Aplicação de modelos de regressão aleatória utilizando diferentes estruturas de dados / Application of random regression models using different data structures

Foram utilizadas 3.202 primeiras lactações de vacas da raça Holandesa de quatro fazendas da região Sudeste, para verificar a influência da estrutura de dados de produção de leite sobre os parâmetros genéticos. Foram testados quatro arquivos com diferentes estruturas: controles semanais (CS), arquivo mensal (CM), bimestral (CB) e trimestral (CT), com 122.842, 30.883, 15.837 e 12.702 controles, respectivamente. Um modelo de regressão aleatória foi empregado nas análises, considerando os efeitos genético aditivo e o de ambiente permanente de animal, como aleatórios. Os efeitos fixos, grupos de contemporâneos (GC) foram comuns para todos os arquivos de dados e foram compostos por fazenda, mês e ano do controle, além da co-variável idade da vaca ao parto (regressão linear e quadrática). As estimativas de herdabilidade apresentaram tendências mais semelhantes entre os arquivos de dados CS, CM e CB. O arquivo de dados CB apresentou estimativas de parâmetros genéticos com as mesmas tendências e magnitudes que os arquivos CS e CM, permitindo afirmar que não houve influência da estrutura dos dados sobre as estimativas dos componentes de (co)variância e que o controle leiteiro poderia ser realizado em uma estrutura CB.

A total of 3.035 lactations of Holstein cows from four farms in the Southeast, to check the influence of data structure of milk yield on the genetic parameters. Four dataset with different structures were tested, weekly controls (CW) with 122.842 controls, monthly controls (CM) 30.883, bimonthly controls (CB) with 15,837 and quarterly controls (CQ) with 12,702. The random regression model was used and was considered as random additive genetic and permanent environment effects, fixed effects of the contemporary groups (herd-year-month of test-day) and age of cow (linear and quadratic effects). Heritability estimates showed similar trends among the data files analyzed, with the greatest similarity between dataset CS, CM and CB. The dataset submitted all the CB estimates of genetic parameters analyzed with the same trend and similar magnitude to the CS and CM dataset, allowing the claim that there was no influence of the data structure on estimates of covariance components for the dataset CS, CM and CB. Thus, milk recording could be accomplished in a CB structure.

Parâmetros genéticos para diferentes relações de peso ao nascer e à desmama em vacas da raça Nelore / Genetic parameters for different birth and weaning weight ratios in Nelore cows

O presente estudo foi desenvolvido com o objetivo de estimar herdabilidade e repetibilidade para diferentes medidas de eficiência produtiva de vacas e determinar a melhor maneira de calcular as relações de peso, visando a sua utilização como critério de seleção em rebanhos da raça Nelore. Os dados analisados são de animais da raça Nelore, pertencentes ao Projeto de Seleção das Raças Zebuínas e Caracu do Centro APTA Bovinos de Corte, do Instituto de Zootecnia de Sertãozinho. Os animais são selecionados para maior peso ao sobreano (rebanhos NeS e NeT, analisados como um único rebanho) e para peso ao sobreano próximo da média (NeC) do grupo de contemporâneos, desde 1980. As características utilizadas no estudo foram: 1) RPN = relação de peso ao nascer do bezerro / peso da vaca ao parto; 2) RPN2 = relação do peso ao nascer do bezerro / peso metabólico da vaca ao parto; 3) RPD = relação de peso à desmama do bezerro / peso da vaca à desmama; e 4) RPD2 = relação do peso à desmama do bezerro / peso metabólico da vaca à desmama. Os parâmetros genéticos foram estimados considerando dois arquivos: vacas com bezerros (CB) e vacas com e sem bezerros (SB). A RPN e a RPN2 foram calculadas somente no arquivo CB, enquanto que RPD e RPD2 foram calculadas em ambos os arquivos (CB e SB). Os parâmetros genéticos foram estimados pelo método da máxima verossimilhança restrita. As estimativas de herdabilidade para as características RPN; RPN2; RPD_CB; RPD2_CB; RPD_SB e RPD2_SB foram: 0,17±0,02; 0,16±0,02; 0,22±0,04; 0,19±0,03; 0,20±0,01 e 0,16±0,01, respectivamente. As repetibilidades estimadas variaram de 0,22 a 0,68. A utilização das relações de peso como critério de seleção deve promover, a longo prazo, melhorias na eficiência produtiva das vacas. As relações de peso têm sido consideradas apenas como informações para o descarte de vacas em alguns programas de seleção, mas poderiam ser incluídas em índices de seleção, principalmente quando calculada considerando o peso metabólico da vaca à desmama, incluindo tanto as vacas que desmamaram um bezerro, quanto aquelas que falharam em desmamar.

