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The objective was to estimate the growth curves and genetic parameters using random regression methodology for Nellore cattle raised in Pantanal, MS, Brazil (6974 calves; n = 53,233 weights), with at least four weighings per individual. The model considered direct and maternal genetic additives and maternal permanent environmental effects at random. Orthogonal Legendre polynomials of cubic order were used to fit the growth curve. Analyses of variance were performed using the GLM procedure. The model used contained the fixed effects of sex, year of birth, farm, and the covariates calf birth month (linear and quadratic) and cow age at calving (linear and quadratic). The adjusted mean weight at 120 days of age was 93.43 ± 19.78 kg, and for 205 days of age, it was 180.42 ± 26.58 kg. Animals born in the dry season had a higher average weight [kg] (219.57 vs. 211.78, 3.7% higher) and, consequently, had higher weights at 646 days of age. Estimates of direct heritabilities (h2a) ranged from 0.35 to 0.75 (high magnitudes), and maternal heritabilities (h2m) along the trajectory of low magnitudes ranged from 0.03 to 0.08, respectively. The use of random regression to evaluate beef animals allows for adjusting the growth curve and selecting the best animals to be the parents of future generations.

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OBJECTIVE: The aim of this study was to identify suitable polynomial regression for modeling the average growth trajectory and to estimate the relative development of the rib eye area, scrotal circumference, and morphometric measurements of Guzerat young bulls. METHODS: A total of 45 recently weaned males, aged 325.8±28.0 days and weighing 219.9±38.05 kg, were evaluated. The animals were kept on Brachiaria brizantha pastures, received multiple supplementations, and were managed under uniform conditions for 294 days, with evaluations conducted every 56 days. The average growth trajectory was adjusted using ordinary polynomials, Legendre polynomials, and quadratic B-splines. The coefficient of determination, mean absolute deviation, mean square error, the value of the restricted likelihood function, Akaike information criteria, and consistent Akaike information criteria were applied to assess the quality of the fits. For the study of allometric growth, the power model was applied. RESULTS: Ordinary polynomial and Legendre polynomial models of the fifth order provided the best fits. B-splines yielded the best fits in comparing models with the same number of parameters. Based on the restricted likelihood function, Akaike's information criterion, and consistent Akaike's information criterion, the B-splines model with six intervals described the growth trajectory of evaluated animals more smoothly and consistently. In the study of allometric growth, the evaluated traits exhibited negative heterogeneity (b<1) relative to the animals' weight (p<0.01), indicating the precocity of Guzerat cattle for weight gain on pasture. CONCLUSION: Complementary studies of growth trajectory and allometry can help identify when an animal's weight changes and thus assist in decision-making regarding management practices, nutritional requirements, and genetic selection strategies to optimize growth and animal performance.

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Feed efficiency plays a major role in the overall profitability and sustainability of the beef cattle industry, as it is directly related to the reduction of the animal demand for input and methane emissions. Traditionally, the average daily feed intake and weight gain are used to calculate feed efficiency traits. However, feed efficiency traits can be analysed longitudinally using random regression models (RRMs), which allow fitting random genetic and environmental effects over time by considering the covariance pattern between the daily records. Therefore, the objectives of this study were to: (1) propose genomic evaluations for dry matter intake (DMI), body weight gain (BWG), residual feed intake (RFI) and residual weight gain (RWG) data collected during an 84-day feedlot test period via RRMs; (2) compare the goodness-of-fit of RRM using Legendre polynomials (LP) and B-spline functions; (3) evaluate the genetic parameters behaviour for feed efficiency traits and their implication for new selection strategies. The datasets were provided by the EMBRAPA-GENEPLUS beef cattle breeding program and included 2920 records for DMI, 2696 records for BWG and 4675 genotyped animals. Genetic parameters and genomic breeding values (GEBVs) were estimated by RRMs under ssGBLUP for Nellore cattle using orthogonal LPs and B-spline. Models were compared based on the deviance information criterion (DIC). The ranking of the average GEBV of each test week and the overall GEBV average were compared by the percentage of individuals in common and the Spearman correlation coefficient (top 1%, 5%, 10% and 100%). The highest goodness-of-fit was obtained with linear B-Spline function considering heterogeneous residual variance. The heritability estimates across the test period for DMI, BWG, RFI and RWG ranged from 0.06 to 0.21, 0.11 to 0.30, 0.03 to 0.26 and 0.07 to 0.27, respectively. DMI and RFI presented within-trait genetic correlations ranging from low to high magnitude across different performance test-day. In contrast, BWG and RWG presented negative genetic correlations between the first 3 weeks and the other days of performance tests. DMI and RFI presented a high-ranking similarity between the GEBV average of week eight and the overall GEBV average, with Spearman correlations and percentages of individuals selected in common ranging from 0.95 to 1.00 and 93 to 100, respectively. Week 11 presented the highest Spearman correlations (ranging from 0.94 to 0.98) and percentages of individuals selected in common (ranging from 85 to 94) of BWG and RWG with the average GEBV of the entire period of the test. In conclusion, the RRM using linear B-splines is a feasible alternative for the genomic evaluation of feed efficiency. Heritability estimates of DMI, RFI, BWG and RWG indicate enough additive genetic variance to achieve a moderate response to selection. A new selection strategy can be adopted by reducing the performance test to 56 days for DMI and RFI selection and 77 days for BWG and RWG selection.

