A mixed-effects height-diameter model for Pinus douglasiana Martínez in temperate forests of Jalisco, Mexico

Abstract

predicting tree-height of Pinus douglasiana in the natural forests of Jalisco, Mexico.

Design/methodology/approach: For this study, we utilized 2,921 pairs of tree-height measurements collected from 65 permanent plots (each 50x50 m) in the study area. For each plot, we estimated the tree density as the number of trees per hectare (N, ha^-1), the basal area per hectare (G, m² ha^-1) and the quadratic mean diameter (dg, cm). Subsequently, we tested several models from the literature and developed a generalized mixed-effects model for tree height prediction.

Results: The Gompertz base model outperformed the other local models, achieving an R² of 0.75 and an RMSE of 3.13. Including the stand variables (N, G, and dg) and incorporating random effects significantly improved the model fit, resulting in an R² of 0.89 and an RMSE of 2.09 m. Calibration and validation steps revealed that selecting the three thickest trees is effective for estimating random effects in new plots or stands, with the RMSE and R² being 2.59 and 0.83, respectively.

Limitations on study/implications: The present model can be applied in areas where P. douglasiana is naturally distributed. However, it is advisable to calibrate the model using a sub-sample to achieve more accurate predictions of tree heights in new plots or areas.

Findings/conclusions: The Gompertz function was used as the base function to develop the final generalized mixed-effects model for predicting the height of Pinus douglasiana. The inclusion of stand variables (N, G, and dg) along with random effects improved the model fit. This model represents a new and more accurate tool for predicting the height of P. douglasiana in areas where it is naturally distributed.