The purpose of this study was to compare estimates of genetic parameters for sequential growth of beef cattle using two models and two data sets. Growth curves of Nellore cattle were analyzed using body weights measured at ages 1 (birth weight) to 733 d. Two data samples were created, one with 71,867 records sampled from all herds (MISS), and the other with 74,601 records sampled from herds with no missing traits (NMISS). Records preadjusted to a fixed age were analyzed by a multiple-trait model (MTM), which included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Analyses were by REML, with five traits at a time. The random regression model (RRM) included the effects of age of animal, contemporary group, age of dam class, additive direct, additive maternal, permanent environment, and maternal permanent environment. All effects were modeled as cubic Legendre polynomials. These analyses were also by REML. Shapes of estimates of variances by MTM were mostly similar for both data sets for all except late ages, where estimates for MISS were less regular, and for birth weight with MISS. Genetic correlations among ages for the direct and maternal effects were less smooth with MISS. Genetic correlations between direct and maternal effects were more negative for NMISS, where few sires were maternal grandsires. Parameter estimates with RRM were similar to MTM cept that estimates of variances showed more artifacts for MISS; the estimates of additive direct-maternal correlations were more negative with both data sets and approached -1.0 for some ages with NMISS. When parameters of a growth model obtained by used for genetic evaluation, these parameters should be examined for consistency with parameters from MTM and prior information, and adjustments may be required to eliminate artifacts.

The objective of this study was to identify issues in genetic evaluation of beef cattle for growth by a random regression model (RRM). Genetic evaluation data included 2,946,847 records of up to nine sequential weights of 812,393 Nellore cattle measured at ages ranging from birth to 733 d. Models considered were a five-trait multiple-trait model (MTM) and a cubic RRM. The MTM included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Both additive effects were assumed correlated. The RRM included the same effects as MTM, with the addition of permanent and random error effects. The purpose of the random error effect, which was in addition to a residual effect with constant variance, was to model heterogeneous residual variances. All effects in RRM were modeled as cubic Legendre polynomials. Expected progeny differences (EPD) were obtained iteratively using a preconditioned conjugate gradient algorithm. Numerically accurate solutions with RRM were not obtained until the random regressions were orthogonalized. Computing requirements of RRM were reduced by more than 50%, without affecting the accuracy by removing regressions corresponding to very low eigen-values and by replacing the random error effects with weights. Afterward, the correlations between EPD from RRM and from MTM for EPD on selected weights were between 0.84 and 0.89. For sires with at least 50 progeny, these correlations increased to 0.92 to 0.97. Low correlations were caused by differences in parameters. The RRM applied to growth i s prone to numerical problems. Estimates of EPD with RRM may be more accurate than those with MTM only if accurate parameters are applied.

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.

Estimativas de componentes de (co)variância para peso e escores visuais de conformação frigorífica em bovinos Nelore RESUMOEstimaram-se os componentes de (co)variância e herdabilidade da conformação frigorífica à desmama (CFD), conformação frigorífica ao sobreano (CFS), peso à desmama (PD) e peso ao sobreano (PS) de animais Nelore, e as correlações genéticas entre essas características. Um modelo animal multicaracterística foi proposto para analisar 6.397 informações de peso e escores visuais de conformação frigorífica, obtidas à desmama e ao sobreano. Esse modelo incluiu os efeitos aleatórios genético aditivo direto, genético aditivo materno, ambiente permanente materno e residual, além dos efeitos fixos de grupo contemporâneo e das covariáveis idade da mãe ao parto  para peso e conformação frigorífica à desmama e ao sobreano  e idade do animal à data da avaliação  para conformação frigorífica, à desmama e ao sobreano. As herdabilidades estimadas para CFD, CFS, PD e PS foram, respectivamente, 0,13, 0,25, 0,22 e 0,29. Correlações genéticas positivas e de alta magnitude entre as características de peso e as características de avaliação visual sugerem que a seleção para uma delas pode resultar em resposta indireta na outra. A característica de conformação frigorífica pode ser selecionada em idade mais precoce em razão da correlação genética alta e positiva entre mensurações feitas nas duas idades estudadas.Palavras-chave: bovino de corte, conformação frigorífica, correlação genética, escore visual, herdabilidade ABSTRACT

Growth curves of Nellore cattle were analyzed using body weights measured at ages ranging from 1 day (birth weight) to 733 days. Traits considered were birth weight, 10 to 110 days weight, 102 to 202 days weight, 193 to 293 days weight, 283 to 383 days weight, 376 to 476 days weight, 551 to 651 days weight, and 633 to 733 days weight. Two data samples were created: one with 79,849 records from herds that had missing traits and another with 74,601 from herds with no missing traits. Records preadjusted to a fixed age were analyzed by a multiple trait model (MTM), which included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Analyses were carried out by a Bayesian method for all nine traits. The random regression model (RRM) included the effects of age of animal, contemporary group, age of dam class, additive direct, permanent environment, additive maternal, and maternal permanent environment. Legendre cubic polynomials were used to describe random effects. MTM estimated covariance components and genetic parameters for birth weight and sequential weights and RRM for all ages. Due to the fact that covariance components based on RRM were inflated for herds with missing traits, MTM should be used and converted to covariance functions.