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Bees play a critical role in pollination and food production, so their preservation is essential, particularly highlighting the importance of detecting diseases in bees early. The Varroa destructor mite is the primary factor contributing to increased viral infections that can lead to hive mortality. This study presents an innovative method for identifying Varroa destructors in honey bees using multichannel Legendre-Fourier moments. The descriptors derived from this approach possess distinctive characteristics, such as rotation and scale invariance, and noise resistance, allowing the representation of digital images with minimal descriptors. This characteristic is advantageous when analyzing images of living organisms that are not in a static posture. The proposal evaluates the algorithm's efficiency using different color models, and to enhance its capacity, a subdivision of the VarroaDataset is used. This enhancement allows the algorithm to process additional information about the color and shape of the bee's legs, wings, eyes, and mouth. To demonstrate the advantages of our approach, we compare it with other deep learning methods, in semantic segmentation techniques, such as DeepLabV3, and object detection techniques, such as YOLOv5. The results suggest that our proposal offers a promising means for the early detection of the Varroa destructor mite, which could be an essential pillar in the preservation of bees and, therefore, in food production.

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Filtering and smoothing algorithms are key tools to develop decision-making strategies and parameter identification techniques in different areas of research, such as economics, financial data analysis, communications, and control systems. These algorithms are used to obtain an estimation of the system state based on the sequentially available noisy measurements of the system output. In a real-world system, the noisy measurements can suffer a significant loss of information due to (among others): (i) a reduced resolution of cost-effective sensors typically used in practice or (ii) a digitalization process for storing or transmitting the measurements through a communication channel using a minimum amount of resources. Thus, obtaining suitable state estimates in this context is essential. In this paper, Gaussian sum filtering and smoothing algorithms are developed in order to deal with noisy measurements that are also subject to quantization. In this approach, the probability mass function of the quantized output given the state is characterized by an integral equation. This integral was approximated by using a Gauss-Legendre quadrature; hence, a model with a Gaussian mixture structure was obtained. This model was used to develop filtering and smoothing algorithms. The benefits of this proposal, in terms of accuracy of the estimation and computational cost, are illustrated via numerical simulations.

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The objective of this study was to estimate the components of variance and genetic parameters of test-day milk yield in first lactation Girolando cows, using a random regression model. A total of 126,892 test-day milk yield (TDMY) records of 15,351 first-parity Holstein, Gyr, and Girolando breed cows were used, obtained from the Associação Brasileira dos Criadores de Girolando. To estimate the components of (co) variance, the additive genetic functions and permanent environmental covariance were estimated by random regression in three functions: Wilmink, Legendre Polynomials (third order) and Linear spline Polynomials (three knots). The Legendre polynomial function showed better fit quality. The genetic and permanent environment variances for TDMY ranged from 2.67 to 5.14 and from 9.31 to 12.04, respectively. Heritability estimates gradually increased from the beginning (0.13) to mid-lactation (0.19). The genetic correlations between the days of the control ranged from 0.37 to 1.00. The correlations of permanent environment followed the same trend as genetic correlations. The use of Legendre polynomials via random regression model can be considered as a good tool for estimating genetic parameters for test-day milk yield records.(AU)

O objetivo deste estudo foi estimar os componentes de variância e os parâmetros genéticos da produção de leite no dia do teste (TDMY) em vacas Girolando de primeira lactação, usando modelo de regressão aleatória. Foram utilizados 126.892 registros de produção de leite no dia controle de 15.351 vacas primíparas das raças Holandesa, Gir e Girolando, obtidas na Associação Brasileira dos Criadores de Girolando. Para estimar os componentes de (co) variância, as funções genéticas aditivas e de covariância ambiental permanente foram estimadas por regressão aleatória em três funções: Wilmink, polinômios de Legendre (terceira ordem) e polinômios splines lineares (três nós). A função polinomial de Legendre apresentou melhor qualidade de ajuste. As variâncias genéticas e de ambiente permanente para produção de leite no dia do controle variaram de 2,67 a 5,14 e de 9,31 a 12,04, respectivamente. As estimativas de herdabilidade aumentaram gradativamente do início (0,13) para o meio da lactação (0,19). As correlações genéticas entre os dias do controle variaram de 0,37 a 1,00. As correlações de ambiente permanente seguiram a mesma tendência das correlações genéticas. A utilização dos polinômios de Legendre via modelos de regressão aleatória pode ser considerada como uma boa ferramenta para estimação de parâmetros genéticos da produção de leite no dia do teste.(AU)

