Nonlinear Quantile Mixed-Effects Models for Prediction of the Maximum Crown Width of Fagus sylvatica L., Pinus nigra Arn. and Pinus brutia Ten.

In the current study, a novel approach combining quantile regression with nonlinear mixed-effects (QR-NLME) modeling was applied to predict the maximum crown width (cw_max) of three economically important forest species—the European beech (Fagus sylvatica L.), the black pine (Pinus nigra Arn.), and the Calabrian pine (Pinus brutia Ten.) at tree level. A power QR-NLME model was fitted first to a dataset including 1414 European beech trees obtained from 29 randomly distributed sample plots, 770 black pine trees from 25 sample plots, and 1880 Calabrian pine trees from 41 sample plots in Greece, to predict the cw_max at tree level. Additionally, a nonlinear mixed-effects model (NLME) was fitted to the same dataset to predict the average crown width at tree level for all species. In the second stage, the crown competition factor (CCF) was estimated based on the population average response of the cw_max predictions. The proposed approach presented sound results when compared with the outcomes of relevant models from other regions fitted to open-grown tree data, and therefore, it can be well implemented on clustered data structures, in cases of absence of open-grown tree data.