Meta-analysis of the experimental coefficient of variation in wheat using the Bayesian and Frequentist approaches

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: [formula] 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.(AU)

Evaluation of Bayesian methods of genomic association via chromosomic regions using simulated data

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.(AU)

Row-Col and Bayesian approach seeking to improve the predictive capacity and selection of passion fruit

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.

Evaluation of a new additive-dominance genomic model and implications for quantitative genetics and genomic selection

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.

Determination of optimal number of independent components in yield traits in rice

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.

Genomic prediction of leaf rust resistance to Arabica coffee using machine learning algorithms

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.

Genomic prediction of leaf rust resistance to Arabica coffee using machine learning algorithms

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.(AU)

Progesterone and estrogen receptor expression by canine cutaneous soft tissue sarcomas / Expressão de receptores para progesterona e estrógeno em sarcomas de tecidos moles cutâneos em cães

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.(AU)

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.(AU)

Nonlinear quantile regression to describe the dry matter accumulation of garlic plants / Regressão quantílica não linear para descrever o acúmulo de matéria seca de alho

The objective of this study was to adjust nonlinear quantile regression models for the study of dry matter accumulation in garlic plants over time, and to compare them to models fitted by the ordinary least squares method. The total dry matter of nine garlic accessions belonging to the Vegetable Germplasm Bank of Universidade Federal de Viçosa (BGH/UFV) was measured in four stages (60, 90, 120 and 150 days after planting), and those values were used for the nonlinear regression models fitting. For each accession, there was an adjustment of one model of quantile regression (τ=0.5) and one based on the least squares method. The nonlinear regression model fitted was the Logistic. The Akaike Information Criterion was used to evaluate the goodness of fit of the models. Accessions were grouped using the UPGMA algorithm, with the estimates of the parameters with biological interpretation as variables. The nonlinear quantile regression is efficient for the adjustment of models for dry matter accumulation in garlic plants over time. The estimated parameters are more uniform and robust in the presence of asymmetry in the distribution of the data, heterogeneous variances, and outliers.(AU)

Este trabalho teve como objetivo ajustar modelos de regressão quantílica não linear para o estudo do acúmulo de matéria seca total em plantas de alho ao longo do tempo, e compará-los com modelos ajustados pelo método dos mínimos quadrados. A matéria seca total de nove acessos de alho pertencentes ao Banco de Germoplasma de Hortaliças da Universidade Federal de Viçosa (BGH/UFV) foi avaliada em quatro períodos (60, 90, 120 e 150 dias após plantio), e estes valores foram utilizados para o ajuste de modelos de regressão - não linear - logística. Para cada acesso, foram ajustados um modelo de regressão quantílica (τ=0,5) e um modelo pela metodologia dos mínimos quadrados. Para avaliar a qualidade de ajuste dos modelos foi utilizado o Critério de Informação de Akaike. Os acessos foram agrupados pelo algoritmo UPGMA, utilizando as estimativas dos parâmetros com interpretação biológica como variáveis. A regressão quantílica não linear foi eficiente no ajuste de modelos para descrição do acúmulo de matéria seca ao longo do tempo. As estimativas de parâmetros foram mais uniformes e robustas na presença de dados assimétricos, variâncias heterogêneas e de valores discrepantes.(AU)

Progesterone and estrogen receptor expression by canine cutaneous soft tissue sarcomas / Expressão de receptores para progesterona e estrógeno em sarcomas de tecidos moles cutâneos em cães

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.(AU)

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.(AU)

Evaluation of Bayesian models for analysis of crude protein requirement for pigs of Brazilian Piau breed