The objective of this study was to estimate heritability and repeatability for different measures of cows' productive efficiency and determine the best way to calculate the weight ratios, in order to use as selection criteria in Nelore herds. Data of Nelore animals from Centro APTA Bovinos de Corte-Sertãozinho, Instituto de Zootecnia were analyzed. The animals are selected for higher yearling weight (NeS and NeT herds, considered as a single herd in this paper) and, for mean yearling weight (NeC) within contemporary group, since 1980. The traits used in this study were: 1) RPN = ratio of birth weight of the calf / cow weight at calving; 2) RPN2 = ratio of birth weight of the calf / metabolic cow weight at calving; 3) RPD = ratio of weaning weight of the calf / cow weight at weaning and, 4) RPD2 = ratio of weaning weight of calf / metabolic cow weaning weight. For estimate genetic and phenotypic parameters, were considered two files: cows with calves (CB) or with and without calves (SB). The RPN and RPN2 were calculated only on CB file, and RPD and RPD2 were calculated in both files (CB and SB). Genetic parameters were estimated by restricted maximum likelihood. Estimates of heritability for traits RPN; RPN2; RPD_CB; RPD2_CB; RPD_SB and RPD2_SB were: 0.17±0.02, 0.16±0.02, 0.22±0.04, 0.19±0.03, 0.20±0.01 and 0.16±0.01, respectively. The repeatability estimates ranged from 0.22 to 0.68. The use of weight ratios as selection criteria should promote, at long-term, improvements in production efficiency. In some breeding programs, weight ratios have been considered only as information for disposal of cows, but could be included in selection indices, especially if it is calculated considering the metabolic weight of cow at weaning from both cows, that weaned a calf as those that failed to wean.

Aplicação de modelos não-lineares para descrever a evolução de características de crescimento e carcaça em bovinos da raça Hereford / Application of nonlinear models to describe the evolution of growth and carcass traits in Hereford cattle

Este trabalho foi desenvolvido com o objetivo de estudar a evolução das características de crescimento e carcaça em função da idade em bovinos da raça Hereford, utilizando modelos não-lineares. Foram utilizados dados de 240 bovinos machos (castrados) da raça Hereford, pertencentes à fazenda Experimental "La Estanzuela" do INIA, Colonia, Uruguai. As características começaram a ser mensuradas a partir da desmama de animais com aproximadamente seis meses de idade, até o abate (dois anos de idade). As medições de peso foram realizadas a cada 15±3 dias durante todo o período e sem jejum prévio. As mensurações de área de olho de lombo, obtidas por ultrassom, e altura dos animais foram obtidas a cada 90 dias, sendo que as medidas de ultrassom foram tomadas entre a 12ª e 13ª costelas. Os modelos não-lineares utilizados foram os modelos de Brody, Gompertz, Logístico e Von Bertalanffy. Para as características peso, altura e área de olho de lombo, todos os modelos avaliados atingiram a convergência. Para descrever a evolução dos dados de peso e área de olho de lombo em função da idade, o modelo de Von Bertalanffy foi o mais indicado, e os modelos de Brody e Logístico mostraram o pior ajuste, respectivamente. A evolução da altura dos animais desde o desmame até os dois anos de idade pode ser modelada através de qualquer um dos modelos não-lineares considerados neste estudo.

The objective of this research was to study the evolution of growth and carcass traits as a function of age in Hereford cattle using nonlinear models. Records from 240 Hereford steers (castrated), belonging to the experimental station "La Estanzuela" of INIA Uruguay, were utilized. The animals were measured from weaning, approximately at 6 months of age, to slaughter (two years of age). The animals were weighed, without fasting, every 15±3 days throughout the period. The measurements of ribeye loin area (between the 12th and 13th rib) were obtained by ultrasound every 90 days. The height of the animals was obtained every 90 days. The Brody, Gompertz, Logistic and Von Bertalanffy nonlinear models were applied to describe the trajectory of weight, height and ribeye loin area along the age. For height, weight and ribeye loin area, all the models reached the convergence. To describe the evolution of weight and ribeye loin area, the Von Bertalanffy nonlinear model was the most suitable. For weight and ribeye loin area, the Brody and Logistic nonlinear models have shown the worst fit, respectively. The height trajectory from weaning until two years of age can be modeled by any of the nonlinear models considered in this research.

