Growth Curve Modeling in Holstein Dairy Calves Using Non-Linear Functions

Background: A growth curve describes body weight changes over time or age using mathematical parameters that are capable of biological interpretation.Today, several growth curves, including Logistic, Richards, Gompertz, Von Bertalanffy, and Brody curves, are used to describe growth in animals and plants.These curves include parameters that can be considered new traits.Regression coefficients and growth parameters play an important role in decisionmaking for management, feeding, breeding, and genetic improvement programs; however, these growth rates vary depending on the breed, individual, and environment.Since the growth of different animals has different growth curves, the process of selecting growth curve models is necessary to determine which one works best under the study conditions.Growth curve parameters are heritable, and the shape of the growth curve can be changed and growth can be improved through selection.The parameter A in the growth curve indicates the asymptotic weight at which the animal reaches the maximum weight of its period.The parameter B is the time-scale parameter (integration constant), which describes the time for an individual to reach its maximum growth rate, characterizing the first part of growth before the point of inflection.The k coefficient is the mature growth rate that characterizes the second part of the growth in which the growth rate decreases until the individual reaches the asymptotic or mature weight (A).This study aims to investigate and determine the best function that represents the growth pattern of dairy calves from birth to weaning to use this information in managing dairy calves and commercial purposes.Methods: In this research, the weight data of 45 dairy calves were used to compare the performance of non-linear models in growth curve analysis and to identify the best growth pattern.The studied non-linear models included logistic, Richards, Gompertz, von Bertalanffy, and Brody models.The non-linear models were fitted using the non-linear least squares (NLIN) procedure of SAS software.The best model was selected using goodness of fit statistics, including the coefficient of determination (R 2 ), root mean of square error (RMSE), and the Akaike information criterion (AIC).Results: All investigated nonlinear functions were fully fitted.Based on the goodness of fit statistics, the highest value of R 2 and the lowest values for AIC and RMSE criteria belonged to the logistic model, which was therefore selected as the best model for modeling the growth curve in Holstein calves.Based on this model, the asymptotic weight was estimated at 85.18 kg.The highest asymptotic weight (A) (final weight of the experiment) in this study was estimated according to the Gomperts model (85.39 kg).The highest and lowest values of parameter B belonged to logistic and Gompertz models.The highest and lowest values of parameter K were estimated using Richards and logistic models.The highest and lowest correlations between the observed data and the predicted data were obtained using the logistic (95.9%) and Richards (94.9%) non-linear functions, respectively.In a literature review, the best models differ based on the breed and geographic location where the modeling takes place.Genetic diversity within and between breeds, selection, and breeding methods and criteria, the management system, and environmental conditions influence the difference in growth patterns and the definition of the best model. Conclusion:In total, five non-linear models of the growth curve were investigated and studied in Holstein calves.According to the results, the logistic model showed the best description of the growth curve for calves and was selected as the best model.Therefore, this model can be used to determine the management strategies and the optimum weaning age in Holstein dairy calves.The absolute growth rate reflects the increase in body weight from birth to the point where growth