Modelling growth in dairy heifers based on linear body measurements (withers height) using non-linear functions

This research communication reports a study to model the growth curves for withers height (WH) and body weight (BW) to withers height ratio (BW:WH) using monthly records (from 1 to 24 months of age) for three breeds of dairy heifer (Holstein, Jersey and Brown Swiss). The data sets used were those reported by the Dairy Heifer Evaluation Project of Penn State Extension (USA) between 1991 and 1992. Four growth functions (monomolecular and Michaelis-Menten, both with diminishing returns behaviour, and Schumacher and López, both with asymptotic sigmoidal behaviour) were fitted using the non-linear regression procedure of the SigmaPlot software and the parameters estimated. The models were judged for goodness of fit using adjusted coefficient of determination ($R_{{\rm adj}}^2 $), root mean square error (RMSE), Akaike's information criterion (AIC) and Bayesian information criterion (BIC). Assessing the goodness of fit by $R_{{\rm adj}}^2 $ (>0.99 in all cases) reveals the generally appropriate fit of the models to the data. The non-sigmoidal functions (i.e. Michaelis-Menten and monomolecular) provided the best fits giving the lowest values of RMSE, AIC and BIC. Based on the chosen statistical criteria, the Schumacher and López equations provided acceptable fits to the WH and BW:WH growth curves, but showed points of inflexion at times before birth, indicating that these growth curves are not sigmoidal. In conclusion, evaluation of the different non-linear growth functions used in this study indicated their potential for modelling growth patterns in dairy heifers.