Innovative approaches to estimating sessile oak stem volume: comparing additive models and ensemble machine learning

Sessile oak is an important deciduous forest tree species across Türkiye and Europe. Estimating individual tree and stand volumes is essential for growth and yield models, as these predictions play a critical role in assessing forest management, economics, and fire risk. In pursuit of this goal, nonlinear seemingly unrelated regression (NSUR) was used for the simultaneous fitting of stem volume components, and compared to three ensemble machine learning techniques: gradient boosting regression (GBr), XGBoost regression (XGBr), and random forest regression (RFr). NSUR accounts for correlations between error terms across different equations, leading to more efficient parameter estimates than if each equation were estimated individually. Ensemble machine learning approaches focus on optimizing base learners, but different approaches use different construction strategies. The statistical analysis revealed that all modeling methods provided accurate and reliable outcomes, with the XGBr technique outperforming the others in terms of effectiveness. Remarkably, the XGBr model substantially improved predictive performance by reducing the root mean square error (RMSE) by 27.92% and 28.19% in the fitting and test datasets, respectively, for the total stem volume compared to the NSUR-based model. Similar improvements were observed in the estimation and prediction of stem-wood volume and stem-bark volume. Specifically, for the stem-wood volume, the XGBr model achieved RMSE reductions of 26.36% and 25.81% in the fitting and test datasets, respectively. For stem-bark volume, the performance improvements were even more pronounced, with reductions of 32.20% and 23.73% in the fitting and test datasets, respectively, compared to the respective NSUR models. While identifying the optimal combination of hyperparameters can be challenging, the results show that the XGBr approach holds great potential as an effective alternative method for estimating the total stem volume and its components for sessile oak trees in the Marmara Region of Türkiye.