Tree height curves of Pinus yunnanensis forest based on nonlinear mixed effects model

Objective Pinus yunnanensis forest is one of the most important forest types in Yunnan Province of southwestern China. The application of a nonlinear mixed effects model to simulate tree height curves of Pinus yunnanensis forests is important for advancing both scientific management and accurately assessing forest quality, not only in central Yunnan Province but also across the entire Yunnan Province.

Method Based on the survey data of 9 sample plots from typical Pinus yunnanensis forests in Jiuguan Forest Farm, Chuxiong City of Yunnan Province, 12 basic models were applied to establish the relationship between tree height and DBH, and the optimal model was selected as the basic model subsequently. The species group was then used as a dummy variable, and the stand variables and random effect of sample plots were incorporated into the model, yielding a nonlinear mixed effects model of tree height-DBH in Pinus yunnanensis forests; and model fit was evaluated using leave-one-out cross-validation.

Result The Schumacher model was found to be the best of 12 basic models. Among many stand variables, the average top height (H_d) and sum of basal area larger than the subject tree (BAL) exhibited strong correlations with tree height and had biological significance; thus, both variables were chosen for constructing the generalized nonlinear model of tree height-DBH. H_d displayed a significant positive correlation with tree height, while BAL showed a negative correlation with tree height. The final nonlinear mixed effects model of Pinus yunnanensis forests accounted for 74% of the variation in tree height, with an RMSE value of 1.57 m. The results of cross-validation showed that the model was not overfitted and the residuals did not show obvious heteroscedasticity.

Conclusion In contrast to basic models established through traditional methods, this study integrated the average top height and the sum of basal area larger than the subject tree into the nonlinear mixed effects model of Pinus yunnanensis forests, which can better describe the relationship between Pinus yunnanensis forest height and DBH. Furthermore, in terms of specific forest management practices, individual competition among forest trees can be reduced to promote high growth using measures such as planting right tree for the right place, adjusting the density of forest stand and optimizing the stand’s structure. This study provides a methodological reference and technical support for the simulation studies of tree height curves in Pinus yunnanensis forests in central Yunnan Province, and has important scientific and practical value for forest resource management and ecological protection.