Prediction of branch growth using quantile regression and mixed-effects models: An example with planted Larix olgensis Henry trees in Northeast China

Branch is an essential component that supports foliage for photosynthesis, and its size appears as a major determinant for log grading. Forest managers have always been facing a challenge to maximize tree increment and timber quality; hence, linking the dynamic relationship between the branch and tree growth will be beneficial for crucial stand managerial decisions (pruning, thinning, and other silvicultural practices). In this study, branch growth models were developed using 77 destructively sampled Korean larch trees (Larix olgensis Henry) from several plantations in the Northeastern area of China. A modified Mitscherlich function that includes dynamic tree height and branch height was used to predict the growth of the branch's diameter and length. The jackknifing technique was utilized to evaluate five alternative modeling approaches: (1) fixed-effects model; (2) calibrated mixed-effects model; (3) three-quantile regression method; (4) five-quantile regression method; and (5) nine-quantile regression method. The results showed that the prediction performance of both calibrated mixed-effects and quantile regression approaches outperformed the fixed-effects model, in which the calibrated mixed-effects provided better performance than quantile regression. In addition, three sampling strategies and various number of branches (1 to 8 branches per sample tree) were used for calibrating the mixed-effect and quantile regression model. The three sampling strategies brought relatively similar prediction performance, specifically for the larger sample size. Model performance improved as the sample size increased, but gains in performance decreased gradually. Overall, a combination of Type I sampling strategy and at least five sample branches per tree was recommended as a win-win solution to minimize the required measurement cost without sacrificing the model's predictive accuracy.