Revista Mexicana de Ciencias Forestales Vol. 15 (84)

Julio - Agosto (2024)

Fecha de recepción/Reception date: 12 de septiembre de 2023.

Fecha de aceptación/Acceptance date: 25 de marzo de 2024.

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¹Campo Experimental Valle de Guadiana, Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias. México.

²Instituto Politécnico Nacional, Centro Interdisciplinario de Investigación para el Desarrollo Integral Regional, Unidad Durango. México.

³Universidad para el Bienestar Benito Juárez García, Sede Tepehuanes Durango. México.

*Autor para correspondencia; correo-e: monarrez.jose@inifap.gob.mx

*Corresponding author; e-mail: monarrez.jose@inifap.gob.mx

Abstract

In forestry, accurate estimation of timber volume is essential for forest management in temperate forests. The objective of the present research was to generate equations of the total tree volume (Vtt), stem volume (Vs), and stem profile for Pinus ayacahuite, Pinus leiophylla, Pinus hartwegii, Pinus montezumae, Pinus patula, Pinus pseudostrobus, Pinus teocote, Abies religiosa and Quercus sp. in productive landscapes of a temperate ecosystem in the state of Puebla, Mexico. A sample of 1 676 trees was collected by destructive sampling. Based on the dendrometric type, the Vs, Vtt, and crown volume (Vc) were obtained. The volume of branches and twigs with diameters less than 5 cm was estimated using a xylometer and the Berkhout nonlinear model. The Schumacher-Hall model was fitted for the Vtt and the Vs with weighted regression in order to correct for heteroscedasticity. The Biging function was used to describe the stem profile, fitted with nonlinear generalized least squares to correct for autocorrelation. The goodness of fit of the equations are above 96 %, and the bias is below 0.04 m³. The statistical results show that the differential equation system predicts with certainty the Vtt, Vs, as well as the taper of commercial species in the temperate forests of Puebla, Mexico.

Key words: Taper, allometric equations, stem profile, Pinus spp., stem volume, total tree volume.

Resumen

En silvicultura, la estimación precisa del volumen maderable es fundamental para el manejo forestal en bosques templados. El objetivo de la presente investigación fue generar ecuaciones de volumen total árbol (Vta), volumen fustal (Vf) y perfil del fuste para Pinus ayacahuite, Pinus leiophylla, Pinus hartwegii, Pinus montezumae, Pinus patula, Pinus pseudostrobus, Pinus teocote, Abies religiosa y Quercus sp. en paisajes productivos de un ecosistema templado en Puebla, México. Mediante un muestreo destructivo se recolectó una muestra de 1 676 árboles. Con base en el tipo dendrométrico se obtuvo el Vf, Vta y volumen de copa (Vc). Con un xilómetro y el modelo no lineal de Berkhout se estimó el volumen de ramas y ramillas con diámetros menores a 5 cm. Para Vta y Vf se ajustó el modelo Schumacher-Hall con regresión ponderada para corregir la heterocedasticidad. La función de Biging se usó para describir el perfil fustal, ajustado con mínimos cuadrados generalizados no lineales para corregir la autocorrelación. La bondad de ajuste de las ecuaciones fue superior a 96 % y un sesgo menor a 0.04 m³. Los resultados estadísticos muestran que el sistema de ecuaciones diferenciado predice con certidumbre el Vta, Vf y ahusamiento de las especies maderables comerciales en los bosques templados de Puebla, México.

Palabras clave: Ahusamiento, ecuaciones alométricas, perfil fustal, Pinus spp., volumen fustal, volumen total árbol.

Introduction

Forest or total volumes are generally estimated based on linear and nonlinear functions. The allometric equations cited in the literature include the following: Combined variable, Korsun, Schumacher-Hall, Australian, Meyer modified, Naslund, Takata, Understandable, Logarithmic, Thornber, Berkhout, Honer, and Wenk (Clutter et al., 1983; Romahn et al., 1994; Prodan et al., 1997). Because of its accuracy and simplicity, the Schumacher-Hall model is one of the most widely used ones (Corral-Rivas and Návar-Cháidez, 2009; Vargas-Larreta et al., 2018).