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B-spline functions have been used in random regression models (RRM) to model animal weight from birth to adulthood because they are less vulnerable to common difficulties of other methods. However, its application to model growth traits of Polled Nellore cattle has been little studied. Therefore, this study aimed to evaluate polynomial functions of different orders and segment numbers to model effects associated with the Polled Nellore cattle growth curve. For this purpose, we used 15,148 weight records of 3,115 animals aged between 1 and 660 days and reared in northern Brazil and born between 1995 and 2010. Random effects were modeled using B-spline polynomials. As random effects, we considered the direct and maternal genetic additives, as well as direct and maternal permanent environments. As fixed effects were included contemporary group, cow age at calving (linear and quadratic) and fourth-order Legendre polynomials to represent average growth curve. The residue was modeled by considering seven age classes. The bestfitted model was the one that considered cubic B-spline functions with four knots for direct additive genetic effects and three knots for maternal genetic, animal permanent environment, and maternal permanent environment effects (C6555). Therefore, covariance functions under B-spline polynomials are efficient and can be used to model the growth curve of Polled Nellore cattle from birth to 660 days of age.(AU)

Os modelos de regressão aleatória (MRA) aplicando funções B-spline são uma alternativa para modelar pesos do nascimento até a idade adulta dos animais, pois estas funções são menos vulneráveis as dificuldades constantemente observadas em outras metodologias. No entanto, são escassas pesquisas sobre aplicação destas funções sobre as características de crescimento em bovinos Nelore Mocho. Funções polinomiais de diferentes ordens e números de segmentos foram avaliadas na modelagem dos efeitos associados à curva de crescimento de bovinos da raça Nelore Mocho. Foram utilizados 15.148 registros de peso de 3.115 animais com idade entre 1 e 660 dias, criados na região norte do Brasil e nascidos entre 1995 e 2010. Os efeitos aleatórios foram modelados usando polinômios do tipo B-splines. Como efeitos aleatórios, foram considerados os efeitos genéticos aditivo direto e materno e os efeitos de ambientes permanentes direto e materno. Foram considerados como efeitos fixos, os grupos de contemporâneos, a idade da vaca ao parto (efeito linear e quadrático) e os polinômios de Legendre de quarta ordem, representando a curva média de crescimento. O resíduo foi modelado por meio de sete classes distribuídas segundo a idade. O modelo que considerou funções B-splines cúbicas com quatro nós para o efeito genético aditivo direto e três nós para os efeitos genético materno, ambiente permanente animal e ambiente permanente materno (C6555) foi o mais adequado. Concluiu-se que funções de covariâncias sob polinômios B-splines são eficientes e podem ser utilizados como alternativas para modelar a curva de crescimento de bovinos da raça Nelore Mocho do nascimento até 660 dias de idade.(AU)

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Autoregressive (AR) and random regression (RR) models were fitted to test-day records from the first three lactations of Brazilian Holstein cattle with the objective of comparing their efficiency for national genetic evaluations. The data comprised 4,142,740 records of milk yield (MY) and somatic cell score (SCS) from 274,335 cows belonging to 2,322 herds. Although heritabilities were similar between models and traits, additive genetic variance estimates using AR were 7.0 (MY) and 22.2% (SCS) higher than those obtained from RR model. On the other hand, residual variances were lower in both traits when estimated through AR model. The rank correlation between EBV obtained from AR and RR models was 0.96 and 0.94 (MY) and 0.97 and 0.95 (SCS), respectively, for bulls (with 10 or more daughters) and cows. Estimated annual genetic gains for bulls (cows) obtained using AR were 46.11 (49.50) kg for MY and -0.019 (-0.025) score for SCS; whereas using RR these values were 47.70 (55.56) kg and -0.022 (-0.028) score. Akaike information criterion was lower for AR in both traits. Although AR model is more parsimonious, RR model assumes genetic correlations different from the unity within and across lactations. Thus, when these correlations are relatively high, these models tend to yield to similar predictions; otherwise, they will differ more and RR model would be theoretically sounder.

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The objective of this work was to estimate growth curves and genetic parameters from birth to 650 days of age of Nelore cattle raised in pasture in two production regions of the Mato Grosso do Sul State, Brazil (233,835 weight records from 47,459 cattle were analyzed). Genetic parameters were determined by random regression using Legendre orthogonal polynomials of cubic order, and age at weighing was considered in the model as a fixed effect to model the average growth trajectory. In the models, the effects of the contemporary group were considered as fixed and, as covariates, the animal age at weighing and the cow age at calving were nested in the animal age class (linear and quadratic effects), forming eight age classes. All models included the direct genetic additive, maternal genetic, and animal permanent environment as random effects, and the most appropriate model to describe the studied effects was defined according to the AIC and BIC criteria. Heritability estimates for birth weight varied between the two production regions, Campo Grande-Dourados (R1) and Alto Taquari-Bolsão (R2) and R1 (0.36 ± 0.02) and R2 (0.28 ± 0.03), and there were variations in the estimates at advanced ages. In both regions, the highest heritability values at 650 days of age were 0.47 ± 0.03 and 0.65 ± 0.02 for R1 and R2, respectively, with high heritability reflecting the high values of additive...(AU)