We evaluated the inclusion of information on genetic relationship into the analysis of crude protein requirement in diets for pigs of Brazilian Piau breed, using Bayesian inference. The animals were assigned to treatments in a completely randomized design in factorial scheme 4 × 2 (crude protein levels × sex) with 12 repetitions per treatment. The evaluations were carried out in the initial, growing and finishing phases, and after slaughter. The traits evaluated were feed conversion (FC), backfat thickness (BF), daily weight gain (DWG), daily feed intake (DFI) and some carcass cuts. Three models were considered to evaluate the inclusion of information on genetic relationship into the analysis: Model I, a simple linear model; Model II, the same effects of Model I with addition of the independent random effect of animal; and Model III, the same effects of Model II, but including the genetic relationship between the animals. Model III presented the best fit and was considered for later inferences. Crude protein (CP) levels did not significantly influence any of the evaluated traits. The effect of sex was significant only for the growing phase, while its interaction with protein levels presented an opposite result for all evaluated traits. Additionally, CP levels of 10.2 %, 9.6 % and 9.0 % can be used in diets for pigs of Brazilian Piau breed in the initial, growing and finishing phases, respectively.

Evaluation of Bayesian models for analysis of crude protein requirement for pigs of Brazilian Piau breed

We evaluated the inclusion of information on genetic relationship into the analysis of crude protein requirement in diets for pigs of Brazilian Piau breed, using Bayesian inference. The animals were assigned to treatments in a completely randomized design in factorial scheme 4 × 2 (crude protein levels × sex) with 12 repetitions per treatment. The evaluations were carried out in the initial, growing and finishing phases, and after slaughter. The traits evaluated were feed conversion (FC), backfat thickness (BF), daily weight gain (DWG), daily feed intake (DFI) and some carcass cuts. Three models were considered to evaluate the inclusion of information on genetic relationship into the analysis: Model I, a simple linear model; Model II, the same effects of Model I with addition of the independent random effect of animal; and Model III, the same effects of Model II, but including the genetic relationship between the animals. Model III presented the best fit and was considered for later inferences. Crude protein (CP) levels did not significantly influence any of the evaluated traits. The effect of sex was significant only for the growing phase, while its interaction with protein levels presented an opposite result for all evaluated traits. Additionally, CP levels of 10.2 %, 9.6 % and 9.0 % can be used in diets for pigs of Brazilian Piau breed in the initial, growing and finishing phases, respectively.(AU)

New insights into genomic selection through population-based non-parametric prediction methods

Genome-wide selection (GWS) is based on a large number of markers widely distributed throughout the genome. Genome-wide selection provides for the estimation of the effect of each molecular marker on the phenotype, thereby allowing for the capture of all genes affecting the quantitative traits of interest. The main statistical tools applied to GWS are based on random regression or dimensionality reduction methods. In this study a new non-parametric method, called Delta-p was proposed, which was then compared to the Genomic Best Linear Unbiased Predictor (G-BLUP) method. Furthermore, a new selection index combining the genetic values obtained by the G-BLUP and Delta-p, named Delta-p/G-BLUP methods, was proposed. The efficiency of the proposed methods was evaluated through both simulation and real studies. The simulated data consisted of eight scenarios comprising a combination of two levels of heritability, two genetic architectures and two dominance status (absence and complete dominance). Each scenario was simulated ten times. All methods were applied to a real dataset of Asian rice (Oryza sativa) aiming to increase the efficiency of a current breeding program. The methods were compared as regards accuracy of prediction (simulation data) or predictive ability (real dataset), bias and recovery of the true genomic heritability. The results indicated that the proposed Delta-p/G-BLUP index outperformed the other methods in both prediction accuracy and predictive ability.

