Category Archives: Original Research Articles

An approximate height growth and site index model for Quercus sideroxyla Bonpl. in mixed-species stands of Durango, Mexico

Introduction: Predictions of dominant or co-dominant height are an important element in planning forest management with timber production objectives. Objective: To develop dominant height growth and site index (SI) equations for Quercus sideroxyla Bonpl. Materials and methods: The height current annual increment model was fitted, and the age of the sections was estimated from a database of 29 stem-mapped plots. A taper analysis data of 37 trees was also used to reconstruct dominant height growth trajectories. Three equations based on algebraic difference approach (ADA; one anamorphic and two polymorphic) and an equation based on generalized algebraic difference approach (GADA) were used to simultaneously model the dominant height and SI. Results and discussion: The ADA polymorphic equations were statistically better than the anamorphic equation, according to the adjusted coefficient of determination, root mean square error, mean bias, Akaike’s information criterion and log-likelihood; however, the GADA equation was better than the ADA equations. The growth curves were biologically realistic and showed SI classes at a base age of 60 years. Conclusions: The developed equations can be used for decision making in forest management when Q. sideroxyla shows dominance over Pinus species and the main objective is timber production

Can an Exponential Function Be Applied to the Asymptotic Density–Size Relationship? Two New Stand-Density Indices in Mixed-Species Forests

Abstract: This study presents two stand-density indices (SDIs) based on exponential density decline as a function of quadratic mean diameter for all species combined in mixed-species forests with 22 species mix grouped in four species groups. The exponential-based density–diameter relationship, as well the density index corresponding to the slope or instantaneous mortality rate parameters, was compared with those based on power-law density–diameter relationship. A dataset of 202 fully stocked circular plots at maximum density was used for fitting the models, and a dataset of 122 circular plots was used for validation stand density index for all species combined of mixed-species stands. The dataset for validation was independent of dataset for model development. The first stand-density index showed a density management graphic (DMG) with a variable intercept and common instantaneous mortality rate, and the second index showed a DMG with common intercept and variable mortality rate. Additionally, the value of the initial density of the fitted line was more realistic than those generated by the potential model for all species combined. Moreover, the density management diagrams showed a curvilinear trend based on the maximum stand density index in graphical log–log scale. The DMGs could be interpreted as forest scenarios based on variable initial density and common management objectives or the same density and different management objectives for forest-rotation periods involving all species combined in mixed-species stands. The fitting of exponential and potential equations for species or species groups showed that the density–size relationships in mixed-species forests should be modeled for all species combined because the disaggregation of mixture species represented a weak tendency for each species or species group and the resultant fitted equations were unrealistic.

Compatible taper, volume, green weight, biomass and carbon concentration system for Quercus sideroxyla Bonpl./Sistema compatible de ahusamiento, volumen, peso verde, biomasa y concentración de carbono para Quercus sideroxyla Bonpl.