According to Burkhart and Tomé (2012), there are several equations for describing a tree’s stem profile. The most commonly used ones are Bruce et al. (1968), Demaerschalk (1972), Ormerod (1973), Max and Burkhart (1976), Cao et al. (1980), Clutter (1980), Biging (1984), Kozak (1998), Rentería-Anima and Ramírez-Maldonado (1998), Bi (2000), Fang et al. (2000), Sharma and Oderwald (2001), among others.

During the last two decades, in Mexico, adjustments of taper functions and commercial volume have been generated for several tree species of the temperate ecosystem: for Abies religiosa (Kunth) Schltdl. & Cham. in various regions of the country (Guzmán-Santiago et al., 2022), for Pinus greggii Engelm. ex Parl. in the state of Hidalgo (Hernández-Ramos et al., 2017), for Quercus sideroxyla Bonpl. in the state of Durango (Quiñonez-Barraza et al., 2019), for Quercus sp. in the state of Puebla (Tamarit et al., 2017); for Pinus pseudostrobus Lindl. in the state of Nuevo León (Flores et al., 2021), for Pinus oocarpa Schiede ex Schltdl., and for Pinus douglasiana Martínez in Durango (López et al., 2015); for Pinus teocote Schltdl. & Cham. in Nuevo Léon (Tapia and Návar, 1998), and for Pinus cooperi C. E. Blanco, Pinus durangensis Martínez, Pinus engelmannii Carrière, Pinus leiophylla Schiede ex Schltdl. & Cham., Pinus herrerae Martínez, Pinus ayacahuite C. Ehrenb. ex Schltdl., Pinus arizonica Engelm., and Pinus teocote in Durango (Corral et al., 1999; Quiñonez-Barraza et al., 2014); for P. ayacahuite in the state of Oaxaca (Ramírez-Martínez et al., 2018) and for P. cooperi in Durango (Cruz-Cobos et al., 2008), among others.

The obtained results with Bigin’s (Biging, 1984) and Fang’s equation (Fang et al., 2000) have been very accurate in describing the stem profile (Corral-Rivas and Návar-Cháidez, 2009; Pompa et al., 2009). Biging’s equation (Biging, 1984) has the advantage of presenting only two parameters, in contrast with other functions.

Understanding and quantifying wood volume is essential to planning and implementing sustainable forest management (Ramírez-Martínez et al., 2018; Flores et al., 2021). Tree volume can be estimated in parts or as a whole, including stem, branches, and twigs (Vargas-Larreta et al., 2018). The stem volume refers to the volume of the straight and cylindrical part of the trunk, or it may be limited to a certain portion of the stem. The latter is determined using taper functions, which predict the profile of the tree trunks at different heights.

In 2013, the Comisión Nacional Forestal (National Forest Commission) and several institutions in Mexico generated the project: “Development of a biometric system for forest management planning in ecosystems with timber potential in Mexico” which was developed for the state of Chihuahua, Guerrero, Jalisco, Durango, Oaxaca, Michoacán, Puebla, Estado de México, Hidalgo, Tlaxcala, Veracruz and Quintana Roo; 6 414 equations in it were generated to estimate volume, taper and site quality (Vargas-Larreta et al., 2018). The Schumacher and Hall model (Schumacher, 1933) was used to calculate the timber volume, and Fang’s compatible model was used for the taper and commercial volumes. For the crown volume, when estimating the total tree volume, this biometric system considered only the volume of branches and twigs with diameters above 5 cm, and did not generate the tree and total tree equations separately; thus, although these estimates are covered by additive equations, in their practical application they correspond to the marketing of the tree; while in the traditional technical management applied in Puebla, the differentiated equations are of greater use and operational importance and also take into account the volume of branches and twigs with diameters of less than 5 cm.

According to Santos (2023), the total stem volume functions by species group, generated as part of the National Forest Inventory more than 40 years ago, are still in use in the state of Puebla. Therefore, the objective was to generate differentiated and simplified equations for the total tree volume, the stem volume, and the stem profile for Pinus ayacahuite, P. hartwegii Lindl., P. leiophylla, P. montezumae Lamb., P. patula Schltdl. & Cham., P. pseudostrobus, P. teocote, Abies religiosa and Quercus sp.,which are themain commercial timber species in the temperate ecosystem of Puebla, Mexico.

