Individual tree basal-area growth parameter estimates for four models

Four sigmoid growth models are fit to basal-area data derived from increment cores and disks taken at breast height from oak trees. Models are rated on their ability to fit growth data from five datasets that are obtained from 10 locations along a longitudinal gradient across the states of Delaware, Pennsylvania, West Virginia, and Ohio in the USA. We examine and compare the estimated parameters for the four models across a range of sample sites and tree ages. We then examine the differences among these models. The Chapman–Richards model is recognized as the best regarding minimum Mean Square Error (MSE) and gives reasonable estimates of maximum basal-area growth for old-age trees. The Weibull model is shown to be the poorest in terms of ability to fit the data. The apparent reason for this lack of fit is discussed. The Richards model ranked third in terms of meeting the MSE criteria but did best in terms of meeting the SAS stop criteria. The von Bertalanffy model is shown to have problems meeting the stop criteria of the SAS non-linear fit algorithm but ranks second in terms of samples meeting the MSE criteria. The von Bertalanffy model also tends to underestimate the long-term maximum value or asymptote of basal area over time.