O objetivo do trabalho foi estimar curvas de crescimento e parâmetros genéticos, do nascimento aos 650 dias de idade de bovinos da raça Nelore criados a pasto em duas regiões de produção do estado de Mato Grosso do Sul, Brasil (Foram analisados 233 registros de peso provenientes de 47.459 animais). Os parâmetros genéticos foram determinados por meio de regressão aleatória, utilizando polinômios ortogonais de Legendre de ordem cúbica, a idade a pesagem foi considerada no modelo como efeito fixo para modelar a trajetória média de crescimento. Nos modelos, os efeitos de grupo de contemporâneos foram considerados como fixos e, como covariáveis, a idade do animal (efeitos linear e quadrático), sendo construídas oito classes etárias. Todos os modelos incluíram os efeitos genético aditivo direto, genético materno e de ambiente permanente direto como aleatórios, e o modelo mais apropriado para descrever os efeitos estudados foi definido de acordo com os critérios AIC e BIC.As estimativas de herdabilidade para peso ao nascimento foram diferentes nas duas regiões produtoras, Campo Grande-Dourados (R1), e Alto Taquari-Bolsão (R2), R1 (0,36 ± 0,02) e R2 (0,28 ± 0,03), e para as idades avançadas ocorreram variações nas estimativas. Em ambas as regiões, os maiores valores de herdabilidade foram aos 650 dias de idade, 0,47 ± 0,03 e 0,65 ± 0,02, respectivamente para R1 e R2, sendo a alta...(AU)

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The objective of this work was to estimate growth curves and genetic parameters from birth to 650 days of age of Nelore cattle raised in pasture in two production regions of the Mato Grosso do Sul State, Brazil (233,835 weight records from 47,459 cattle were analyzed). Genetic parameters were determined by random regression using Legendre orthogonal polynomials of cubic order, and age at weighing was considered in the model as a fixed effect to model the average growth trajectory. In the models, the effects of the contemporary group were considered as fixed and, as covariates, the animal age at weighing and the cow age at calving were nested in the animal age class (linear and quadratic effects), forming eight age classes. All models included the direct genetic additive, maternal genetic, and animal permanent environment as random effects, and the most appropriate model to describe the studied effects was defined according to the AIC and BIC criteria. Heritability estimates for birth weight varied between the two production regions, Campo Grande-Dourados (R1) and Alto Taquari-Bolsão (R2) and R1 (0.36 ± 0.02) and R2 (0.28 ± 0.03), and there were variations in the estimates at advanced ages. In both regions, the highest heritability values at 650 days of age were 0.47 ± 0.03 and 0.65 ± 0.02 for R1 and R2, respectively, with high heritability reflecting the high values of additive...

O objetivo do trabalho foi estimar curvas de crescimento e parâmetros genéticos, do nascimento aos 650 dias de idade de bovinos da raça Nelore criados a pasto em duas regiões de produção do estado de Mato Grosso do Sul, Brasil (Foram analisados 233 registros de peso provenientes de 47.459 animais). Os parâmetros genéticos foram determinados por meio de regressão aleatória, utilizando polinômios ortogonais de Legendre de ordem cúbica, a idade a pesagem foi considerada no modelo como efeito fixo para modelar a trajetória média de crescimento. Nos modelos, os efeitos de grupo de contemporâneos foram considerados como fixos e, como covariáveis, a idade do animal (efeitos linear e quadrático), sendo construídas oito classes etárias. Todos os modelos incluíram os efeitos genético aditivo direto, genético materno e de ambiente permanente direto como aleatórios, e o modelo mais apropriado para descrever os efeitos estudados foi definido de acordo com os critérios AIC e BIC.As estimativas de herdabilidade para peso ao nascimento foram diferentes nas duas regiões produtoras, Campo Grande-Dourados (R1), e Alto Taquari-Bolsão (R2), R1 (0,36 ± 0,02) e R2 (0,28 ± 0,03), e para as idades avançadas ocorreram variações nas estimativas. Em ambas as regiões, os maiores valores de herdabilidade foram aos 650 dias de idade, 0,47 ± 0,03 e 0,65 ± 0,02, respectivamente para R1 e R2, sendo a alta...