Materials and Methods

Study area

The study was conducted in forest areas with timber harvesting in Puebla, Mexico, specifically in the Forest Management Units (Umafor, by its acronym in Spanish) No. 2101, Izta Popo (642 676 ha); No. 2103, Teziutlán (324 329 ha); No. 2105, Centro y Pico de Orizaba (414 817 ha), and No. 2108, Chignahuapán-Zacatlán (271 853 ha) (Conafor, 2023). The Umafors are located between the coordinates 97°10’ and 98°45’ W and 18°10’ and 20°15’ N (Figure 1). The species of timber forest importance for Puebla―Pinus ayacahuite, P. hartwegii, P. leiophylla, P. montezumae, P. patula, P. pseudostrobus, P. teocote, Abies religiosa, and Quercus sp.―were identified in the course of interactions with technical forest service providers, producers, and government officials— through training programs and demand collection.

Figure 1. Location of the study area.

Data collection and measured variables

Data were collected from 1 676 random selected trees through a destructive sampling that included the felling and cutting down of the specimens. The diametric and height distributions were considered in the selection process. In order to measure and calculate the volume, each tree was divided into stem and crown. The shaft was initially cut at a height of 0.30 m above the ground level. Measurements were taken in two 0.30 m sections, one just above the stump, and the other, up to the normal diameter height (1.3 m). Subsequently, measurements of the trunk were taken at intervals of 2 m in length, until the tip of the tree was reached. The last section should not exceed 1.3 m in length. The crown was divided into two parts: (a) Branches with minor section diameters >5 cm and lengths no longer than 2 m; and (b) Branch tips and twigs with minor section diameters <5 cm. Branches and twigs with diameters under 5 cm were weighed with a model 29966 Pretul^® 40 kg commercial scale and three samples were obtained (upper, middle, and lower part of the crown); its volume was estimated with a Xilometer (water drum, previously calibrated to measure volume). Measurements were made with a model 283D Forestry Suppliers^® diameter tape, with a model TP30M Truper^® 30 m flexometer, and the cuts were made with a model MOT-5120 Truper^® 51cc 2.7 hp gasoline chainsaw.

The recorded variables were: diameter at breast height (DBH, cm), total tree height (H, m), stump height (hs, m), diameter outside-bark for each section (Dob, cm), section lengths (l, m), bark thickness (Bt, mm), outside-bark diameter for each branch section (Dob, cm), section length for branches with diameters above 5 cm (Bls, m), total crown weight (CWT, kg), sample weight (Ws, kg), and branch sample volume (Vsbr, cm³). 

Volume calculation

The volume of each section was calculated based on the corresponding dendrometric type (Table 1), except for the volume of the branches and twigs with a diameter of less than 5 cm, which was estimated using a weight/volume ratio and then fitted to a regression model. The total volume of the tree with bark (Vttob) was estimated by adding the volume of the stump+volume of the stem+volume of the tip+volume of the crown in branches with diameters greater than 5 cm+volume of the branches and twigs with diameters less than 5 cm. The stem volume with bark (Vsob) was estimated by adding stump volume+trunk volume+tip volume.

V = Volume (m³); So = Surface area of the smaller section (m²); S1 = Surface area of the larger section (m²); S₀ and S₁= Larger and smaller surface areas; l = Length (m). Source: Romahn et al. (1994).

Prior to the statistical analysis, outliers were reviewed and a database was created using Microsoft Office Excel (Pérez, 2006).

Adjustment of equations for total tree volume and stem volume

Berkhout’s allometric equation (Prodan et al., 1997) (Equation 1) was adjusted to estimate the volume of the branches and twigs under 5 cm. This volume component was determined at the genus level because of the complexity of the measurement and the minimal proportional contribution to the total tree volume. A database of 31 trees was used for the Abies genus, of 134 trees for Pinus L., and of seven trees for Quercus.

Where:

Vbt = Volume of the branches and twigs (m³)

β_i = Coefficients

DBHob = Outside-bark diameter at breath height (cm)

The Schumacher-Hall expression (Schumacher, 1933) was used to estimate the total tree and stem volume by species (Equation 2).

Where:

V = Volume (m³)

β_i = Parameters

DBHob = Outside-bark diameter breast height (cm)

H = Total tree height (m)

The independence and homogeneous distribution of errors with zero mean and constant variance were verified: multicollinearity, autocorrelation, and heteroscedasticity. The graphical analysis of residuals versus estimates showed problems of heteroscedasticity in all the species; therefore, a weighted regression with a weight equal to the inverse of the variance of each observation was used. To evaluate the fit, the statistics of the Standard error of the estimator (Ese) and the Coefficient of determination or adjusted R² (R²_ADJ) were estimated. 

