Tree size and relative height interactions enhance generalized additive models for Chinese fir stem taper prediction.

Abstract

Tree stem taper varies dynamically with tree size due to biomechanical constraints governing stability, yet capturing this size-dependent shape plasticity remains a challenge in forest biometrics. Traditional variable-exponent models impose rigid functional forms, while emerging machine learning approaches often obscure these biological relationships within black-box structures. Furthermore, previous applications of generalized additive models (GAMs) have predominantly focused on additive effects, overlooking the critical interactions between tree size and relative position along the stem. To address this gap, we investigated whether explicitly modeling the nonlinear interactions between tree size and relative height could resolve systematic biases in taper prediction. Using a dataset of 516 felled Chinese fir (Cunninghamia lanceolata) trees, we constructed GAMs incorporating tensor product interaction smooths and benchmarked them against the widely used parametric models and two machine learning algorithms. We found that GAMs relying solely on main effects failed to outperform the parametric benchmark. However, introducing explicit interaction terms, specifically between diameter at breast height and relative height, substantially reduced the root mean square error by 52.3% compared to the additive GAM and surpassed both the established Kozak-II benchmark and the optimized machine learning models in validation accuracy. Variable importance analysis confirmed that these interactions act as critical modifiers that drive the model improvement by accurately capturing the ontogenetic drift in stem form, such as the pronounced basal flare in larger trees. These findings demonstrate that interaction-inclusive GAMs serve as a powerful tool to bridge the trade-off between algorithmic flexibility and parametric interpretability, offering a biologically grounded approach for precision forest inventory.