Nonlinear mixed-effect branch growth model development for planted Korean pine in Northeast China

Branch growth is an important aspect of the tree growth process. Studying the branch growth pattern is important for understanding the growth of trees and optimizing forest management decisions. A total of 48 planted Korean pine sample trees from northeast China were selected, and a total of 327 sample branches were measured for branch diameter growth model development and 323 sample branches for branch length. Based on the aforementioned research objectives and the obtained data, the impact of individual tree variables, branch variables, and forest stand competition variables on branch growth were initially investigated in this study. Finally, we constructed nonlinear mixed-effects models at the individual tree level. The results show that the Mitscherlich growth equation had the best fitting accuracy and was selected as the base model for developing the Korean pine branch growth model. Forest stand competition of the ratio of the basal area of the subject tree to the mean basal area of the stand (CI₂) and branch variables of the branch length and branch diameter had the most significant contributions and were selected and introduced into the branch growth models. The branch growth became larger with increasing CI₂, branch length and branch diameter, but the effects of the branch height and diameter at the breast height on branch growth should be considered in combination with their parameters and other variables together. In addition, the introduction of random effects effectively improves the fitting accuracy of the branch growth model. Overall, the Korean pine branch growth models developed in this study have good fitting performance and have important theoretical and practical value.