Adjustment of the taper equation

The Biging equation (Biging, 1984) was utilized to model and describe the stem profile. This expression is based on the integral form of the Bertalanffy-Richards equation with two parameters (Biging, 1984) (Equation 3).

Where:

d = Diameter at different heights of the stem (cm)

DBH = Diameter at breast height (cm)

β_i = Parameters to be estimated

log = Natural logarithm

h = Height for each section with respect to the ground (m)

H = Total treeheight (m)

exp = Exponential function

m = Constant value of 3 (Corral et al., 1999)

Given that a correlation was detected in the observations, which breaks the principle of independence of errors, the nonlinear generalized least squares technique was applied (Huang et al., 2000); the error term was expanded by a continuous autoregressive model of order x [CAR(x)] (Equation 4).

Where:

e_ij = j^th ordinary residue of the i^th tree

e_ij-k = j^th ordinary residue of the i-k^th tree

l_k= 1 for j>k and is zero for j≤k

 = Autoregressive parameter of order k to be estimated

h_ij-h_ij-k = Distance separating the j^th-k^th observation within each tree with h_ij>h_ij-k

 = Error term under independence condition

The referred error structure was fitted simultaneously with the Biging taper and Schumacher-Hall volume expressions.

In order to increase efficiency in detecting outliers in the taper, a nonparametric quadratic local adjustment (assuming a normal distribution of errors) was performed for each of the species using LOESS local regression, with a smoothing parameter of 0.3 for each species (Pompa et al., 2009). The volume and taper equations were adjusted by species was carried out with the MODEL and NLIN procedure of SAS (SAS Institute Inc., 2015), which allows a dynamic update of the residuals. 

Results

Table 2 shows the descriptive statistics by species for the diameter and height variables.

Table 2. Descriptive statistics of the analyzed database.

The fit of the Berkhout model for estimating the volume of branches and twigs by gender with diameter <5 cm was good; Table 3 shows the significant parameters and high values in the R²_ADJ.

Table 3. Statistical parameters of the equation for estimating the volume of the branches and twigs under and equal to 5 cm by genus.

Vbt = Volume of the branches and twigs (m³); DBH = Outside-bark diameter at breast height (cm); β_i = Estimated parameters; R²_ADJ = Coefficient of determination.

The Schumacher-Hall model fit for Vs and Vtt by species showed low bias and significant parameters (Tables 4 and 5).

Table 4. Parameters and statistics of the equations for estimating the volume of the stem.

β_i = Estimated parameters; seβ_i = Standard error of the estimator; R²_ADJ = Adjusted coefficient of determination.

Table 5. Parameters and statistics of the equations for estimating the total tree volume.

β_i = Estimated parameters; seβ_i = Standard error of the estimator; R²_ADJ = Adjusted coefficient of determination. 

The Vs equations fitted for the eight timber species and one at the genus level were found to be accurate. The Vs model for A. religiosa, P. ayacahuite, P. leiophylla, and P. montezumae had the lowest values for standard error and bias, as well as the highest value for the Coefficient of determination.

The adjustment of Vtt equations show adequate coefficients of determination and standard error for the eight species and for the genus Quercus. The Vtt equation for A. religiosa, P. ayacahuite, P. leiophylla, and P. montezumae had the lowest values for standard error, bias and best fit. Table 6 shows the final equations for estimating the Vs and the Vtt by species.

Table 6. Volumetric equations determined for timber species in the temperate ecosystem of Puebla, Mexico.

Vs = Stem volume (m³); DBH = Outside-bark diameter at breast height (cm); H = Total tree height (m); Vtt = Total tree volume (m³).

Table 7 shows the parameters of the taper functions by species. The residuals and the values of the Root Mean Square Error statistics (RMSE) and the adjusted Coefficient of determination (R²_ADJ) were reviewed. 

Table 7. Parameters and fit statistics of the Biging taper equation.

β_i = Estimated parameters of the estimators; seβ_i = Standard error of the estimator; RMSE = Root Mean Square Error; R²_ADJ = Adjusted coefficient of determination. 