Triple categorical regression for genomic selection: application to cassava breeding

Genome-wide selection (GWS) is currently a technique of great importance in plant breeding, since it improves efficiency of genetic evaluations by increasing genetic gains. The process is based on genomic estimated breeding values (GEBVs) obtained through phenotypic and dense marker genomic information. In this context, GEBVs of N individuals are calculated through appropriate models, which estimate the effect of each marker on phenotypes, allowing the early identification of genetically superior individuals. However, GWS leads to statistical challenges, due to high dimensionality and multicollinearity problems. These challenges require the use of statistical methods to approach the regularization of the estimation process. Therefore, we aimed to propose a method denominated as triple categorical regression (TCR) and compare it with the genomic best linear unbiased predictor (G-BLUP) and Bayesian least absolute shrinkage and selection operator (BLASSO) methods that have been widely applied to GWS. The methods were evaluated in simulated populations considering four different scenarios. Additionally, a modification of the G-BLUP method was proposed based on the TCR-estimated (TCR/G-BLUP) results. All methods were applied to real data of cassava (Manihot esculenta) with to increase efficiency of a current breeding program. The methods were compared through independent validation and efficiency measures, such as prediction accuracy, bias, and recovered genomic heritability. The TCR method was suitable to estimate variance components and heritability, and the TCR/G-BLUP method provided efficient GEBV predictions. Thus, the proposed methods provide new insights for GWS.

Analysis of the adaptability of black bean cultivars by means of quantile regression / Análise da adaptabilidade de cultivares de feijão preto por meio de regressão quantílica

The aim of this study was to use quantile regression (QR) to characterize the effect of the adaptability parameter throughout the distribution of the productivity variable on black bean cultivars launched by different national research institutes (research centers) over the last 50 years. For this purpose, 40 cultivars developed by Brazilian genetic improvement programs between 1959 and 2013 were used. Initially, QR models were adjusted considering three quantiles (τ = 0.2, 0.5 and 0.8). Subsequently, with the confidence intervals, quantile models τ = 0.2 and 0.8 (QR0.2 and QR0.8) showed differences regarding the parameter of adaptability and average productivity. Finally, by grouping the cultivars into one of the two groups defined from QR0.2 and QR0.8, it was reported that the younger cultivars were associated to the quantile τ = 0.8, i.e., those with higher yields and more responsive conditions indicating that genetic improvement over the last 50 years resulted in an increase in both the productivity and the adaptability of cultivars.(AU)

Neste estudo objetivou-se utilizar a regressão quantílica (RQ) para caracterizar o efeito do parâmetro de adaptabilidade ao longo de toda a distribuição da variável produtividade em cultivares de feijão preto lançadas por diferentes instituições nacionais de pesquisa nos últimos 50 anos. Para tanto utilizou-se 40 cultivares desenvolvidas pelos programas brasileiros de melhoramento genético entre os anos de 1959 a 2013. Inicialmente foram ajustados modelos de RQ considerando três quantis (τ=0,2, 0,5, 0,8). Posteriormente, com os intervalos de confiança verificou-se que os modelos quantílicos τ=0,2 e 0,8 (RQ0,2 e RQ0,8) apresentaram diferenças quanto ao parâmetro de adaptabilidade e produtividade média. Finalmente, por meio do agrupamento das cultivares em um dos dois grupos definidos a partir de RQ0,2 e RQ0,8, constatou-se que as cultivares mais novas foram associadas ao quantil τ = 0,8, ou seja, aquelas com maiores produtividades e mais responsivas as condições ambientais indicando que o melhoramento ao longo dos últimos 50 anos possibilitou o incremento tanto na produtividade quanto na adaptabilidade das cultivares.(AU)

Ingestive behavior of dairy goats fed diets containing increasing levels of neutral detergent fiber and particle size using multivariate analysis

The purpose of this study was to evaluate the effect of interaction between increasing neutral detergent fiber content and particle sizes on ingestive behavior of dairy goats. Forty-eight lactating, multiparous Saanen and Alpine goats, with average milk production of 1.4 ±0.57 kg d-1, around 60th ±12 day of lactation were distributed in a 3 x 4 factorial completely randomized design. The diets consisted: three particles sizes (02, 05 or 15 cm) and four levels of neutral detergent fiber (34, 41, 49 or 57% NDFf) from forage (Tifton 85 hay). The ingestive behavior was monitored during 24 hours. A regression and a multivariate time series cluster analysis were performed. No interaction was found (p > 0.05) between treatments. Feeding time was different according to the particle size, having an increasing linear effect. Rumination and idle times were not affected (p > 0.05). The temporal feeding behavior was clustered into two groups according to the profile of particle size of the diet. Rumination peaks were randomly distributed with more intense activity before morning and afternoon meals. The increase in NDFf content in the diet did not change the ingestive behavior. The multivariate cluster analysis in a time series data is useful to interpret animal feeding behavior.(AU)

