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 Ixtlán de Juárez, Oaxaca, Mexico. The data used come from a timber forest inventory, where n = 1041 sampling plots of 1000 m² 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 (R²_adj), root mean square error (RMSE) and absolute average bias in the prediction (Ē). 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.

Aim of study: To generate a mathematical system to distribute structural products of bamboo culms. Study area: Northeastern region of the state of Puebla, Mexico. Materials and methods: Eighty-seven culms of Bambusa oldhamii Munro, Guadua aculeata Rupr. and Guadua angustifolia Kunth were collected in Puebla, Mexico. Four taper functions were evaluated, the one with the best predictive capacity was fitted to model the diameter over and under wall together with a wall thickness model. The fitting strategy consisted of a system of additive equations using Weighted-Nonlinear Seemingly Unrelated Regression (WNSUR) procedure with autocorrelation correction, in combination with the Dummy Variable technique. Main results: The Fang & Bailey case 1-a model was selected to describe the diameter over and under wall; the Cao and Papper model was used to model the wall thickness. The R2adj of the system fitted were 0.977, 0.944 and 0.918, and RMSE values 0.186 cm, 0.200 cm and 0.134 cm, for diameter over wall, diameter under wall, and wall thickness, respectively. G. angustifolia had the greatest taper and wall thickness, followed by G. aculeata. The highest proportion of primary product was presented by G. angustifolia. The system generated had parameters specific for each bamboo taxon. Research highlights: The diameter profile of bamboo culms can be modeled by taper functions. A mathematical system for distribution by structural product type was developed consisting of: (1) a taper model for the diameter over wall and, (2) a function to estimate the commercial height.

Bamboo species have a high potential to produce biomass and stock carbon. However, biometric tools are not available to estimate biomass production for most giant bamboo taxa. The aim was to develop an additive equation system to estimate the aboveground biomass by structural component and the total of the three bamboo species. Destructive sampling was applied, and a sample of 101 mature bamboo specimens was collected. The nonlinear power allometric model was used to integrate two additive equations systems, which were formed by the structural components of biomass: culm, branches and leaves as well as aboveground biomass total. The predictor variables were: diameter at breast height (D) for the S1 system, and D in combination with the total height (D²H) for the S2 system.

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.

La altura total (At) de los culmos de bambú es fundamental para realizar inventarios de volumen, biomasa, almacenes de carbono y distribución de productos. Su medición directa en campo se dificulta por la alta densidad del dosel y la inclinación natural de la parte alta de la copa. Las ecuaciones alométricas son una alternativa viable para estimar eficientemente la altura en función del diámetro normal (Dn). El objetivo fue evaluar la calidad de ajuste de modelos matemáticos At-Dn y seleccionar el de mejor capacidad predictiva para estimar la At de culmos de Bambusa oldhamii Munro, Guadua aculeata Rupr. y Guadua angustifolia Kunth en la Sierra Nororiental de Puebla, México. En el análisis se utilizaron 101 pares de observaciones At-Dn con los que se ajustaron por regresión no lineal seis modelos alométricos y tres de crecimiento. Se compararon las técnicas de mínimos cuadrados ordinarios no lineales con variables indicadoras (MCO-NL-VI) y modelos de efectos mixtos no lineales (MEM-NL), se usó el paquete “nlme” del programa R. Los modelos se evaluaron con base en el coeficiente de determinación ajustado (R²_adj), la raíz del error medio cuadrático (REMC) y el sesgo promedio (S). MCO-NL-VI explicó el 83.5 % y MEM-NL el 83.2 % de la variabilidad observada. El modelo con el mejor desempeño fue el Logístico ajustado con MCO-NL-VI (R²_adj = 0.835, REMC= 2.280 m y S= 0.005 m). El modelo At-Dn generado es factible para estimar la At para culmos de los tres taxones de bambú con errores bajos.