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Longer-lived cows tend to be more profitable and the stayability trait is a selection criterion correlated to longevity. An alternative to the traditional approach to evaluate stayability is its definition based on consecutive calvings, whose main advantage is the more accurate evaluation of young bulls. However, no study using this alternative approach has been conducted for Zebu breeds. Therefore, the objective of this study was to compare linear random regression models to fit stayability to consecutive calvings of Guzerá, Nelore and Tabapuã cows and to estimate genetic parameters for this trait in the respective breeds. Data up to the eighth calving were used. The models included the fixed effects of age at first calving and year-season of birth of the cow and the random effects of contemporary group, additive genetic, permanent environmental and residual. Random regressions were modeled by orthogonal Legendre polynomials of order 1 to 4 (2 to 5 coefficients) for contemporary group, additive genetic and permanent environmental effects. Using Deviance Information Criterion as the selection criterion, the model with 4 regression coefficients for each effect was the most adequate for the Nelore and Tabapuã breeds and the model with 5 coefficients is recommended for the Guzerá breed. For Guzerá, heritabilities ranged from 0.05 to 0.08, showing a quadratic trend with a peak between the fourth and sixth calving. For the Nelore and Tabapuã breeds, the estimates ranged from 0.03 to 0.07 and from 0.03 to 0.08, respectively, and increased with increasing calving number. The additive genetic correlations exhibited a similar trend among breeds and were higher for stayability between closer calvings. Even between more distant calvings (second v. eighth), stayability showed a moderate to high genetic correlation, which was 0.77, 0.57 and 0.79 for the Guzerá, Nelore and Tabapuã breeds, respectively. For Guzerá, when the models with 4 or 5 regression coefficients were compared, the rank correlations between predicted breeding values for the intercept were always higher than 0.99, indicating the possibility of practical application of the least parameterized model. In conclusion, the model with 4 random regression coefficients is recommended for the genetic evaluation of stayability to consecutive calvings in Zebu cattle.

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ABSTRACT The distribution of externally studentized midrange was created based on the original studentization procedures of Student and was inspired in the distribution of the externally studentized range. The large use of the externally studentized range in multiple comparisons was also a motivation for developing this new distribution. This work aimed to derive analytic equations to distribution of the externally studentized midrange, obtaining the cumulative distribution, probability density and quantile functions and generating random values. This is a new distribution that the authors could not find any report in the literature. A second objective was to build an R package for obtaining numerically the probability density, cumulative distribution and quantile functions and make it available to the scientific community. The algorithms were proposed and implemented using Gauss-Legendre quadrature and the Newton-Raphson method in R software, resulting in the SMR package, available for download in the CRAN site. The implemented routines showed high accuracy proved by using Monte Carlo simulations and by comparing results with different number of quadrature points. Regarding to the precision to obtain the quantiles for cases where the degrees of freedom are close to 1 and the percentiles are close to 100%, it is recommended to use more than 64 quadrature points.

RESUMO A distribuição da midrange estudentizada externamente foi criada com base nos procedimentos de estudentização de Student e foi inspirada na distribuição da amplitude estudentizada externamente. O amplo uso da amplitude estudentizada externamente em comparações múltiplas também foi uma das motivações para desenvolver esta nova distribuição. Neste trabalho objetivou-se derivar expressões analíticas da distribuição da midrange estudentizada externamente, obtendo a função de distribuição, função densidade de probabilidade, função quantil e geradores de números aleatórios. Essa é uma nova distribuição que os não há relatos na literatura especializada. Um segundo objetivo foi construir um pacote R para obter numericamente as funções mencionadas e torná-las disponíveis para a comunidade científica. Os algoritmos foram propostos e implementados usando os métodos de quadratura Gauss-Legendre e Newton-Raphson no software R, resultando no pacote SMR, disponível para baixar na página do CRAN. As rotinas implementadas apresentaram alta acurácia, sendo verificadas usando simulação Monte Carlo e pela comparação com diferentes pontos de quadratura. Quanto a precisão para se obter os quantis da distribuição da midrange estudentizada externamente para 1 grau de liberdade ou percentis próximo de 100%, é sugerido utilizar mais do que 64 pontos de quadratura.

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The objective of this study is to compare random-regression models used to describe changes in evaluation parameters for growth in Tabapuã bovine raised in the Northeast of Brazilian. The M4532-5 random-regression model was found to be best for estimating the variation and heritability of growth characteristics in the animals evaluated. Estimates of direct additive genetic variance increased with age, while the maternal additive genetic variance demonstrated growth from birth to up to nearly 420 days of age. The genetic correlations between the first four characteristics were positive with moderate to large ranges. The greatest genetic correlation was observed between birth weight and at 240 days of age (0.82). The phenotypic correlation between birth weight and other characteristics was low. The M4532-5 random-regression model with 39 parameters was found to be best for describing the growth curve of the animals evaluated providing improved selection for heavier animals when performed after weaning. The interpretation of genetic parameters to predict the growth curve of cattle may allow the selection of animals to accelerate slaughter procedures.

