Comparison of non-linear models for growth characterization of purebred Ayrshire and crossbred cattle

The objective of this study was to compare four non-linear mathematical models in terms of evaluating the growth pattern of Ayrshire and crossbred (Norwegian Red  $\times$ Ayrshire) cattle. Monthly live-weight (kg) records of 725 cows were collected from birth to 540 d of age. The growth curves were analyzed using negative exponential, logistic, Richard, and Gompertz models. Parameters were estimated with the NLMIXED procedure, and model fit was assessed using Akaike's information criterion (AIC), the Bayesian information criterion (BIC), the overall standard error (OSE), and the adjusted coefficient of determination (Adj- $R^2$ ). The Gompertz model occasionally provided higher explanatory power (Adj- $R^2$ up to 0.95) and lower prediction error (OSE as low as 4.5), but the Richard model consistently yielded the lowest AIC and BIC values, making it the most reliable and parsimonious choice. Growth curves showed that females attained substantially higher mature body weights than males, with crossbred cattle generally being heavier than purebred Ayrshire. These findings demonstrate the utility of the Richard model for accurately describing and predicting cattle growth, providing valuable information for genetic selection, herd management, and breeding strategies.