According to the values of the fit statistics and significance of the parameters, the equations adequately explain the stem profile for each species (Table 8).

Table 8. Stem profile equations by timber species of the temperate ecosystem of Puebla, Mexico.

d = Diameter at a given height of the stem (cm); DBH = Outside-bark diameter at breast height (cm); H = Total tree height (m); h = Height determined for estimation with respect to the ground (m); exp = Exponential constant; log = logarithm. 

Discussion

Equations for Vs and Vtt were fitted with the Schumacher-Hall model (Schumacher, 1933) and for stem profile with the Biging model (Biging, 1984), for eight commercial timber conifers and the Quercus sp. from the temperate ecosystem in Puebla, Mexico. A total of 27 equations were obtained; the results exhibit similarities with those obtained by Ramírez-Martínez et al. (2018), who fitted several models to estimate the total volume in Pinus ayacahuite, and concluded that the Schumacher-Hall model had the lowest bias (Bias=0.026 m³). Tapia and Návar (2011) fitted and validated eight volume equations for P. pseudostrobus, and the Schumacher-Hall model proved to be accurate with a high level of reliability (R²_ADJ=0.96).

Ramos-Uvilla et al. (2014) generated volume equations for Pinus lawsonii Roezl ex Gordon and P. oocarpa; the authors evaluated five models and the best fit was the Schumacher-Hall model (R²_ADJ=0.99). Corral-Rivas and Návar-Cháidez (2009) evaluated seven models for estimating stem volume in Pinus cooperi, P. durangensis, P. engelmannii, P. leiophylla, and P. herrerae of Durango; again, the Schumacher-Hall model had the highest coefficients of determination, and the lowest standard errors and normally distributed errors. Rodríguez-Flores et al. (2019) utilized the linearized Schumacher-Hall model to estimate the volume components of nine common species or taxa groups in the temperate forests of Northwestern Mexico, and their findings show that the model fit the data adequately.

Guzmán-Santiago et al. (2022) reported that the Schumacher-Hall equation used in the estimation of the total tree crown for Abies religiosa in the state of Puebla was the most accurate. Vargas-Larreta et al. (2018) applied the Schumacher-Hall model to estimate the stem volume of wood in timber species of the states of Chihuahua, Guerrero, Jalisco, Durango, Oaxaca, Michoacán, Puebla, Estado de Mexico, Hidalgo, Tlaxcala, Veracruz and Quintana Roo, and their equations were grouped in the Forest Biometric System (Sibifor).

The Biging model (Biging, 1984) has been widely used in forest management to describe the stem profile as a function of the normal diameter. Rentería-Anima and Ramírez-Maldonado (1998) evaluated ten taper equations for P. cooperi in Durango and observed that the models showed problems in predicting the stump diameter (0.3 m). Corral et al. (1999) validated six taper models for P. cooperi, P. durangensis, P. engelmannii, P. leiophylla and P. herrerae in the forest region of El Salto, Durango, Mexico; their statistical tests showed that the Biging model (Biging, 1984) predicted the diameter profile with a good fit.

In a similar way, Pompa et al. (2009) compared thinning models and determined for P. arizonica in the Southwestern region of Chihuahua that the Biging model (Biging, 1984) had the greatest predictive ability and allowed the design of a compatible volume equation. Corral-Rivas and Návar-Cháidez (2009) determined that the taper function of the Biging model for Pinus cooperi, P. durangensis, P. engelmannii, P. leiophylla, and P. herrerae in Durango provides comparable volumes at the tree or stand level with conventional (Smalian, Huber or Newton) volume equations. Tamarit et al. (2017) generated a cubing system for the genus Quercus sp. in Puebla using the segmented model of Fang et al. (2000), with very good prediction.

Conclusions

The fitted equations based on the Schumacher-Hall expression at the species level provide reliable and accurate estimates for determining the stem volume and total tree volume of Pinus ayacahuite, P. leiophylla, P. hartwegii, P. montezumae, P. patula, P. pseudostrobus, P. teocote, Abies religiosa, and Quercus sp. in temperate forests of Puebla, Mexico. Equations based on the Biging model were generated to model the tapering of the same species.

Given the technical management and timber harvesting currently carried out in Puebla, it is considered convenient to use the equations generated to replace those developed 46 years ago by the then Forest Undersecretary of the Secretariat of Agriculture and Hydraulic Resources. Therefore, their implementation is recommended in the elaboration and execution of timber harvesting management programs in this state.

