenesis of these tumors. Future studies should explore the potential for selective progesterone receptor modulators as therapeutic agents in canine STS, as well as evaluating PR expression as a predictor of prognosis.

Resumo: O objetivo deste trabalho foi avaliar a aplicação de diferentes métodos de redução de dimensionalidade no modelo aditivo-dominante e compará-los ao método genômico da melhor predição linear não viesada (G-BLUP). Os métodos de redução avaliados foram: regressão via componentes principais (PCR), quadrados mínimos parciais (PLS) e regressão via componentes independentes (ICR). Utilizou-se um conjunto de dados simulados composto por 1.000 indivíduos e 2.000 polimorfismos de nucleotídeo único, analisados em quatro cenários: dois níveis de herdabilidade × duas heranças genéticas. Para auxiliar na escolha do número de componentes, os resultados foram avaliados quanto às informações genômicas aditiva, dominante e total. De modo geral, a PCR apresentou maiores valores de acurácia em comparação aos demais métodos. No entanto, nenhuma das metodologias consegue capturar as herdabilidades genômicas reais e todas apresentam estimativas viesadas, tendo subestimado ou superestimado os valores genéticos genômicos. Para a estimação simultânea dos efeitos de marcadores aditivos e devidos à dominância, a melhor alternativa é a escolha do número de componentes que conduz o valor genômico devido à dominância à maior acurácia.

Abstract: The objective of this work was to evaluate the application of different dimensionality reduction methods in the additive-dominant model and to compare them with the genomic best linear unbiased prediction (G-BLUP) method. The dimensionality reduction methods evaluated were: principal components regression (PCR), partial least squares (PLS), and independent components regression (ICR). A simulated data set composed of 1,000 individuals and 2,000 single-nucleotide polymorphisms was used, being analyzed in four scenarios: two heritability levels × two genetic architectures. To help choose the number of components, the results were evaluated as to additive, dominant, and total genomic information. In general, PCR showed higher accuracy values than the other methods. However, none of the methodologies are able to recover true genomic heritabilities and all of them present biased estimates, under- or overestimating the genomic genetic values. For the simultaneous estimation of the additive and dominance marker effects, the best alternative is to choose the number of components that leads the dominance genomic value to a higher accuracy.