Triple categorical regression for genomic selection: application to cassava breeding

Genome-wide selection (GWS) is currently a technique of great importance in plant breeding, since it improves efficiency of genetic evaluations by increasing genetic gains. The process is based on genomic estimated breeding values (GEBVs) obtained through phenotypic and dense marker genomic information. In this context, GEBVs of N individuals are calculated through appropriate models, which estimate the effect of each marker on phenotypes, allowing the early identification of genetically superior individuals. However, GWS leads to statistical challenges, due to high dimensionality and multicollinearity problems. These challenges require the use of statistical methods to approach the regularization of the estimation process. Therefore, we aimed to propose a method denominated as triple categorical regression (TCR) and compare it with the genomic best linear unbiased predictor (G-BLUP) and Bayesian least absolute shrinkage and selection operator (BLASSO) methods that have been widely applied to GWS. The methods were evaluated in simulated populations considering four different scenarios. Additionally, a modification of the G-BLUP method was proposed based on the TCR-estimated (TCR/G-BLUP) results. All methods were applied to real data of cassava (Manihot esculenta) with to increase efficiency of a current breeding program. The methods were compared through independent validation and efficiency measures, such as prediction accuracy, bias, and recovered genomic heritability. The TCR method was suitable to estimate variance components and heritability, and the TCR/G-BLUP method provided efficient GEBV predictions. Thus, the proposed methods provide new insights for GWS.(AU)

Combined index of genomic prediction methods applied to productivity / Índice combinado de métodos de predição genômica aplicado em características de produtividade em arroz

Rice cultivation has great national and global importance, being one of the most produced and consumed cereals in the world and the primary food for more than half of the worlds population. Because of its importance as food, developing efficient methods to select and predict genetically superior individuals in reference to plant traits is of extreme importance for breeding programs. The objective of this research was to evaluate and compare the efficiency of the Delta-p, G-BLUP (Genomic Best Linear Unbiased Predictor), BayesCpi, BLASSO (Bayesian Least Absolute Shrinkage and Selection Operator), Delta-p/G-BLUP index, Delta-p/BayesCpi index, and Delta-p/BLASSO index in the estimation of genomic values and the effects of single nucleotide polymorphisms on phenotypic data associated with rice traits. Use of molecular markers allowed high selective efficiency and increased genetic gain per unit time. The Delta-p method uses the concept of change in allelic frequency caused by selection and the theoretical concept of genetic gain. The Index is based on the principle of combined selection, using the information regarding the additive genomic values predicted via G-BLUP, BayesCpi, BLASSO, or Delta-p. These methods were applied and compared for genomic prediction using nine rice traits: flag leaf length, flag leaf width, panicles number per plant, primary panicle branch number, seed length, seed width, amylose content, protein content, and blast resistance. Delta-p/G-BLUP index had higher predictive abilities for the traits studied, except for amylose content trait in which the method with the highest predictive ability was BayesCpi, being approximately 3% greater than that of the Delta-p/G-BLUP index.(AU)