Effect of lactation length adjustment procedures on genetic parameter estimates for buffalo milk yield

The objectives of this study were to estimate the genetic parameters for milk yield unadjusted and adjusted for days in milk and, subsequently, to assess the influence of adjusting for days in milk on sire rank. Complete lactations from 90 or 150 days of lactation to 270 or 350 days in milk were considered in these analyses. Milk yield was adjusted for days in milk by multiplicative correction factors, or by including lactation length as a covariable in the model. Milk yields adjusted by different procedures were considered as different traits. Heritability estimates varied from 0.17 to 0.28. Genetic correlation estimates between milk yields unadjusted and adjusted for days in milk were greater than 0.82. Adjusting for days in milk affected the parameter estimates. Multiplicative correction factors produced the highest heritability estimates. More reliable breeding value estimates can be expected by including short length lactation records in the analyses and adjusting the milk yields for days in milk, regardless of the method used for the adjustment. High selection intensity coupled to the inclusion of short length lactations and adjustment with multiplicative factors can change the sire rank..

Genetic parameters and relationships between growth traits and scrotal circumference measured at different ages in Nellore cattle

Records from 106,212 Nellore animals, born between 1998 and 2006, were used to estimate (co)variance components and genetic parameters for birth weight (BW), average weight gains from birth to weaning (GBW), average weight gains from weaning to after yearling (GWAY), weaning hip height (WHH), postweaning hip height (PHH) and scrotal circumferences at 9 (SC9), 12 (SC12) and 15 (SC15) months of age. (Co)variance components were estimated by an animal model using multi-trait analysis. Heritability estimates for BW, GBW, GWAY, WHH, PHH, SC9, SC12 and SC15 were 0.31 ± 0.01; 0.25 ± 0.02; 0.30 ± 0.04; 0.51 ± 0.04; 0.54 ± 0.04; 0.39 ± 0.01; 0.41 ± 0.01 and 0.44 ± 0.02, respectively. Genetic correlations between growth traits ranged from 0.09 ± 0.01 to 0.88 ± 0.01, thereby implying that, at any age, selection to increase average weight gains will also increase stature. Genetic correlations between BW and average weight gains with scrotal circumferences were all positive and moderate (0.15 ± 0.03 to 0.38 ± 0.01). On the other hand, positive and low genetic associations were estimated between hip height and scrotal circumference at different ages (0.09 ± 0.01 to 0.17 ± 0.02). The results of this study pointed out that selection to larger scrotal circumferences in males will promote changes in average weight gains. In order to obtain Nellore cattle with the stature and size suitable for the production system, both weight gain and hip height should be included in a selection index.

Genetic parameters for milk, fat and protein yields in Murrah buffaloes (Bubalus bubalis Artiodactyla, Bovidae)

The objective of the present study was to estimate genetic parameters for test-day milk, fat and protein yields and 305-day-yields in Murrah buffaloes. 4,757 complete lactations of Murrah buffaloes were analyzed. Co-variance components were estimated by the restricted maximum likelihood method. The models included additive direct genetic and permanent environmental effects as random effects, and the fixed effects of contemporary group, milking number and age of the cow at calving as linear and quadratic covariables. Contemporary groups were defined by herd-year-month of test for test-day yields and by herd-year-season of calving for 305-day yields. The heritability estimates obtained by two-trait analysis ranged from 0.15 to 0.24 for milk, 0.16 to 0.23 for protein and 0.13 to 0.22 for fat, yields. Genetic and phenotypic correlations were all positive. The observed population additive genetic variation indicated that selection might be an effective tool in changing population means in milk, fat and protein yields.

