| چکیده انگلیسی مقاله |
Extended abstract
Introduction and Objective: The importance of studying growth in domestic animals is a key economic aspect, particularly in raising cattle. Adult cattle weight plays a crucial role in breeding programs, affecting various economic traits such as maintenance needs, reproduction, and other biological characteristics. To understand growth capacity and the statistical relationship between age and weight, researchers often employ mathematical models like Logistic, Gompertz, Van Bertalanffy, Brody, and Richards.
This study focuses on mathematical models that summarize growth patterns using biologically interpretable parameters. These models provide valuable insights for developing breeding strategies by allowing for adjustments in management practices and genetic structures related to growth curves. As a result, analyzing growth curves serves as a foundation for adapting breeding policies, determining nutritional requirements, and making informed decisions about specific technologies. In this study, we explore the growth pattern of Holstein calves using the dynamic nonlinear model (DOLS) for the first time. We compare its effectiveness with other nonlinear models like Gompertz and Logistic.
Materials and Methods: For this study, we utilized birth weight and body weight records from 10 to 90 days of age collected at the Kohan Aberdej Agriculture and Industry Unit in Tehran Province. We recorded approximately 10 body weight measurements for each weanling calf, which were initially analyzed using Excel 2007 software. Subsequently, we performed statistical analyses using non-linear Gompertz and logistic models from the nlme statistical package in R software. To estimate growth parameters, we employed numerical calculations and the Gauss-Newton algorithm. In the DOLS method, a nonlinear method based on the law of diminishing returns is used to estimate the parameters of the growth model, which correctly estimates the regression coefficients of the growth stages. We evaluated the goodness of fit of the models based on the corrected coefficient of determination (R_Adj^2) and mean square error (MSE). Finally, the value of R_Adj^2 was compared using Student's t-test.
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Results: The results of this study indicate that both the logistic and dynamic nonlinear least squares (DOLS) models provide the best description of the growth pattern. These models exhibit high values of R_Adj^2 and the lowest mean squared error (MSE). While the logistic model has demonstrated strong performance in estimating growth parameters for dairy calves in previous studies, it does have a weakness: it tends to overestimate or underestimate body weight at different time points. However, the DOLS model, as demonstrated in this study, accurately predicts body weights at various times without such biases. This is a key strength of the DOLS model. Notably, the Gompertz model ranked last among the non-linear models. Evaluation indicators confirm that the DOLS model excels, with a high R_Adj^2 value and low MSE. Furthermore, it effectively calibrates time and body weight at turning points, ensuring accurate predictions within the available field data.
Conclusion: The results showed that unlike Gompertz and logistic nonlinear models, the DOLS growth model exhibits dynamics in the estimation of growth model parameters. Additionally, while logistic and Gompertz models do not allow for achieving the maximum economic productivity using food inputs, the dynamic nonlinear least squares model, effectively establishes a relationship between the amount of consumed inputs and maximum productivity. Consequently, this model can be employed to provide expert recommendations.
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