A cultura do arroz tem grande importância nacional e mundial por ser um dos cereais mais produzidos e consumidos no mundo, caracterizando-se como o principal alimento de mais da metade da população mundial. Em função de sua importância alimentar, desenvolver métodos eficientes que visam a predição e a seleção de indivíduos geneticamente superiores, quanto a características da planta, é de extrema importância para os programas de melhoramento. Diante disso, o objetivo deste trabalho foi avaliar e comparar a eficiência do método Delta-p, G-BLUP, BayesCpi, BLASSO e o índice Delta-p/G-BLUP, índice Delta-p/BayesCpi e índice Delta-p/BLASSO, na estimação de valores genômicos e dos efeitos de marcadores SNPs (Single Nucleotide Polymorphisms) em dados fenotípicos associados a características de arroz. A utilização de marcadores moleculares permite alta eficiência seletiva e o aumento do ganho genético por unidade de tempo. O método Delta-p utiliza o conceito de mudança na frequência alélica devido à seleção e o conceito teórico de ganho genético. O Índice é baseado no princípio da seleção combinada, utiliza conjuntamente as informações dos valores genômicos aditivos preditos via G-BLUP, BayesCpi ou BLASSO e via Delta-p. Estes métodos foram aplicados e comparados quanto à predição genômica utilizando nove características de arroz (Oryza sativa), sendo elas: comprimento da folha bandeira, largura da folha bandeira; número de panículas por planta; número de ramos da panícula primária; comprimento de semente; largura de semente; teor de amilose; teor de proteína; resistência a bruzone. O índice Delta-p/G-BLUP obteve maiores capacidades preditivas para as características estudadas, exceto para a característica Conteúdo de amilose, em que o método que obteve maior capacidade preditiva foi o BayesCpi, sendo aproximadamente 3% superior ao índice Delta-p/G-BLUP.(AU)

New insights into genomic selection through population-based non-parametric prediction methods

Genome-wide selection (GWS) is based on a large number of markers widely distributed throughout the genome. Genome-wide selection provides for the estimation of the effect of each molecular marker on the phenotype, thereby allowing for the capture of all genes affecting the quantitative traits of interest. The main statistical tools applied to GWS are based on random regression or dimensionality reduction methods. In this study a new non-parametric method, called Delta-p was proposed, which was then compared to the Genomic Best Linear Unbiased Predictor (G-BLUP) method. Furthermore, a new selection index combining the genetic values obtained by the G-BLUP and Delta-p, named Delta-p/G-BLUP methods, was proposed. The efficiency of the proposed methods was evaluated through both simulation and real studies. The simulated data consisted of eight scenarios comprising a combination of two levels of heritability, two genetic architectures and two dominance status (absence and complete dominance). Each scenario was simulated ten times. All methods were applied to a real dataset of Asian rice (Oryza sativa) aiming to increase the efficiency of a current breeding program. The methods were compared as regards accuracy of prediction (simulation data) or predictive ability (real dataset), bias and recovery of the true genomic heritability. The results indicated that the proposed Delta-p/G-BLUP index outperformed the other methods in both prediction accuracy and predictive ability.(AU)

Ingestive behavior of dairy goats fed diets containing increasing levels of neutral detergent fiber and particle size using multivariate analysis

The purpose of this study was to evaluate the effect of interaction between increasing neutral detergent fiber content and particle sizes on ingestive behavior of dairy goats. Forty-eight lactating, multiparous Saanen and Alpine goats, with average milk production of 1.4 ±0.57 kg d-1, around 60th ±12 day of lactation were distributed in a 3 x 4 factorial completely randomized design. The diets consisted: three particles sizes (02, 05 or 15 cm) and four levels of neutral detergent fiber (34, 41, 49 or 57% NDFf) from forage (Tifton 85 hay). The ingestive behavior was monitored during 24 hours. A regression and a multivariate time series cluster analysis were performed. No interaction was found (p > 0.05) between treatments. Feeding time was different according to the particle size, having an increasing linear effect. Rumination and idle times were not affected (p > 0.05). The temporal feeding behavior was clustered into two groups according to the profile of particle size of the diet. Rumination peaks were randomly distributed with more intense activity before morning and afternoon meals. The increase in NDFf content in the diet did not change the ingestive behavior. The multivariate cluster analysis in a time series data is useful to interpret animal feeding behavior.