Fitting of non-linear models to characterize the growth of five zebu cattle breeds

The analyzed database contained growth information of five zebu breeds with live weight (LW) measurements in the range from birth to 1095 days of age. The objectives of this study were to identify the non-linear model (NLM) with the best fit to describe the growth curve. The number of LWs analyzed, per breed and sex (males and females), were: 21152 and 8269 in Indubrasil (IND), 40071 and 20968 in Nelore (NEL), 20143 and 12294 in Gyr (GYR), 5585 and 4727 in Guzerat (GUZ), 29310 and 9347 in Sardo Negro (SAN). The evaluated NLMs were Brody (BRO), Bertalanffy, Gompertz, Mitscherlich (MIT), Meloun III (ME3), and Logistic. The models fitness was compared using the: Akaike and Bayesian information criteria, coefficient of determination, Durbin-Watson statistic, mean prediction error, prediction error variance, standard error of the model. The linear relationship between the LW and the predicted data (PRE) was analyzed. All the NLMs showed a goodness of fit of 94 % or higher and tend to underestimate the predictions. A positive autocorrelation in the residuals was observed in IND and GUZ females, and in GUZ males. For both sexes, in IND and GUZ the selected model was BRO, for GYR and SAN was MIT. In NEL, MIT was selected for males and ME3 for females. For the estimated adult weight, the mean values (males and females) were: 744.9 and 506.4 kg in IND, 804.5 and 393.5 kg in NEL, 695.4 and 527.3 kg in GYR, 855.0 and 754.5 kg in GUZ, 871.6 and 615.8 kg in SAN. With the selected models, the populations show a growth curve without an inflection point, and a constant growth rate. The correlation between growth rate and adult weight was negative in all the analyses. The average correlation between LW and PRE was 0.87. The PRE explained, on average, 76 % of the LW variability. In the analysis of predictive capacity, the LW change rate per change unit in the PRE showed a one-to-one relationship in almost every analysis, for GUZ, SAN, and GYR males, the LW change was 1.09, 1.03, and 1.01, respectively.