Acknowledgments

The authors would like to thank the National Forest Commission, the Secretariat of Rural Development, Sustainability and Land Management of the Government of Puebla, and the technical forest service providers, owners, and holders of forest resources for their support in the development of this study.

Conflict of interest

The authors declare that they have no conflicts of interest. José Carlos Monárrez-González and Gerónimo Quiñones Barraza declare that they did not participate in any stage of the editorial process of this article.

Contribution by author

José Carlos Monárrez-González: conceptualization of the research, data collection, statistical analysis, drafting of the manuscript; Marco Antonio Márquez-Linares: review, statistical analysis and correction of the manuscript; Juan Antonio López Hernández: in-field data collection and correction of the manuscript; Gustavo Pérez Verdín and Gerónimo Quiñones Barraza: drafting of the manuscript and statistical analysis; Xavier García Cuevas: drafting, revision and correction of the manuscript.

References

Bi, H. 2000. Trigonometric variable-form taper equations for Australianeucalyptus. Forest Science 46(3):397-409. Doi: 10.1093/forestscience/46.3.397.

Biging, G. S. 1984. Taper equations for second-growth mixed conifers of Northern California. Forest Science 30(4):1103-1117. Doi: 10.1093/forestscience/30.4.1103.

Bruce, D., R. O. Curtis and C. Vancoevering. 1968. Development of a system of taper and volume tables for red alder. Forest Science 14(3):339-350. Doi: 10.1093/forestscience/14.3.339.

Burkhart, H. E. and M. Tomé. 2012. Modeling forest trees and stands. Springer Dordrecht. Berlin, Bel., Germany. 458 p.

Cao, Q. V., H. E. Burkhart and T. A. Max. 1980. Evaluation of two methods for cubic-volume prediction of Loblolly pine to any merchantable limit. Forest Science 26(1):71-80. Doi: 10.1093/forestscience/26.1.71.

Clutter, J. L. 1980. Development of taper functions from variable-top merchantable volume equations. Forest Science 26(1):117-120. Doi: 10.1093/forestscience/26.1.117.

Clutter, J. L., J. C. Fortson, L. V. Pienaar, G. H. Brister and R. L. Bailey. 1983. Timber management: A quantitative approach. Wiley. New York, NY, United States of America. 333 p.

Comisión Nacional Forestal (Conafor). 2023. Memorias de estudios Regionales de Puebla, México (2101, 2103, 2105, 2108). Conafor. http://www.conafor.gob.mx:8080/documentos/default.aspx?grupo=9&tema=164. (13 de enero de 2023).

Corral R., S., J. de J. Návar C. y F. Fernández S. 1999. Ajuste de funciones de ahusamiento a los perfiles fustales de cinco Pináceas de la región de El Salto, Durango. Madera y Bosques 5(2):53-65. Doi: 10.21829/myb.1999.521347.

Corral-Rivas, S. y J. de J. Návar-Cháidez. 2009. Comparación de técnicas de estimación de volumen fustal total para cinco especies de pino de Durango, México. Revista Chapingo Serie Ciencias Forestales y del Ambiente 15(1):5-13. https://www.scielo.org.mx/pdf/rcscfa/v15n1/v15n1a1.pdf. (13 de agosto de 2023).

Cruz-Cobos, F., H. M. De los Santos-Posadas y J. R. Valdez-Lazalde. 2008. Sistema compatible de ahusamiento-volumen para Pinus cooperi Blanco en Durango, México. Agrociencia 42(4):473-485. https://www.scielo.org.mx/scielo.php?pid=S1405-31952008000400010&script=sci_arttext. (13 de agosto de 2023).

Demaerschalk, J. P. 1972. Converting volume equations to compatible taper equations. Forest Science 18(3):241-245. Doi: 10.1093/forestscience/18.3.241.

Fang, Z., B. E. Borders and R. L. Bailey. 2000. Compatible volume-taper models for Loblolly and slash pine based on a system with segmented-stem form factors. Forest Science 46(1):1-12. Doi: 10.1093/forestscience/46.1.1.

