Modelling and localizing a stem taper function for Pinus radiata in Spain

Abstract

The parsimonious taper function proposed by Riemer et al. (1995. Allg. Forst.- Jagdztg. 166(7): 144–147) was fitted for radiata pine (Pinus radiata D. Don) stems in Spain by using a nonlinear mixed modelling approach. Eight candidate models (all possible expansion combinations of the three fixed parameters with random effects) were assessed, and the mixed model with three random effects performed the best according to the goodness-of-fit statistics. An evaluation data set was used to assess the performance of these models in predicting stem diameter along the bole, as well as total stem volume. Four prediction approaches were compared: one subject (tree) specific (SS) and three population specific (ordinary least squares (OLS), mean (M), and population averaged (PA)). The SS responses for a tree were estimated from a prior stem diameter measurement available for that tree, whereas OLS, M, and PA were obtained from the fixed-effects model, from the fixed parameters of mixed-effects models, and by computing mean predictions from the mixed-effects models over the distribution of random effects, respectively. Prediction errors were greater for the M and PA responses than for the OLS response, and therefore, from the prediction point of view, the use of the mixed-effects models is not recommended when an additional stem diameter measurement is not available. The mixed model with three random effects was also selected as the best model for SS estimations. Measurement of an additional stem diameter at a relative tree height of approximately 0.5 provided the best calibrations for stem diameters along the bole and total stem volume predictions. The SS approach increased the flexibility and efficiency of the selected mixed-effects model for localized predictions and thus improved the overall predictive capacity of the base model.