Modelling growth in lowland sheep using nonlinear functions

Modelling the growth profiles of sheep not only provides information about how body weight changes with age but also distills these serial measures into biologically important parameters which can be used in genetic evaluation programs. The objective of the present study was to evaluate a series of different functions applied to serial body weight measures of lowland sheep and, in doing so, also explore the relationship between the parameters within and across functions. The evaluated functions were Brody, Gompertz, Logistic, negative exponential, Richards and von Bertalanffy. The data set used consisted of 158,463 body weight records (range of 6 to 38 records per animal) from 13,090 female sheep. The functions were fitted to each animal separately. The coefficient of determination (R²) and root mean square error (RMSE) per animal, along with the ease of model convergence, were used to evaluate model fit. The percentage of animals that achieved convergence per function ranged from 82.39% (Richards) to 100.00% (negative exponential and Logistic). The mean R² value for the Logistic function was the lowest (0.94), while that for the Richards function was the highest (0.98). A weak negative correlation (r = -0.23 to -0.13) was estimated between the A (asymptotic weight) and B (integrated constant related to initial weight) parameters for all the functions except for Richards. The A and K (maturity rate) parameters of all the functions were negatively correlated and ranged from -0.55 (Brody) to -0.41 (Logistic). The values of the A parameter across all the functions were strongly positively correlated. The estimates for the B parameter of Logistic and Richards functions exhibited a very weak correlation (r = -0.04). A weak to strong correlation between the K parameter values across all functions was observed. Results suggested that all the evaluated functions, except the Richards function, can be applied to model the growth of lowland sheep. The Gompertz and von Bertalanffy functions were considered as the best fitting functions to describe the body weight profiles of Irish female lowland sheep based on their fit to the data, the ease of convergence, and the biological sensibility of the estimated function parameters.