Forest Biometrics refers to the use of statistical and mathematical modeling in the evaluation and analysis of forest resources (Gregoire & Köhl, 2001; Salas & Real 2013). Growth and site index models and those used for estimation of volume, biomass and carbon content are part of forest biometrics. The information generated from biometric models is of great importance in forest management; however, its application is based on quantitative and qualitative verifications and validations of the model behavior, which characterizes its complexity (Salas & Real, 2013).
The first biometric model was proposed by Cotta in 1804 (Spurr, 1952). Since then, models have emerged for the various existing weather conditions, slope, exposure or soil types. These models have been adapted with the addition of new parameters to describe and explain the factors influencing the biological behavior of trees, which has allowed us to develop and validate models per species, for regional and local uses (Corral, Barrio, Aguirre, & Diéguez, 2007; Shao & Reynolds, 2006).
The state of the art in biometric models can measure the impact they have had and the distribution of its use; also describes how the issue has been addressed, the degree of advancement of knowledge and their tendencies (Londoño, Maldonado, & Calderón, 2014). On forest biometric models, several authors agree on the widespread use of growth models, the tendency to the integration of simulators from already created models and the growing interest in models of biomass and carbon content by fitting allometric equations (Cheng, Gamarra, & Birigazzi, 2014; Fernández, 2005; Hong-gang, Jian-guo, Ai-oguo, & Cai-yun, 2007; Porté & Bartelink, 2002; Vacchiano, Magnani & Collati, 2012). Others authors such as Landsberg (2003), Mäkelä et al. (2000) and Peng (2000) have presented the state of the art of forest modeling to a wider scale. These authors note that process-based models should be combined with static (volume, height-diameter) and dynamic (growth) models; identify the needs of users; and continue research on the behavior of processes of carbon, nutrients and its consumption.
In Mexico, forest growth modeling has been done since the 1970s (Garzón & Flores, 1977; Ramírez & Musalem, 1977). However, it is necessary to update, validate and calibrate existing biometric systems, otherwise considerable volumes of wood could be underestimated or overestimated and to schedule cutting intensities outside the range of forestry potential of a site (Comisión Nacional Forestal [CONAFOR], 2014). In the state of Hidalgo, the forest area (temperate forests, rainforest, arid areas and disturbed vegetation) covers approximately 51 % of the state territory (20,813 km2); the wooded area covers 403,685 ha, of which 57 % are temperate forests and the remaining percentage corresponds to rainforests (Instituto Nacional de Estadística y Geografía [INEGI], 2013, 2015). From this wooded area, on average, 123,592 m3 of roundwood is extracted (Secretaría de Medio Ambiente y Recursos Naturales [SEMARNAT], 2010, 2011, 2012, 2013, 2014), which represents approximately 2 % national. The harvesting method used in Hidalgo has been the Silvicultural Development Method (Castelán-Lorenzo & Arteaga-Martínez, 2009), Pinus and Quercus are the most harvested in order of importance (SEMARNAT, 2014). The state has 36 protected natural areas covering 139,357 ha and account for nearly 7 % of the state territory, (Consejo Nacional de Ciencia y Tecnología [CONACYT], 2015).
The aim of this study was to collect, organize, analyze and synthesize research papers, dissemination documents and publications related to biometric models used for forest management in Hidalgo, Mexico. With the above, it is intended to present the current state of forestry research and show the tendencies in the study area.
Materials and methods
The analysis focuses on biometric models developed in the state of Hidalgo, located between 21° 24’ - 19° 36’ N and 97° 58’ - 99° 53’ W. The state of Hidalgo borders the states of Mexico, Puebla, Querétaro, San Luis Potosí, Tlaxcala and Veracruz (INEGI, 2013). The state of Hidalgo is listed as a state with low-timber production (SEMARNAT, 2013); Pinus and Quercus provide greater volume to the state timber production with 70 and 23 %, respectively. The logging percentage of the state for Pinus coincides with the national percentage (70 %), but in the case of Quercus is two times higher than the 10 % national (SEMARNAT, 2010, 2011, 2012, 2013). Figure 1 shows the main types of vegetation in the state of Hidalgo.
