Using Nonlinear Regression Functions to Growth Curve Description of Sanjabi Sheep

Introduction
Growth traits are among the most critical components determining productivity and economic efficiency in sheep production systems. Body weight gain over time directly influences feed conversion efficiency, carcass yield, meat quality, and profitability. Accurate characterization of growth patterns enables producers and researchers to optimize management practices, improve feeding strategies, and design effective breeding programs. Growth curve analysis provides a comprehensive approach to describe longitudinal body weight changes by fitting mathematical models with biologically interpretable parameters. These models allow prediction of body weight at different ages, identification of growth acceleration and deceleration phases, and estimation of mature body weight and growth rate. However, the suitability and performance of growth models may vary depending on breed, environmental conditions, management system, and data structure. Therefore, it is essential to evaluate breed-specific growth models to obtain reliable and applicable results.
Sanjabi sheep is a native fat-tailed breed predominantly raised in Kermanshah province, located in western Iran. This breed is known for its large body size, adaptability to harsh environmental conditions, acceptable growth performance, and high market preference due to meat quality. Sanjabi sheep play a significant role in regional red meat production and rural livelihoods. Despite its economic and genetic importance, limited information is available about growth pattern characterization and appropriate nonlinear growth models for this breed. A clear understanding of growth dynamics in Sanjabi sheep is essential to improv production efficiency and support sustainable breeding strategies.
The primary objective of this study was to describe the growth curve of Sanjabi lambs using different nonlinear regression models and to compare their performance in predicting body weight changes from birth to nine months of age. An additional objective was to identify the most appropriate model based on goodness-of-fit criteria, which could be applied in breeding, nutritional planning, and management decision-making for Sanjabi sheep.
Method
The data used in this study consisted of body weight records of Sanjabi lambs measured at birth and at 1, 2, 3, 6, and 9 months of age. Records were collected from lambs raised at the Mehrgan Research Station located in Kermanshah province during the period 2018 to 2024. The flock was managed under a semi-intensive production system. Animals grazed on natural rangelands and cultivated pastures from spring to early autumn, while indoor feeding was practiced during late autumn and winter. Diets were formulated according to age, sex, and physiological status, and lambs were weaned at approximately three months of age.
All lambs were identified and ear-tagged at birth, and body weights were recorded at predetermined intervals. Prior to statistical analysis, data editing was performed to remove incomplete records and biologically implausible weight changes between consecutive ages, ensuring data reliability. Four nonlinear growth models, including Gompertz, Logistic, Von Bertalanffy, and Brody models, were fitted to the body weight data using nonlinear regression procedures in SAS software.
Each model included three parameters: A, representing asymptotic or mature body weight; B, an integration constant related to initial body weight; and K, the maturity or growth rate parameter indicating the growth rate of animals to mature weight. Model were compared and selected using multiple goodness-of-fit criteria, including the coefficient of determination (R²), mean square error (MSE), and Akaike information criterion (AIC). Models with higher R² values and lower MSE and AIC values were considered to provide a better fit to the observed data.
Results
Descriptive statistics indicated a steady increase in mean body weight from birth to nine months of age, accompanied by an increase in standard deviation and coefficient of variation at later stages of growth. This pattern reflects increasing phenotypic variability among animals as growth progresses, likely due to cumulative effects of genetic differences and environmental factors.
Estimated values of the mature weight parameter (A) varied among the evaluated models. The highest estimate of mature weight was obtained from the Brody model, while the lowest estimate was observed in the Logistic model. The differences in mature weight estimates reflect structural differences among models and their sensitivity to data from later stages of growth. The maturity rate parameter (K) also differed considerably among models. The Logistic model produced the highest K value, indicating a faster growth rate during early life. In contrast, the Brody model showed the lowest K value, suggesting a slower but more gradual growth rate.
Correlation analysis between growth curve parameters revealed a consistent negative relationship between mature weight (A) and maturity rate (K) across all models. This inverse relationship suggests that animals exhibiting faster early growth do not necessarily achieve higher mature weights. Such relationships have important implications for breeding programs, as selection solely for rapid early growth may result in reduced mature body size.
In terms of model performance, the Gompertz model exhibited the highest coefficient of determination, indicating strong explanatory power. However, the Brody model showed the lowest AIC and MSE values, reflecting superior overall goodness-of-fit and lower prediction error. Considering all evaluation criteria simultaneously, the Brody model was identified as the most appropriate model for describing the growth curve of Sanjabi lambs.
Conclusions
The results of this study demonstrate that nonlinear growth models are practical tools for describing and analyzing growth patterns in Sanjabi sheep. Although all evaluated models were capable of fitting body weight data reasonably well, the Brody model provided the best overall fit based on information criteria and prediction accuracy. The superiority of the Brody model suggests that it more accurately reflects the biological growth pattern of Sanjabi lambs, characterized by rapid growth during early life followed by a gradual reduction in growth rate at later stages.
The findings of this research have practical implications for sheep production systems. The selected growth model can be used to predict body weight at different ages, identify growth slowdown points, optimize feeding and management strategies, and determine appropriate slaughter age. Furthermore, growth curve parameters derived from the Brody model may serve as valuable auxiliary traits in selection indices, enabling simultaneous improvement of growth performance and economic efficiency in Sanjabi sheep breeding programs.