Additive volume-equation systems for Pinus ayacahuite and Pinus douglasiana in temperate forests of the Sierra Norte, Oaxaca, Mexico

Volume models are essential tools for quantifying timber stocks and optimising forest utilisation. This study aimed to develop additive volume systems based on one- and two-entry simultaneous equations for Pinus ayacahuite Ehrenb. ex Schltdl. and Pinus douglasiana Martínez. Destructive sampling of 55 P. ayacahuite trees and 65 P. douglasiana trees was conducted in the communal forest of Ixtlán de Juárez, Oaxaca, southern Mexico. The additive systems were fitted using non-linear seemingly unrelated regression to estimate tree-volume components: stem and branch volumes, with whole-tree volume being the sum of both. The systems were evaluated using the relative ranking method, considering statistical indicators of accuracy, variability, and relative errors. Additionally, the predictive capacity of the equations was assessed through linear regression between observed and predicted values for each volume component, and the biological consistency was verified. The results indicate that two-entry additive systems provide greater accuracy in estimating stem, branch, and whole-tree volumes for both species. These equations are based on the Schumacher-Hall model, and their recommended range of application for both species is for diameter at breast height (DBH) between 9 cm and 75 cm, and for total height (H) between 9 m and 34 m. Therefore, their application is recommended for forest inventories and the planning of sustainable forest management.