Objetivou-se com esta pesquisa comparar diferentes modelos de regressão aleatória e determinar o mais adequado para descrever mudanças nos parâmetros de avaliação do crescimento de bovinos da raça Tabapuã criados no Nordeste brasileiro. O modelo de regressão aleatória M4532-5 foi definido como sendo o de melhor ajuste para descrição das estimativas de variância e herdabilidades das características de crescimento dos animais avaliados. As estimativas de variância genética aditiva direta aumentaram em função da idade, já as de variância genética aditiva materna mostraram crescimento do nascimento até próximo aos 420 dias. As correlações genéticas entre as quatro primeiras características foram positivas e de magnitudes moderada a alta. A maior correlação genética foi observada entre o peso ao nascer e aos 240 dias (0,82). A correlação fenotípica entre peso ao nascimento e demais características foi baixa. O modelo de regressão aleatória M4532-5 com 39 parâmetros apresentou-se como aquele de melhor ajuste para descrever a curva de crescimento dos animais avaliados. Resposta à seleção para obtenção de animais mais pesados será eficiente quando realizada em idades posteriores ao desmame. Ao se avaliar a curva de crescimento de bovinos por meio da interpretação dos parâmetros genéticos estimados, é possível selecionar animais com maior precocidade de abate.

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The objective of this study is to compare random-regression models used to describe changes in evaluation parameters for growth in Tabapuã bovine raised in the Northeast of Brazilian. The M4532-5 random-regression model was found to be best for estimating the variation and heritability of growth characteristics in the animals evaluated. Estimates of direct additive genetic variance increased with age, while the maternal additive genetic variance demonstrated growth from birth to up to nearly 420 days of age. The genetic correlations between the first four characteristics were positive with moderate to large ranges. The greatest genetic correlation was observed between birth weight and at 240 days of age (0.82). The phenotypic correlation between birth weight and other characteristics was low. The M4532-5 random-regression model with 39 parameters was found to be best for describing the growth curve of the animals evaluated providing improved selection for heavier animals when performed after weaning. The interpretation of genetic parameters to predict the growth curve of cattle may allow the selection of animals to accelerate slaughter procedures.(AU)

Objetivou-se com esta pesquisa comparar diferentes modelos de regressão aleatória e determinar o mais adequado para descrever mudanças nos parâmetros de avaliação do crescimento de bovinos da raça Tabapuã criados no Nordeste brasileiro. O modelo de regressão aleatória M4532-5 foi definido como sendo o de melhor ajuste para descrição das estimativas de variância e herdabilidades das características de crescimento dos animais avaliados. As estimativas de variância genética aditiva direta aumentaram em função da idade, já as de variância genética aditiva materna mostraram crescimento do nascimento até próximo aos 420 dias. As correlações genéticas entre as quatro primeiras características foram positivas e de magnitudes moderada a alta. A maior correlação genética foi observada entre o peso ao nascer e aos 240 dias (0,82). A correlação fenotípica entre peso ao nascimento e demais características foi baixa. O modelo de regressão aleatória M4532-5 com 39 parâmetros apresentou-se como aquele de melhor ajuste para descrever a curva de crescimento dos animais avaliados. Resposta à seleção para obtenção de animais mais pesados será eficiente quando realizada em idades posteriores ao desmame. Ao se avaliar a curva de crescimento de bovinos por meio da interpretação dos parâmetros genéticos estimados, é possível selecionar animais com maior precocidade de abate.(AU)

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The aim of this study was to estimate (co)variance components and genetic parameters from birth to yearling weight (550 days of age) in Guzerá cattle, using random regression models. Data set from animals (male and female) born between 1993 and 2011 belonging to ten farms in seven Brazilian States were used. The best-fit model considering direct and maternal genetic effect and permanent environmental animal effect were adjusted by fourth, third, and second order, respectively, using orthogonal polynomials of Legendre. The higher estimated values of direct heritability were observed in birth (0.88) and yearling weight (0.70). The genetic correlations were moderate to high magnitude, remaining up even with the increase in the ages gap.(AU)

O objetivo do presente trabalho foi estimar componentes de (co)variâncias e parâmetros genéticos para características de pesos do nascimento ao sobreano (550 dias de idade) para bovinos da raça Guzerá, por meio de modelos de regressão aleatória. Os dados utilizados são de animais (machos e fêmeas) nascidos entre 1993 e 2011 e pertencentes a dez fazendas de sete estados brasileiros. O modelo de melhor ajuste considerou os efeitos genéticos aditivos diretos e maternos e os de ambiente permanente do animal ajustado usando polinômios ortogonais de Legendre de quarta, terceira e segunda ordem, respectivamente. As maiores estimativas de herdabilidade diretas foram observadas para os pesos ao nascimento (0,88) e ao sobreano (0,70). As correlações genéticas foram de moderada a alta magnitude, mantendo-se elevada mesmo com o aumento da distância entre as idades.(AU)

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The aim of this study was to estimate (co)variance components and genetic parameters from birth to yearling weight (550 days of age) in Guzerá cattle, using random regression models. Data set from animals (male and female) born between 1993 and 2011 belonging to ten farms in seven Brazilian States were used. The best-fit model considering direct and maternal genetic effect and permanent environmental animal effect were adjusted by fourth, third, and second order, respectively, using orthogonal polynomials of Legendre. The higher estimated values of direct heritability were observed in birth (0.88) and yearling weight (0.70). The genetic correlations were moderate to high magnitude, remaining up even with the increase in the ages gap.

