Construction of the height to crown base mixed model for Korean pine

  Objective  Based on the data of 2 972 Korean pine trees in 63 sample plots of Korean pine plantation in Maor Mountain of northeastern China, a nonlinear mixed model was used to construct the height to crown base model of Korean pine, which provided a theoretical basis for further research on growth and yield model.

  Method  Firstly, the optimal basic model was selected from eight commonly used models of height to crown base. Secondly, the influence of stand variables or individual tree variables on height to crown base was studied, and a generalized model was established. Finally, on the basis of the basic model and the generalized model, considering the effects of sample plot on the height to crown base of Korean pine, the basic mixed effect model and generalized mixed effect model of height to crown base for Korean pine were constructed. Four alternatives of height to crown base (HCB) sampling designs (the randomly selected trees and selecting the maximum, medium-size and minimum trees) and eight sample sizes (1−8 trees) were studied for sampling correction of basic mixed effect model and generalized mixed effect model respectively.

  Result  Logistic model had good fitting accuracy and biological significance, and its form was simple, so it was chosen as the the optimal basic model. In addition to tree height (H) and DBH, there was a significant correlation between the basal area sum larger than subject tree (BAL), dominant height (HD), crown width (CW) and HCB, and the fitting accuracy of the model was improved obviously. The fitting effect of height to crown base generalized mixed effect model was better than that of other models. The model validation showed that when the basic mixed effect model was used to predict, it was recommended to select four samples with the smallest DBH, and when the generalized mixed effect model was used to predict, it was recommended to randomly select four samples.

  Conclusion  The generalized mixed effect model is superior to the other three models in fitting effect and prediction accuracy. It is recommended that this model can be used as the height to crown base model for Korean pine. When applying generalized mixed effect model prediction, it is recommended that four samples can be randomly selected.