Introduction: Estimation of total and merchantable tree volume, as well as of biomass and carbon, implies the generation of biometric tools essential in forest management and planning.
Objectives: To fit a compatible taper, volume, green weight, dry biomass and carbon concentration system for Quercus sideroxyla Bonpl. species using wood density.
Materials and methods: A database of 522 diameter-height measurements, obtained from 37 trees, was used in the fitting equations. The compatible system (CS) was integrated by 34 equations, which were simultaneously fitted by generalized nonlinear least squares. Taper and volume were the base variables for estimating green weight, dry biomass and carbon concentration.
Results and discussion: All equations were compatible with the stem volume equation, and the merchantable equations with the taper and merchantable volume equations. The fit statistics showed the efficiency of the equations in global terms and by relative height classes.
Conclusions: The CS has the property of estimating taper, merchantable volume, green weight, dry biomass and carbon concentration at upper-height and by components (stem, total tree and branches).
Introducción: La estimación de volumen total y comercial de árboles, así como la de biomasa y carbono, implica la generación de herramientas biométricas esenciales en el manejo y planeación forestal.
Objetivos: Ajustar un sistema compatible (SC) de ahusamiento, volumen, peso verde, biomasa seca y concentración de carbono para la especie Quercus sideroxyla Bonpl., con el uso de la densidad de la madera.
Materiales y métodos: Una base de datos de 522 pares de diámetro-altura, obtenida de 37 árboles, se utilizó en el ajuste. El SC se conformó de 34 ecuaciones ajustadas simultáneamente por mínimos cuadrados generalizados no lineales. El ahusamiento y volumen fueron las variables base para la estimación del peso verde, biomasa seca y concentración de carbono.
Resultados y discusión: Todas las ecuaciones fueron compatibles con la ecuación de volumen de fuste, y las ecuaciones comerciales, con los parámetros del ahusamiento y volumen comercial. Los estadísticos de ajuste mostraron la eficiencia de las ecuaciones en términos globales y por clases de altura relativa.
Conclusiones: El SC posee la cualidad de estimar el ahusamiento, volumen comercial, peso verde, biomasa seca y concentración de carbono a una altura comercial y por componentes (fuste, total árbol y ramas).

My First Research Article

Diameter, height and volume estimation from the stump of forest species of Durango state / Estimación del diámetro, altura y volumen a partir del tocón para especies forestales de Durango.


When a forest mass has been harvested following a management program and the size of the stumps are the only evidence, it is possible to estimate diameter, height and volume of standing trees by allometric relationships. In this paper is described an experiment in which 12 mathematical models were fitted to predict normal diameter, total height and stem volume from the diameter of the stump of Pinus arizonica, P. ayacahuite, P. durangensis, P. leiophylla, P. teocote and Quercus sideroxila in San Diego de Tezains, Santiago Papasquiaro municipality, which is located at the northwestern region of the state of Durango and belongs to the Sierra Madre Occidental. A sample of 267 felled trees and linear and non-linear models were used. The fitting of models indicates that there is a linear tendency between normal diameter and total height, in terms of stump diameter, while for the volume of the stump, there is a logarithmic relationship. Also, a similitude among species in regard to the relations of the studied variables was observed. The resulting equations may be applied in the reconstruction of scenes after a forestry intervention occurs or when a catastrophic event takes place.

Key words: Height of stem, diameter at breast-height , stump diameter, mathematical model, allometric relationships, stem volume


Cuando una masa forestal ha sido aprovechada mediante un programa de manejo y solo se tiene como evidencia las dimensiones de los tocones, es posible estimar a través de relaciones alométricas el diámetro y la altura, así como el volumen de los árboles en pie. En el presente trabajo se describe un experimento en el que se ajustaron 12 modelos matemáticos para predecir el diámetro normal, la altura total y el volumen del fuste, a partir del diámetro del tocón para Pinus arizonica, P. ayacahuite, P. durangensis, P. leiophylla, P. teocote y Quercus sideroxila en el ejido San Diego de Tezains, municipio Santiago Papasquiaro, Durango, que se ubica en la región noroeste del estado, en la Sierra Madre Occidental. Para ello, se utilizó una muestra de 267 árboles derribados y se emplearon modelos lineales y no lineales. El ajuste de los modelos indica que existe una tendencia lineal entre las variables diámetro normal y altura total, en función del diámetro del tocón; mientras que para el volumen del fuste, la relación es logarítmica. Así mismo, se observó que existe similitud entre especies, con respecto a las relaciones de las variables estudiadas. Las ecuaciones obtenidas pueden aplicarse en la reconstrucción de escenarios después de una intervención silvícola o la ocurrencia de fenómenos naturales catastróficos.

Palabras clave: Altura de fuste, diámetro del tocón, diámetro normal, modelo matemático, relaciones alométricas, volumen de fuste.

1. Quiñonez-Barraza et al. (2012). Rev Mex Cienc For 3(9): 23-39