O objetivo do presente trabalho foi estimar componentes de (co)variâncias e parâmetros genéticos para características de pesos do nascimento ao sobreano (550 dias de idade) para bovinos da raça Guzerá, por meio de modelos de regressão aleatória. Os dados utilizados são de animais (machos e fêmeas) nascidos entre 1993 e 2011 e pertencentes a dez fazendas de sete estados brasileiros. O modelo de melhor ajuste considerou os efeitos genéticos aditivos diretos e maternos e os de ambiente permanente do animal ajustado usando polinômios ortogonais de Legendre de quarta, terceira e segunda ordem, respectivamente. As maiores estimativas de herdabilidade diretas foram observadas para os pesos ao nascimento (0,88) e ao sobreano (0,70). As correlações genéticas foram de moderada a alta magnitude, mantendo-se elevada mesmo com o aumento da distância entre as idades.

Assuntos

RESUMO

Abstract The aim of this study was to estimate (co)variance components and genetic parameters from birth to yearling weight (550 days of age) in Guzerá cattle, using random regression models. Data set from animals (male and female) born between 1993 and 2011 belonging to ten farms in seven Brazilian States were used. The best-fit model considering direct and maternal genetic effect and permanent environmental animal effect were adjusted by fourth, third, and second order, respectively, using orthogonal polynomials of Legendre. The higher estimated values of direct heritability were observed in birth (0.88) and yearling weight (0.70). The genetic correlations were moderate to high magnitude, remaining up even with the increase in the ages gap.

Resumo O objetivo do presente trabalho foi estimar componentes de (co)variâncias e parâmetros genéticos para características de pesos do nascimento ao sobreano (550 dias de idade) para bovinos da raça Guzerá, por meio de modelos de regressão aleatória. Os dados utilizados são de animais (machos e fêmeas) nascidos entre 1993 e 2011 e pertencentes a dez fazendas de sete estados brasileiros. O modelo de melhor ajuste considerou os efeitos genéticos aditivos diretos e maternos e os de ambiente permanente do animal ajustado usando polinômios ortogonais de Legendre de quarta, terceira e segunda ordem, respectivamente. As maiores estimativas de herdabilidade diretas foram observadas para os pesos ao nascimento (0,88) e ao sobreano (0,70). As correlações genéticas foram de moderada a alta magnitude, mantendo-se elevada mesmo com o aumento da distância entre as idades.

RESUMO

ABSTRACT: The objective of this study was to compare the functions of Wilmink and Ali and Schaeffer with Legendre polynomials in random regression models using heterogeneous residual variances for modeling genetic parameters during the first lactation in the Holstein Friesian breed. Five thousand eight hundred and eighty biweekly records of test-day milk production were used. The models included the fixed effects of group of contemporaries and cow age at calving as covariable. Statistical criteria indicated that the WF.33_HE2, LEG.33_HE2, and LEG.55_HE4 functions best described the changes in the variances that occur throughout lactation. Heritability estimates using WF.33_HE2 and LEG.33_HE2 models were similar, ranging from 0.31 to 0.50. The LEG.55_HE4 model diverged from these models, with higher estimates at the beginning of lactation and lower estimates after the 16th fortnight. The LEG55_HE4, among the three better models indicated by the index, is the one with highest number of parameters (14 vs 34) and resulted in lower estimation of residual variance at the beginning and at the end of lactation, but overestimated heritability in the first fortnight and presented a greater difficulty to model genetic and permanent environment correlations among controls. Random regression models that used the Wilmink and Legendre polynomials functions with two residual variance classes appropriately described the genetic variation during lactation of Holstein Friesians reared in Rio Grande do Sul.

RESUMO: Objetivou-se comparar as funções de Wilmink e Ali e Schaeffer com polinômios de Legendre em modelos de regressão aleatória, utilizando variâncias residuais heterogêneas, para modelar parâmetros genéticos ao longo da primeira lactação na raça Holandesa. Foram utilizados cinco mil oitocentos e oitenta registros quinzenais de produção de leite no dia do controle. Os modelos incluíram os efeitos fixos de grupo de contemporâneos e a idade da vaca ao parto como covariável. Os critérios estatísticos apontaram as funções WF.33_HE2, LEG.33_HE2 e a LEG.55_HE4 como as melhores em descrever as mudanças nas variâncias que ocorrem ao longo da lactação. As herdabilidades estimadas pelos modelos WF.33_HE2 e LEG.33_HE2 foram semelhantes, variando de 0,31 a 0,50. O LEG.55_HE4 divergiu destes, no início da lactação, com estimativas superiores e, a partir da 16ª quinzena, com estimativas inferiores. O LEG55_HE4, entre os três melhores modelos indicados pelo índice, é o mais parametrizado (14 vs 34) e resultou em menores estimativas de variância residual no início e no final da lactação, mas superestimou a herdabilidade na primeira quinzena e apresentou maior dificuldade em modelar as correlações genéticas e de ambiente permanente entre os controles. Os modelos de regressão aleatória que usaram a função de Wilmink e Polinômios de Legendre com duas classes de variâncias residuais descreveram adequadamente a variação genética ao longo da lactação de vacas da raça Holandesa, criadas no Rio Grande do Sul.