Bayesian inference in genetic parameter estimation of visual scores in Nellore beef-cattle

The aim of this study was to estimate the components of variance and genetic parameters for the visual scores which constitute the Morphological Evaluation System (MES), such as body structure (S), precocity (P) and musculature (M) in Nellore beef-cattle at the weaning and yearling stages, by using threshold Bayesian models. The information used for this was gleaned from visual scores of 5,407 animals evaluated at the weaning and 2,649 at the yearling stages. The genetic parameters for visual score traits were estimated through two-trait analysis, using the threshold animal model, with Bayesian statistics methodology and MTGSAM (Multiple Trait Gibbs Sampler for Animal Models) threshold software. Heritability estimates for S, P and M were 0.68, 0.65 and 0.62 (at weaning) and 0.44, 0.38 and 0.32 (at the yearling stage), respectively. Heritability estimates for S, P and M were found to be high, and so it is expected that these traits should respond favorably to direct selection. The visual scores evaluated at the weaning and yearling stages might be used in the composition of new selection indexes, as they presented sufficient genetic variability to promote genetic progress in such morphological traits.

Modelos de dimensão finita para a estimação de parâmetros genéticos para a produção de leite de primeiras lactações de vacas da raça Holandesa / Finite dimension models to estimate genetic parameters for first lactation milk yields of Holstein cows

Foram estimados parâmetros genéticos para produção de leite acumulada até 305 dias (P305) e produção de leite no dia do controle (PLDC) de 50.171 controles mensais de 9.281 primeiras lactações de vacas da raça Holandesa. A P305 e as PLDC foram analisadas por meio de modelo animal uni e bicaracterísticas. Para a P305 o modelo incluiu como aleatório, o efeito genético e como efeitos fixos o grupo de contemporâneos e a covariável idade da vaca ao parto. Para as PLDC foi usado o mesmo modelo descrito para a P305, incluindo como covariável o número de dias em lactação. Os componentes de variância foram estimados pelo Método da Máxima Verossimilhança Restrita. As estimativas de herdabilidade (h²) para as PLDC oscilaram entre 0,07 e 0,19 em análises unicaracterísticas e, de 0,12 a 0,22 nas bicaracterísticas. Para a P305, as h² resultantes das análises uni-característica e bicaracterística foram 0,26 e 0,27, respectivamente. As correlações genéticas das PLDC com a P305 foram todas positivas e elevadas, variando de 0,63 a 1,00. As correlações genéticas entre as PLDC variaram de 0,30 a 1,00. A seleção para a P305 parece ser o melhor critério de seleção a ser adotado, uma vez que proporciona maiores ganhos genéticos para as produções de leite em, praticamente, todos os controles da lactação.

Genetic parameters for 50,171 first lactation test-day milk yields and 305 day milk yield (Y305) of 9,281 Holstein cows were estimated, applying uni and bi-trait animal models. The model for Y305 included the additive genetic effect as random and the fixed effects of contemporary group and age of cow at calving as covariable. For TDMY the same animal model described for Y305 was used, including days in milk as covariable. Variance components were estimated by Restricted Maximum Likelihood. Heritability estimates obtained for TDMY ranged from 0.07 to 0.19 and from 0.12 to 0.22 by uni-trait and bi-trait analysis, respectively. Heritability for Y305 was 0.26 by uni-trait and 0.27 by bi-trait analysis. The genetic correlations between TDMY and Y305 were all positive and high, ranging from 0.63 to 1.00. The genetic correlations between TDMY ranged from 0.30 to 1.00. Selection for Y305 seems to be the best selection criterion to be adopted, since it provides larger genetic gain for milk productions in, practically, all test days.

Variance component estimates applying random regression models for test-day milk yield in Caracu heifers (Bos taurus Artiodactyla, Bovidae)

Random regression models (RRM) were used to estimate covariance functions for 2,155 first-lactation milk yields of native Brazilian Caracu heifers. The models included contemporary group (defined as year-month of test and paddock) fixed effects, and quadratic effect of age of cow at calving. Genetic and permanent environmental effects were fitted by a random regression model and Legendre polynomials of days in milk (DIM). Schwarz's Bayesian information criteria (BIC) indicated that the best RRM assumed a six coefficient function for both random effects and a sixth order variance function for residual structure. Akaike's information criteria suggested a model with the same number of coefficients for both effects and a residual structure fitted by a step function with 15 variances. Phenotypic, additive genetic, permanent environmental and residual variances were higher at the beginning and declined during lactation. The RRM heritability estimates were 0.09 to 0.26 and generally higher at the beginning and end of lactation. Some unexpected negative genetic correlations emerged when higher order covariance functions were used. A model with four coefficients for additive genetic covariance function explains more parsimoniously the changes in genetic variation with DIM since the genetic parameter was more acceptable and BIC was close to that for a six coefficient covariance function.

