A Comparison of Nonlinear Models for Describing Weight-Age Relationships in Cattle1

TLDR

Five nonlinear models were fitted to female cattle weight‑age data from diverse breeds and management systems, and they were compared for goodness of fit, biological interpretability of parameters, and computational ease. The Richards four‑parameter model provided the most accurate fit, especially before 10 months, though it is computationally more demanding, while the Brody model, easier to compute, fits ages beyond 6 months almost as well, and the von Bertalanffy, Gompertz, and logistic models overestimated early weights and underestimated mature weight, and parameter estimates across models share a biological interpretation but are not perfectly correlated, revealing genetic variation in growth rates and mature size.

Abstract

Five nonlinear models were used to fit weight-age data for female cattle of diverse breeding and management. Comparisons were made among these models for goodness of fit, biological interpretability of parameters and computational ease. Three models, von Bertalanffy, Gompertz and logistic, consistently overestimated weights at early ages and the logistic underestimated mature weight. A four-parameter model, Richards, more accurately fit the data but was computationally more difficult than the three-parameter models. The Richards model which has a variable point of inflection is most appropriate for fitting weight-age data when goodness of fit, especially prior to 10 months of age, is critical. The Brody model is computationally easier and fit the weight-age data for ages past 6 months almost as well as the Richards model. Parameter estimates, or functions thereof, from all models can be interpreted as measures of size and rates of gain and maturing. However, parameter estimates from different models, although having the same biological interpretation, were not perfectly correlated. Genetic variations in rates of gain and maturing and mature size were observed.