RESUMO

The objective of this study was to compare the functions of Wilmink and Ali and Schaeffer with Legendre polynomials in random regression models using heterogeneous residual variances for modeling genetic parameters during the first lactation in the Holstein Friesian breed. Five thousand eight hundred and eighty biweekly records of test-day milk production were used. The models included the fixed effects of group of contemporaries and cow age at calving as covariable. Statistical criteria indicated that the WF.33_HE2, LEG.33_HE2, and LEG.55_HE4 functions best described the changes in the variances that occur throughout lactation. Heritability estimates using WF.33_HE2 and LEG.33_HE2 models were similar, ranging from 0.31 to 0.50. The LEG.55_HE4 model diverged from these models, with higher estimates at the beginning of lactation and lower estimates after the 16th fortnight. The LEG55_HE4, among the three better models indicated by the index, is the one with highest number of parameters (14 vs 34) and resulted in lower estimation of residual variance at the beginning and at the end of lactation, but overestimated heritability in the first fortnight and presented a greater difficulty to model genetic and permanent environment correlations among controls. Random regression models that used the Wilmink and Legendre polynomials functions with two residual variance classes appropriately described the genetic variation during lactation of Holstein Friesians reared in Rio Grande do Sul.(AU)

Objetivou-se comparar as funções de Wilmink e Ali e Schaeffer com polinômios de Legendre em modelos de regressão aleatória, utilizando variâncias residuais heterogêneas, para modelar parâmetros genéticos ao longo da primeira lactação na raça Holandesa. Foram utilizados cinco mil oitocentos e oitenta registros quinzenais de produção de leite no dia do controle. Os modelos incluíram os efeitos fixos de grupo de contemporâneos e a idade da vaca ao parto como covariável. Os critérios estatísticos apontaram as funções WF.33_HE2, LEG.33_HE2 e a LEG.55_HE4 como as melhores em descrever as mudanças nas variâncias que ocorrem ao longo da lactação. As herdabilidades estimadas pelos modelos WF.33_HE2 e LEG.33_HE2 foram semelhantes, variando de 0,31 a 0,50. O LEG.55_HE4 divergiu destes, no início da lactação, com estimativas superiores e, a partir da 16ª quinzena, com estimativas inferiores. O LEG55_HE4, entre os três melhores modelos indicados pelo índice, é o mais parametrizado (14 vs 34) e resultou em menores estimativas de variância residual no início e no final da lactação, mas superestimou a herdabilidade na primeira quinzena e apresentou maior dificuldade em modelar as correlações genéticas e de ambiente permanente entre os controles. Os modelos de regressão aleatória que usaram a função de Wilmink e Polinômios de Legendre com duas classes de variâncias residuais descreveram adequadamente a variação genética ao longo da lactação de vacas da raça Holandesa, criadas no Rio Grande do Sul.(AU)

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Repeated measures from the same individual have been analyzed by using repeatability and finite dimension models under univariate or multivariate analyses. However, in the last decade, the use of random regression models for genetic studies with longitudinal data have become more common. Thus, the aim of this research was to estimate genetic parameters for body weight of four experimental chicken lines by using univariate random regression models. Body weight data from hatching to 84 days of age (n = 34,730) from four experimental free-range chicken lines (7P, Caipirão da ESALQ, Caipirinha da ESALQ and Carijó Barbado) were used. The analysis model included the fixed effects of contemporary group (gender and rearing system), fixed regression coefficients for age at measurement, and random regression coefficients for permanent environmental effects and additive genetic effects. Heterogeneous variances for residual effects were considered, and one residual variance was assigned for each of six subclasses of age at measurement. Random regression curves were modeled by using Legendre polynomials of the second and third orders, with the best model chosen based on the Akaike Information Criterion, Bayesian Information Criterion, and restricted maximum likelihood. Multivariate analyses under the same animal mixed model were also performed for the validation of the random regression models. The Legendre polynomials of second order were better for describing the growth curves of the lines studied. Moderate to high heritabilities (h(2) = 0.15 to 0.98) were estimated for body weight between one and 84 days of age, suggesting that selection for body weight at all ages can be used as a selection criteria. Genetic correlations among body weight records obtained through multivariate analyses ranged from 0.18 to 0.96, 0.12 to 0.89, 0.06 to 0.96, and 0.28 to 0.96 in 7P, Caipirão da ESALQ, Caipirinha da ESALQ, and Carijó Barbado chicken lines, respectively. Results indicate that genetic gain for body weight can be achieved by selection. Also, selection for body weight at 42 days of age can be maintained as a selection criterion.

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