Test-day milk yield as a selection criterion for dairy buffaloes (Bubalus bubalis Artiodactyla, Bovidae)

Due to the great demand for buffalo milk by-products the interest in technical-scientific information about this species is increasing. Our objective was to propose selection criteria for milk yield in buffaloes based on total milk yield, 305-day milk yield (M305), and test-day milk yield. A total of 3,888 lactations from 1,630 Murrah (Bubalus bubalis) cows recorded between 1987 and 2001, from 10 herds in the State of São Paulo, Brazil, were analyzed. Covariance components were obtained using the restricted maximum likelihood method applied to a bivariate animal model. Additive genetic and permanent environmental effects were considered as random, and contemporary group and lactation order as fixed effects. The heritability estimates were 0.22 for total milk yield and 0.19 for M305. For test-day yields, the heritability estimates ranged from 0.12 to 0.30, with the highest values being observed up to the third test month, followed by a decline until the end of lactation. The present results show that test-day milk yield, mainly during the first six months of lactation, could be adopted as a selection criterion to increase total milk yield.

Maternal effects on weaning weight of mice

A importância do efeito maternal sobre o peso à desmama foi analisada em uma populaçäo de camundongos selecionada para esta característica, utilizando-se um total de 7042 dados. O peso individual à desmama foi significativamente influenciado por sexo, classe de tamanho da ninhada ao nascer, numero de geraçöes de seleçäo bem como pela endogamia da mäe, efeitos linear e quadrático. A endogamia do indivíduo näo foi significativa para o peso à desmama. Foram estimadas as covariàncias entre meio irmäos paternos, irmäos germanos, mäe-descendente e indivíduos com o mesmo avô materno. As covariâncias entre parentes estimadas, foram consideradas como variáveis dependentes e os coeficientes teóricos dos componentes causais de variância genética e de ambiente, como variáveis independentes em uma série de equaçöes. A partir dos componentes causais foram estimados os coeficientes de herdabilidade dos efeitos maternal e direto, cujos valores foram 0,286 e 0.275 respectivamente. O componente de variância de ambiente comum a membros da mesma ninhada, foi responsável por 41,83% da variância fenotípica, constituindo-se na principal fonte de variaçäo para o peso à desmama. A covariância genética entre os efeitos maternal e direto foi negativa, sendo o coeficiente de correlaçäo igual a -0,652. A herdabilidade total do peso à desmama foi de 0.79, näo chegando a 30% da magnitude do coeficiente de herdabilidade estimado por correlaçäo entre meio-irmäos paternos

Fatores genéticos e de ambiente que influenciam os componentes da curva de lactaçäo de bovinos da raça Holandesa / Genetic and environmental factors affecting the lactation curve components of Holstein cattle

Estudaram-se pelo método dos quadrados mínimos 1710 lactaçöes completas de 672 vacas da raça Holandesa, filhas de 75 touros, distribuidas em sete anos. As médias ajustadas para as características produçäo total de leite (PTL), produçäo inicial ascendente (PI), produçäo no pico da lactaçäo (PP) e persistência da lactaçäo (P60) foram 5003,10 ñ 120,54 kg/lactaçäo, 22,53 ñ 0,42 kg/dia, 24,22 ñ 0,41 kg/dia e 2,72 ñ 0,61, respectivamente. As médias observadas de duraçäo da lactaçäo e da fase ascendente foram: 312,52 ñ 50,46 dias e 69,48 ñ 5,98 dias, respectivamente. O ano do parto e a idade da vaca afetaram, significativamente, todas as características estudadas. A estaçäo de pariçäo foi uma importante fonte de variaçäo somente para a PI e P60. Os coeficientes de repetibilidade estimados foram 0,50 ñ 0,03, 0,26 ñ 0,03, 0,33 ñ 0,03 e 0,24 ñ 0,03, para PTL, PI, PP e P60, respectivamente. As herdabilidades foram 0,27 ñ 0,11, 0,17 ñ 0,09, 0,23 ñ 0,10 e 0,13 ñ 0,08, na mesma ordem da citaçäo anterior. As correlaçöes genéticas entre PTL e demais características foram positivas e apresentaram valores moderados. Os coeficientes de herdabilidade estimados para as características estudadas e as correlaçöes genéticas e fenotípicas entre as carcterísticas que compoem a curva de lactaçäo e a PTL indicaram a possibilidade de seleçäo indireta para a PTL utilizando-se, como critério, os componentes da curva