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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.

Estimaram-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.

Expected progeny differences (EPD) of Nellore cattle estimated by random regression model (RRM) and multiple trait model (MTM) were compared. Genetic evaluation data included 3,819,895 records of up nine sequential weights of 963,227 animals measured at ages ranging from one day (birth weight) to 733 days. Traits considered were weights at birth, ten to 110-day old, 102 to 202-day old, 193 to 293-day old, 283 to 383-day old, 376 to 476-day old, 551 to 651-day old, and 633 to 733-day old. Seven data samples were created. Because the parameters estimates biologically were better, two of them were chosen: one with 84,426 records and another with 72,040. Records preadjusted to a fixed age were analyzed by a 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 REML, with five traits at a time. The RRM included the effects of age of animal, contemporary group, age of dam class, additive direct, permanent environment, additive maternal, and maternal permanent environment. Different degree of Legendre polynomials were used to describe random effects. MTM estimated covariance components and genetic parameters for weight at birth and sequential weights and RRM for all ages. Due to the fact that correlation among the estimates EPD from MTM and all the tested RM were not equal to 1.0, it is not possible to recommend RRM to genetic evaluation to large data sets.Compararam-se as diferenças esperadas nas progênies (DEPs) de gado Nelore, estimadas por meio de um modelo de características múltiplas (MTM), com um modelo de regressão aleatória (RRM). Foram utilizados 3.819.895 dados de peso corporal sequenciais para a avaliação genética de 963.227 animais, coletados do nascer aos 733 dias de idade. As características consideradas foram: peso ao nascer e pesos dos 10 aos 110, dos 102 aos 202, dos 193 aos 293, dos 283 aos 383, dos 376 aos 476, dos 467 aos 567, dos 551 aos 651, e dos 633 aos 733 dias. Sete amostras foram geradas. Duas amostras resultaram em estimativas de parâmetros mais consistentes do ponto de vista biológico, sendo, portanto consideradas representativas da população em estudo. A primeira amostra constituiu-se de 84.426 medidas, e a segunda, de 72.040. Os pesos pré-ajustados para as idades fixas foram analisados por meio de um MTM, com cinco características por processamento, no qual se incluíram efeito de grupo contemporâneo, classe de idade da vaca, aditivo direto, aditivo materno e ambiente materno permanente, utilizando-se a metodologia de máxima verossimilhança restrita (REML). Diferentes graus dos polinômios de Legendre foram utilizados em um RRM, para os efeitos aleatórios. As correlações entre as DEPs estimadas por meio do modelo para características múltiplas e de regressão aleatória não foram iguais a 1,0, portanto, não se recomenda a utilização dos modelos de regressão aleatória para avaliação genética para grande massa de dados.

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.