Generalized height-diameter models with random effects for natural forests of central Mexico

Abstract

Background: Tree height is an important variable in forestry, as it is commonly used to estimate volume and biomass, and to evaluate site productivity. In this study, we developed four generalized equations to model height-diameter ( h-d) relationships for coniferous and broadleaf species. For this purpose, we used information from 49 permanent sampling plots located in the natural forests of Puebla, Mexico. Non-linear fixed and mixed-effects modeling approaches were used to fit generalized versions of the Gompertz function to Pinus patula and the Pinus group, the Näslund function to Abies religiosa, and the Curtis function to the 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 model efficiency (EF) = 0.91 and root mean square error (RMSE) = 2.04 for P. patula, as well as an EF = 0.91 and RMSE = 1.63 for the Pinus group. The EF and 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 from different quantiles of the diameter distribution is required to make accurate predictions. No stand-level variables related to tree height are included in any of the selected models, thus no additional measurements beyond tree diameter are required. Conclusion: Compared to conventional non-linear least squares (ONLS), mixed-effects models are more flexible and accurate and represent a new tool for sustainable forest management of natural forests in the study area.