Flores M., E. A., A. C. Rodríguez A., O. A. Aguirre C., E. Alanís R. y G. Quiñonez B. 2021. Sistema compatible de ahusamiento-volumen para Pinus pseudostrobus Lindl. en el ejido Corona del Rosal, Nuevo León, México. Madera y Bosques 27(2):1-12. Doi: 10.21829/myb.2021.2722130.

Guzmán-Santiago, J. C., B. Vargas-Larreta, M. Gómez-Cárdenas y G. Quiñonez-Barraza. 2022. Función ahusamiento-volumen comercial de Abies religiosa (Kunth) Schltdl. & Cham. en varias regiones de México. Colombia Forestal 25(1):77-94. Doi: 10.14483/2256201x.17814.

Hernández-Ramos, J., A. Hernández-Ramos, J. de J. García-Magaña, X. García-Cuevas, … y E. H. Olvera-Delgadillo. 2017. Sistema compatible de ahusamiento-volumen comercial para plantaciones de Pinus greggii Engelm. en Hidalgo, México. Revista Mexicana de Ciencias Forestales 8(39):59-70. https://www.scielo.org.mx/scielo.php?pid=S2007-11322017000100059&script=sci_arttext. (13 de agosto de 2023).

Huang, S., D. Price and S. J. Titus. 2000. Development of ecoregion-based-heigth-diameter models for white spruce in boreal forests. Forest Ecology and Management 129(1-3):125-141. Doi: 10.1016/S0378-1127(99)00151-6.

Kozak, A. 1998. Effects of upper stem measurements on the predictive ability of a variable-exponent taper equation. Canadian Journal of Forest Research 28(7):1078-1083. Doi: 10.1139/x98-120.

López M., J. C., F. Cruz C., J. A. Nájera L. y F. J. Hernández. 2015. Modelos de ahusamiento y volumen comercial para Pinus oocarpa y Pinus douglasiana en la región de Pueblo Nuevo, Durango. Investigación y Ciencia 23(64):47-53. https://www.redalyc.org/pdf/674/67441039007.pdf. (13 de agosto de 2023).

Max, T. A. and H. E. Burkhart. 1976. Segmented polynomial regression applied to taper equations. Forest Science 22(3):283-289. Doi: 10.1093/forestscience/22.3.283.

Ormerod, D. W. 1973. A simple bole model. The Forestry Chronicle 49:136-138. Doi: 10.5558/tfc49136-3.

Pérez G., L. O. 2006. Microsoft Excel: una herramienta para la investigación. MediSur 4(3):68-71. https://www.redalyc.org/articulo.oa?id=180019873015. (23 de agosto de 2023).

Pompa G., M., J. J. Corral R., M. A. Díaz V. y M. Martínez S. 2009. Función de ahusamiento y volumen compatible para Pinus arizonica Engelm. en el Suroeste de Chihuahua. Revista Ciencia Forestal en México 34(105):119-136. https://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1405-35862009000100006. (23 de agosto de 2023).

Prodan, M., R. Peters, F. Cox. y P. Real. 1997. Mensura forestal. Instituto Interamericano de Cooperación para la Agricultura (IICA) y Deutsche Gesellschaft für Technische Zusammenarbeit (GTZ). San José, SJ, Costa Rica. 561 p. https://repositorio.iica.int/handle/11324/15038. (23 de agosto de 2022).

Quiñonez-Barraza, G., D. Zhao, H. M. de los Santos-Posadas, W. Santiago-García, J. C. Tamarit-Urias and J. A. Nájera-Luna. 2019. Compatible taper, volume, green weight, biomass and carbon concentration system for Quercus sideroxyla Bonpl. Revista Chapingo Serie Ciencias Forestales y del Ambiente 25(1):49-69. Doi: 10.5154/r.rchscfa.2018.06.050.

Quiñonez-Barraza, G., H. M. De los Santos-Posadas, J. G. Álvarez-González y A. Velázquez-Martínez. 2014. Sistema compatible de ahusamiento y volumen comercial para las principales especies de Pinus en Durango, México. Agrociencia 48(5):553-567. https://www.agrociencia-colpos.org/index.php/agrociencia/article/view/1102/1102. (23 de agosto de 2023).

Ramírez-Martínez, A., W. Santiago-García, G. Quiñonez-Barraza, F. Ruiz-Aquino y P. Antúnez. 2018. Modelación del perfil fustal y volumen total para Pinus ayacahuite Ehren. Madera y Bosques 24(2):1-15. Doi: 10.21829/myb.2018.2421496.

