Individual Tree Diameter Growth Models of Larch–Spruce–Fir Mixed Forests Based on Machine Learning Algorithms

Individual tree growth models are flexible and commonly used to represent growth dynamics for heterogeneous and structurally complex uneven-aged stands. Besides traditional statistical models, the rapid development of nonparametric and nonlinear machine learning methods, such as random forest (RF), boosted regression tree (BRT), cubist (Cubist) and multivariate adaptive regression splines (MARS), provides a new way for predicting individual tree growth. However, the application of these approaches to individual tree growth modelling is still limited and short of a comparison of their performance. The objectives of this study were to compare and evaluate the performance of the RF, BRT, Cubist and MARS models for modelling the individual tree diameter growth based on tree size, competition, site condition and climate factors for larch⁻spruce⁻fir mixed forests in northeast China. Totally, 16,619 observations from long-term sample plots were used. Based on tenfold cross-validation, we found that the RF, BRT and Cubist models had a distinct advantage over the MARS model in predicting individual tree diameter growth. The Cubist model ranked the highest in terms of model performance (RMSE_cv [0.1351 cm], MAE_cv [0.0972 cm] and R²_cv [0.5734]), followed by BRT and RF models, whereas the MARS ranked the lowest (RMSE_cv [0.1462 cm], MAE_cv [0.1086 cm] and R²_cv [0.4993]). Relative importance of predictors determined from the RF and BRT models demonstrated that the competition and tree size were the main drivers to diameter growth, and climate had limited capacity in explaining the variation in tree diameter growth at local scale. In general, the RF, BRT and Cubist models are effective and powerful modelling methods for predicting the individual tree diameter growth.