GENERALIZED HEIGHT-DIAMETER MODELS WITH RANDOM EFFECTS FOR NATURAL FORESTS OF CENTRAL MEXICO

Abstract

Background: Tree height is an important variable in forestry, it is commonly used to estimate volume, biomass, and to evaluate site productivity. In this study, we developed four generalized equations to model the height-diameter (h-d) relationships for coniferous and broadleaf species. For this purpose, we used information from 49 permanent sampling plots located in natural forests of northwestern Puebla, Mexico. Non-linear fixed and mixed-effects modeling approaches were used to fit generalized versions of the Gompertz function to Pinus patula and Pinus group; Näslund function to Abies religiosa; and Curtis function to Quercus group.

Results: Stand variables included in the models were the number of trees per hectare (N), quadratic mean diameter (dg), and basal area per hectare (G). The results showed a R² = 0.91 and RMSE = 2.04 for P. patula and R² = 0.91, RMSE = 1.63 for Pinus group. The R² and a RMSE for Abies religiosa were 0.88 and 2.21, while for the Quercus group these values were 0.72 and 1.9, respectively. From the mixed-effects model calibration, only a sub-sample of three trees is required to make accurate predictions. None of the selected models include stand-level variables related to tree height and do not require additional measurements additional to tree diameter.

Conclusion: Compared to conventional non-linear least squares (ONLS), mixed-effects models are more flexible, accurate, and represent a new tool for sustainable forest management of natural forests in the study area.