The state of the art was constructed by a review in thesis, journals, brochures and technical reports on aspects related to biometric systems for economically important forest species in Hidalgo. The search for information was made in libraries of academic and research institutions related to forestry, through site visits (Table 1). Also, digital libraries (Table 1) and scientific journals (Table 2) were consulted online.
|Institution||State||Type of query|
|Universidad Nacional Autónoma de México (UNAM)||Ciudad de México||Site visit Presencial|
|Instituto Nacional de Investigaciones Forestales Agrícolas y Pecuarias (INIFAP)||Ciudad de México||Site visit|
|Universidad Autónoma Metropolitana (UAM)||Estado de México||Site visit Presencial|
|Universidad Autónoma Chapingo (UACh)||Estado de México||Site visit Presencial|
|Colegio de Postgraduados (ColPos)||Estado de México||Site visit Presencial|
|Tecnológico de Estudios Superiores de Valle de Bravo||Estado de México||Site visit|
|Journal||Institution concerned||Type of query|
|Revista Bosque||Universidad Austral de Chile||Online|
|Interciencia||Asociación Interciencia, Venezuela||Online|
|Revista Mexicana de Ciencias Forestales||Instituto Nacional de Investigaciones Forestales Agrícolas y Pecuarias||Site visit Presencial|
|Revista Chapingo Serie Ciencias Forestales y del Ambiente||Universidad Autónoma Chapingo||Site visit Presencial|
|Botanical Sciences||Sociedad Botánica de México||Online|
|Madera y Bosques||Instituto de Ecología||Online|
|Revista Fitotecnia Mexicana||Sociedad Mexicana de Fitogenética||Online|
|Terra Latinoamericana||Sociedad Mexicana de la Ciencia del Suelo||Online|
|Agrociencia||Colegio de Postgraduados||Site visit Presencial|
The information was collected using the technique of “snowball”, where documents through their literature suggested other documents with the same topic that have been developed in the study area. The information was classified into seven groups of models according to their use: volume and taper equations (static models); site index (productivity indicator); biomass, carbon and growth estimation (dynamic models); and density and mortality (description of the stand). The literature cited in each of the collected documents was also collected to know the sources of information that support them. References were grouped according to the type of source (articles, reports, books and theses) and language of publication.
Results and discussion
Institutions, information sources and species studied
Institutions and information sources. A total of 32 research documents (Appendix 1) were found in two of the five Forest Management Units (UMAFOR) in the state of Hidalgo: 52 % at the UMAFOR 1302 Zacualtipán-Molango (Table 3) and 43 % at the UMAFOR 1303 Pachuca-Tulancingo (Table 4). The forest inventory (Secretaría de Agricultura y Ganadería [SAG], 1976) is the only study carried out at state level (Table 5). Most research papers, 27 in total, were published in the last eight years (2007-2015). In 2013, the year with the highest number of publications, seven researches were found.
