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Spatial structure refers to the horizontal and vertical arrangement of individual trees, and the most accurate way to describe it within a community is to characterize tree strata in terms of their dimensions. The aim of this study was to determine the horizontal and vertical structure of pure stands of Pinus ayacahuite Ehrenb. ex Schltdl., in forests of southern Mexico. Forest measurement data from 24 sample plots were used. For analysis of the horizontal structure, diameters within a range of 0.20 cm to 77 cm were used, while for the vertical structure, heights were from 0.09 m to 40.9 m. Non-parametric histograms and Kernel density methods were used in the analysis, and Fisher and Marron multimodality tests were performed. The homogeneity of the forest stands was determined by the coefficient of homogeneity, and the vertical and horizontal structures were described using the stratification proposed by Pretzsch. The results indicate that the horizontal structure corresponds to a diameter distribution with a reversed "J" shape in 79.2% of the sample plots, while 91.8% of the sites were classified as irregular with coefficients of homogeneity of 1.0 to 3.0. In the vertical structure, it was observed that the lower stratum predominated in 75% of the plots, while 25% had a higher concentration of individuals in the middle stratum. The upper stratum had accumulation percentages ranging from 1.3% to 33.3% but did not predominate in any of the plots. According to the multimodality tests, 50% of the plots present multimodality in the horizontal structure, while in the vertical structure this condition is present in 38% of the plots. Knowledge of the spatial structure of Pinus ayacahuite forest stands is essential to define silvicultural strategies that ensure the sustainable functioning of the ecosystem in terms of yield continuity and conservation.

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 (R2adj), 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.

La comunidad de Ixtlán de Juárez, Oaxaca, posee un potencial maderable importante debido a la productividad alta de su bosque. Una de las especies con mayor importancia es Pinus patula debido a la distribución y valor comercial alto; además, es de crecimiento rápido. Por lo tanto, es necesario determinar los límites de la densidad máxima posible que los rodales pueden sustentar para dirigir acciones encaminadas al control de la competencia y redistribución del espacio de crecimiento. En este estudio se estimó la línea de densidad máxima (límite superior del autoaclareo) con el modelo de Reineke mediante dos enfoques de estimación de los parámetros: (1) mínimos cuadrados ordinarios (MCO) y (2) regresión de frontera estocástica (RFE) con los modelos de tipo seminormal (half-normal) y normal truncado (truncated-normal). Para el ajuste del modelo se utilizaron datos de 64 parcelas permanentes de investigación silvícola de 400 m2 de rodales puros y coetáneos de P. patula. La estimación del límite superior del autoaclareo con el modelo de RFE en la forma seminormal fue eficiente y permitió conocer el índice de densidad máxima de los rodales estudiados. La línea de densidad máxima representó el insumo primordial para construir una guía de densidad; herramienta indispensable para la definición de regímenes de aclareo y optimización del espacio de crecimiento.