Non-linear height-diameter models for oriental beech (Fagus orientalis Lipsky) in the Hyrcanian forests, Iran

摘要

The relationship between tree height and diameter is an important element in growth and yield models, in carbon budget and timber volume models, and in the description of stand dynamics. Six non-linear growth functions (i.e. Chapman-Richards, Schnute, Lundqvist/Korf, Weibull, Modified Logistic and Exponential) were fitted to tree height-diameter data of oriental beech in the Hyrcanian mixed hardwood forests of Iran. The predictive performance of these models was in the first place assessed by means of different model evaluation criteria such as adjusted R squared (adj R2), root mean square error (RMSE), Akaike information criterion (AIC), mean difference (MD), mean absolute difference (MAD) and mean square (MS) error criteria. Although each of the six models accounted for approximately 75% of total variation in height, a large difference in asymptotic estimates was observed. Apart from this, the predictive performance of the models was also evaluated by means of cross-validation and by splitting the data into 5-cm diameter classes. Plotting the MD in relation to these diameter at breast height (DBH) classes showed for all growth functions, except for the Modified Logistic function, similar mean prediction errors for small- and medium-sized trees. Large-sized trees, however, showed a higher mean prediction error. The Modified Logistic function showed the worst performance due to a large model bias. The Exponential and Lundqvist/Korf models were discarded due to their showing biologically illogical behavior and unreasonable estimates for the asymptotic coefficient, respectively. Considering all the above-mentioned criteria, the Chapman-Richards, Weibull, and Schnute functions provided the most satisfactory height predictions. However, we would recommend the Chapman-Richards function for further analysis because of its higher predictive performance.