Ramos-Uvilla, J. A., J. J. García-Magaña, J. Hernández-Ramos, X. García-Cuevas, … y G. G. García E. 2014. Ecuaciones y tablas de volumen para dos especies de Pinus de la Sierra Purépecha, Michoacán. Revista Mexicana de Ciencias Forestales 5(23):92-109. https://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S2007-11322014000300008. (25 de agosto de 2023).

Rentería-Anima, J. B. y H. Ramírez-Maldonado. 1998. Sistema de cubicación para Pinus cooperi Blanco mediante ecuaciones de ahusamiento en Durango. Revista Chapingo Serie Ciencias Forestales y del Ambiente 4(2):315-321. https://backup.chapingo-cori.mx/articulosPDF-rchscfa/revista/articulos/rchscfaIV2146.pdf. (25 de agosto de 2023).

Rodríguez-Flores, F. de J., P. A. Domínguez-Calleros and J. Návar. 2019. Estimating tree volume components for temperate forests of northwestern México. Foresta Veracruzana 21(1):1-10. https://www.redalyc.org/journal/497/49759430001/49759430001.pdf. (24 de agosto de 2023).

Romahn de la V., C. F., H. Ramírez M. y J. L. Treviño G. 1994. Dendrometría. Universidad Autónoma Chapingo. Texcoco, Edo. Méx., México. 353 p.

Santos de J., A. Z. 2023. SIBIFOR vs INF: Comparaciones informadas de modelos de cubicación para programas de manejo en la sierra norte de Puebla. Tesis de Maestría. Postgrado en Ciencias Forestales. Colegio de Postgraduados. Texcoco, Edo. Méx., México. 68 p. http://colposdigital.colpos.mx:8080/xmlui/bitstream/handle/10521/5115/Santos_Jesus_AZ_MC_Ciencias_Forestales_2023.pdf?sequence=1&isAllowed=y. (10 de febrero de 2024).

SAS Institute Inc. 2015. SAS/STAT^® 14.1 User’s Guide. SAS Institute Inc. Cary, NC, United States of America. 10380 p. https://support.sas.com/documentation/cdl/en/statug/68162/PDF/default/statug.pdf. (10 de septiembre de 2022).

Schumacher, H. 1933. Logarithmic expression of timber-tree volume. Journal Agricultural Research 47:719-734. https://www.semanticscholar.org/paper/Logarithmic-expression-of-timber-tree-volume-Schumacher/919a9aceffc6e12e6702a10a07c6722301543545. (13 de agosto de 2023).

Sharma, M. and R. G. Oderwald. 2001. Dimensionally compatible volume and taper equations. Canadian Journal of Forest Research 31(5):797-803. Doi: 10.1139/cjfr-31-5-797.

Tamarit U., J. C., E. Rojas D., G. Quiñonez B., C. Ordoñez P. y J. C. Monárrez G. 2017. Sistema de cubicación para árboles individuales de Quercus sp. en bosques bajo manejo de Puebla, México. Revista Mexicana de Ciencias Forestales 8(40):69-88. Doi: 10.29298/rmcf.v8i40.37.

Tapia, J. y J. Návar. 1998. Ajuste de modelos de volumen y funciones ahusamiento para Pinus teocote en bosques de pino de la Sierra Madre Oriental. Ciencia e investigación Forestal 12(1):5-23. https://simef.minagri.gob.cl/bibliotecadigital/handle/20.500.12978/25736. (22 de agosto de 2023).

Tapia, J. y J. Návar. 2011. Ajuste de modelos de volumen y funciones de ahusamiento para Pinus pseudostrobus Lindl. en bosques de pino de la Sierra Madre Oriental de Nuevo León, México. Foresta Veracruzana 13(2):19-28. https://www.redalyc.org/articulo.oa?id=49721457004. (20 de agosto de 2023).

Vargas-Larreta, B., O. A. Aguirre-Calderón, C. G. Aguirre-Calderón, F. J. Zamudio-Sánchez, … y J. O. López-Martínez. 2018. Manual del Sistema Biométrico Forestal (SiBiFor): Herramientas para el manejo de los bosques templados y tropicales de México. Comisión Nacional Forestal (Conafor). Zapopan, Jal., México. 89 p.

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