Regression analysis and artificial neural networks for predicting pine species volume in community forests

Volume prediction models are fundamental in forestry, as they support forest inventories, sustainable forest management strategies, and comprehensive environmental planning. The main objective of this study was to implement and compare two prominent approaches—regression and machine learning—for modeling whole-tree volume and stem volume in two Pinus species in community forests of southern Mexico. Destructive sampling provided data from 56 P. patula and 51 P. pseudostrobus trees, covering a wide range of diameters and heights. The regression approach employed seemingly unrelated nonlinear regression (NSUR) to fit simultaneous additive volume systems using both one- and two-variable models. In this approach, volume was modeled as a function of diameter at breast height (d) alone and as a function of both d and total tree height (h). Species and volume type were implicitly accounted for within the structure of the additive systems structure. For the machine learning approach, multilayer perceptron (MLP) artificial neural networks (ANNs) were trained using four input variables: diameter at breast height, total tree height, species, and volume type. These variables were explicitly incorporated into the ANN structure, enabling the model to learn complex, non-linear interactions. The ANN was optimized using L1 regularization and the Adam optimizer. The quantitative variables were diameter at breast height and total tree height, while the qualitative variables were species (P. patula and P. pseudostrobus) and volume type (whole-tree volume and stem volume), both coded as 1 and 0, respectively. The relative rank method was used to identify the most effective models based on goodness-of-fit statistics, including the coefficient of determination (R²), average absolute error (AAE), total relative error (TRE), average systematic error (ASE), and mean percent standard error (MPSE). The ANN approach consistently outperformed the regression model, achieving higher R² values and lower error metrics across all evaluations. Specifically, the ANN model reduced AAE, TRE, and ASE while maintaining biologically consistent predictions. This proposed ANN model represents a significant advancement in modeling both whole-tree and stem volume simultaneously and independently across different species, providing reliable and precise estimates. Given its ability to handle complex, non-linear relationships and its superior accuracy, we recommend the use of ANN as a practical tool in forestry applications, including forest resource evaluation and the development of sustainable forest management plans.