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.

Funciones alométricas de altura total para pinos tropicales en Puebla, México

“…Al respecto, Ogana et al (2020) lo han aplicado para modelar las relaciones at y dn de árboles en bosques naturales de Nigeria, y Zhang (1997) en coníferas del noreste de los Estados Unidos. En concordancia, Rubio et al (2022) emplearon la función de Weibull para relacionar at y dn para un grupo de coníferas en bosques naturales del norte de Puebla, México.…”

“…Investigaciones realizadas para predecir la at en función del dn para pinos tropicales establecidos en regiones tropicales de México, son escasos. Por el contrario, para especies de interés comercial de bosques de clima templado se han realizado varios estudios (Hernández-Ramos et al 2018, Corral-Rivas et al 2019, Santiago-García et al 2020, Rubio et al 2022. Dada la demanda de madera proveniente de plantaciones comerciales de pinos tropicales de rápido crecimiento, es necesario monitorear y estimar con precisión el rendimiento maderable para la toma de decisiones en el manejo de dichas plantaciones.…”

Mixed-Effects Height Prediction Model for Juniperus procera Trees from a Dry Afromontane Forest in Ethiopia

“…The calibration response of the best local mixed-effect and generalized mixed-effects models was assessed using a completely independent dataset from the Menagesha Suba Dry Afromontane Forest (Table 1). Overall, nine different sampling alternatives (Table 4) were evaluated, and the best sample size (the number of trees) and method were identified, following the procedure in Camacho et al [81]. We evaluated the effectiveness of the sampling alternatives for estimating the random effects by examining the root mean square error (RMSE) values and contrasting them with the RMSE estimates obtained from using the best local mixed-effects and generalized mixed-effects models, which consider all the trees within the sample plot.…”

“…The use of additional predictor variables in height-diameter models is a common practice, often used to enhance the accuracy of height prediction (e.g., [15,30,81,86]. This underscores the notion that the variability in height-diameter relationships among trees can be elucidated to some extent by considering additional stand variables.…”