Estimation beech (Fagus Orientalis L) and hornbeam (Carpinus betulus L) trees height using nonlinear models and mixed-effects model

The aim of this study was to develop the Mixed-effects model and compare it with nonlinear models for estimating beech (Fagus Orientalis Lipsky) and hornbeam (Carpinus betulus L.) heights in the Shast-kalateh forests (district 1 and 2) of Gorgan. We applied a systematic sampling method to collect the field data within a 150×200 m network (308 circular plots) and in each plot, tree species were identified and height and diameter at breast height (DBH) of all trees were measured. Model fitting was done in two stages: Fixed-effect approach was used in the first stage wherein candidate models where height (dependent variable) and DBH (independent variable). These were refitted in the second stage using a mixed-effect approach. The adjusted coefficient of determination and root mean square error, were used to assess the models. The results of fitting nonlinear models showed that for the beech, Curtis and Naslund models had the highest coefficient of determination of 0.76 and the lowest root mean square error of 3.35 and 3.40, respectively. For hornbeam, Naslund and Michailoff models with the coefficient of determination of 0.40 and the root mean square error of 2.95 and 2.90 were selected as the best models. The results of nonlinear mixed effects model showed that the R2 for beech and hornbeam species increased by 10% and 30% respectively, and the RMSE improved about 0.65 for beech and 0.6 for hornbeam.