La aplicación de silvicultura intensiva en el manejo forestal sustentable requiere de herramientas cuantitativas eficientes para estimar de manera adecuada los patrones de crecimiento de los árboles y rodales. El desarrollo de modelos matemáticos con bases científicas representa un insumo vital para realizar proyecciones de crecimiento y rendimiento de especies forestales comerciales a través del tiempo. El objetivo de este estudio fue ajustar ecuaciones dinámicas de diferencia algebraica (ADA) y diferencia algebraica generalizada (GADA) para crecimiento en altura dominante e índice de sitio en Pinus patula Schiede ex Schltdl. & Cham. que crece en rodales coetáneos de Ixtlán de Juárez, Oaxaca. Los datos usados provinieron de 66 sitios permanentes de muestreo establecidos en 2015 y remedidos en 2016 y 2017. Las ecuaciones se ajustaron mediante el método iterativo anidado, que es una técnica invariante de la edad base. Los indicadores estadísticos de bondad de ajuste, los análisis gráficos y la capacidad predictiva de los modelos sugieren que la mejor ecuación para modelar el crecimiento en altura dominante es la formulación GADA derivada del modelo de Bertalanffy-Richards. La altura dominante promedio a la edad base de 40 años fue de 29 m. El modelo tipo GADA propuesto permitirá estimar adecuadamente la productividad de los rodales de P. patula. Los enfoques empleados para modelar el crecimiento en altura dominante demuestran ser metodologías eficientes para generar herramientas biométricas de apoyo en la toma de decisiones del manejo forestal para predecir la producción actual y futura.

Generalized height-diameter at breast height (D) models are essential for the estimation of the timber stocks of a forest stand, as well as in the generation of base information to develop forest growth models, and as basic inputs in the development of forest management plans. Generalized models were developed to estimate total height (TH) based on the D and stand variables, of five Pinus species in forests under forest management of Ixtl an de Ju arez, Oaxaca, Mexico. The data used come from a timber forest inventory, where n ¼ 1041 sampling plots of 1000 m 2 each were established based on a stratified-systematic sampling design. The species selected according to their relative abundance were: Pinus patula, Pinus oaxacana, Pinus ayacahuite, Pinus teocote and Pinus leiophylla. Five nonlinear equations were fitted using regression techniques to predict the TH of the trees under several silviculture regimes and forest management conditions. The statistical criteria of goodness of fit used were: adjusted coefficient of determination (R 2 adj ), root mean square error (RMSE) and absolute average bias in the prediction ( E). Likewise, the graphic analysis of the predictive capacity of the equations was considered. The D and the stand variables (quadratic mean diameter, dominant diameter and dominant height) for these species explained between 75 and 83% of the variability of the TH data. The predicting variables to apply the developed generalized models to estimate tree's total height require less sampling effort and are derived from conventional forest inventory data, which allows to reduce costs and time in field work.

Sustainable forest management requires accurate biometric tools to estimate forest site quality. This is particularly relevant for prescribing adequate silvicultural treatments of forest management planning. The aim of this research was to incorporate topographic and climatic variables into dominant height growth models of patula pine stands to improve the estimation of forest stand productivity. Three generalized algebraic difference approach (GADA) models were fit to a dataset from 66 permanent sampling plots, with six re-measurements and 77 temporary inventory sampling plots established on forest stands of patula pine. The nested iterative approach was used to fit the GADA models, and goodness-of-fit statistics such as the root mean square error, Akaike’s Information Criterion, and Bias were used to assess their performance. A Hossfeld IV GADA equation type that includes altitude, slope percentage, mean annual precipitation, and mean annual minimum temperature produced the best fit and estimation. Forest site productivity was negatively affected by altitude, while increasing the mean annual minimum temperature suggested the fastest-growing rates for dominant tree height.

Site index models allow for the characterization of forest site productivity and the development of management strategies to achieve objectives of production and conservation of forest resources. The goal of this study was to fit and validate growth models of dominant height and site index for Pinus oaxacana Mirov. The database was derived from 4 inventories in 44 permanent plots and 58 temporary plots, established in even-aged stands located in Ixtlán de Juárez, Oaxaca, Mexico. The data were randomly partitioned into subsets of 50 %, 60 %, 70 %, and 80 % for the model adjustments and the remaining data for each subset were used for cross-validation. The models fitted were Korf, Hossfeld IV and Chapman-Richards, in their expressions ADA (algebraic difference approach) and GADA (generalized algebraic difference approach), using the nested iterative method under the non-linear least squares technique. The models that presented the best statistics for fit and validation were: in ADA, anarmorphic Korf b 0 (70 %) and polymorphic Korf b 1 (80 %); in GADA, Chapman-Richards (70 %) and Korf (80 %). The Chapman-Richards GADA model presented the most suitable graphical behavior and was selected to classify the forest site productivity. The dominant height and site index model applied to quantify the productive potential of P. oaxacana stands constitutes a valuable tool for the sustainable management of this species in the forests of Oaxaca, Mexico.

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