Revealing the driving factors of crown width variation in Chinese fir plantations using random forest and SHAP algorithms

Crown width (CW) is a key geometric descriptor of tree crown architecture that reflects the integrated effects of individual tree size, stand structure, competition, and site conditions. Although CW has been extensively modeled using allometric and mixed-effects approaches, these parametric frameworks require the analyst to pre-specify interaction structures, leaving higher-order interactive effects among multiple drivers largely unexplored, particularly in marginal populations where environmental constraints may alter the relative importance of different factors. This study quantified the associations between CW variation and multidimensional predictors in Chinese fir ( Cunninghamia lanceolata ) plantations across 90 plots (6463 trees) at three sites in Anhui Province, the northern margin of the species' range. A multi-parameter optimized Random Forest (RF) model was coupled with SHapley Additive exPlanations (SHAP) for feature attribution and Partial Least Squares Structural Equation Modeling (PLS-SEM) for path analysis, with a nonlinear mixed-effects (NLME) model (CW = a · DBH b ) serving as an allometric benchmark. On an independent plot-grouped testing set, the RF model ( R ² = 0.509, RMSE = 0.807 m) outperformed the NLME baseline ( R ² = 0.498, RMSE = 0.836 m) across all metrics, although by modest margins, indicating that the principal value of the interpretable machine-learning framework lies in diagnostic resolution rather than predictive gain. SHAP analysis identified DBH as the dominant predictor (33.6% of total importance), followed by the distance-independent competition index CI8 (12.0%), quadratic mean diameter (10.9%), and the crown closure index CI9 (7.3%). CI8 was consistently negatively associated with CW, whereas the apparent size-conditional response of CI9 was more parsimoniously explained by its geometric coupling with tree size rather than to a distinct competitive effect. Interaction analysis revealed that the effects of competition, stand structure, and morphological variables on CW were concentrated among smaller trees and converged toward zero beyond approximately 35 cm DBH, with the DBH × Dg interaction reversing polarity at approximately 32 cm. PLS-SEM supported the hypothesized hierarchical structure, with competition negatively associated with tree size ( β = −0.658) and tree size positively associated with crown width ( β = 0.704), yielding a strong indirect Competition → DBH → CW association ( β = −0.464), whereas the direct Competition → CW path was non-significant. Based on these convergent but preliminary signals, we suggest that release consideration may focus on crop trees experiencing CI8 > 0.20 while still below the approximately 32 cm size transition, using these values as an indicative operational window rather than a joint threshold, within a multi-objective framework balancing crown dimensions with stand-level productivity and carbon storage.