|Authors*||Area of influence||Equations||Type of model||Number of samples||Species studied||Type of pulbication|
|Brosovich (1998)||Zacualtipán de Ángeles||10||Density, site index and volume||52 (D)||Thesis|
|Tenorio (2003)||Estatal||2||Volume||101 (D)||Thesis|
|Carrillo, Acosta, y Tenorio (2004)||Estatal||1||Volume||101 (D)||Brochure|
|Cruz (2007)||Zacualtipán de Ángeles||13||Biomass, volume||62 (D)||
|Aguirre et al. (2008)||Zacualtipán de Ángeles||1||Cabon||75 (ND)**||Article|
|Santiago (2009)||Zacualtipán de Ángeles||23||Growth, density, site index, mortality and volume||84 (ND)||Thesis|
|Cruz, Valdez, Ángeles, y De los Santos (2010)||Zacualtipán de Ángeles||4||Volume||114 (ND)**||
|Figueroa (2010)||Zacualtipán de Ángeles||9||Biomass||18 (D)||
|Olvera (2010)||Barranca de Metztitlán||4||Volume||87 (D)||Thesis|
|Acosta, Carrillo, y Gómez (2011)||Zacualtipán de Ángeles||4||Biomasa y carbono||40 (D)||
|Vásquez (2011)||Zacualtipán de Ángeles||5||Carbon||18 (D)||Thesis|
|Hernández (2012)||Zacualtipán de Ángeles||12||Volume||78 (D)||Thesis|
|Muñoz et al. (2012)||Barranca de Metztitlán||4||Volume||87 (D)||Article|
|Santiago (2013)||Zacualtipán de Ángeles||1||Volume||42 (ND)**||Thesis|
|Soriano, Ángeles, Martínez, Plascencia, y Razo (2013)||Zacualtipán de Ángeles||3||Biomass||25 (D)||Latifoliadas and
|González (2014)||UMAFOR 1302 Zacualtipán - Molango||16||Site index and Volume||159 (D)||
|Soriano (2014)||Zacualtipán de Ángeles||12||Biomass and volume||71 (D)||
|Authors*||Area of influence||Equations||Type of model||Number of samples||Species studied||Type of pulbication|
|Rodríguez (2000)||Acaxochitlán||8||Growth||12 (D)||Thesis|
|Pacheco et al. (2007)||Cuaunepantla y Acaxochitlán||2||Biomass and Carbon||20 (D)||Article|
|Acosta and Carrillo (2008)||UMAFOR 1303, Pachuca-Tulancingo||2||Volume||43 (D)||
|Rodríguez (2009)||Singuilucan, Zempoala, Tepeapulco y Cuautepec de Hinojosa||2||Density||122 (ND)||
|Hernández (2012)||Sureste de Hidalgo, Singuilucan||1||Growth||36 (D)||
|Velarde (2012)||UMAFOR 1303 Pachuca-Tulancingo||106||Growth and Volume||185 (D)||
|González (2013)||Mineral del Monte||2||Biomass and Volume||4 (D)||Thesis|
|Hernández et al. (2013)||UMAFOR 1303, Pachuca-Tulancingo||2||Density||131 (ND)||Article|
|Razo, Gordillo, Rodríguez, Maycotte, y Acevedo (2013)||Parque Nacional El Chico||2||Biomass and Carbon||5 (ND)||Article|
|Rodríguez and Calva (2013)||Parque Nacional El Chico||2||Biomass and Carbon||250 (ND)||Chapter|
|Rodríguez (2013)||Sierra de Pachuca||12||Biomass Carbon and Growth||250 (ND)||Thesis|
|Hernández et al. (2014)||Metztitlán||3||Site index||25 (D)||Article|
|Velarde (2014)||UMAFOR 1303 Pachuca-Tulancingo||8||Site index and Volume||120 (D)||
|Hernández et al. (2015)||Acaxochitlán, Cuautepec de Hinojosa, Singuilucan y Tulancingo de Bravo||1||Site index||345 (ND)||Article|
|Author||Area of influence||Equations||Type of Model||Number of samples||Species studied||Type of publication|
|Secretaría de agricultura y Ganadería (SAG, 1976)||State level||12||Volume||899 (D)||
The institutions that have generated the greatest number of theses (bachelor, master and PhD) are the Colegio de Postgraduados (ColPos) and the Universidad Autónoma Chapingo (UACh) with six and four theses, respectively. The Universidad Nacional Autónoma de México (UNAM) contributed with two theses. The Universidad Michoacana de San Nicolás de Hidalgo (UMSNH) and the Universidad Agraria Autónoma Antonio Narro (UAAAN) had. The fact that the ColPos and the UACh have generated greater quantity of theses, it is due to the age of their academic programs, because the UACh started the bachelor’s programs in 1933 and the master’s program in 1986, while the ColPos created the forestry postgraduate program in 1976 (Caballero, 2004).
All articles analyzed were published in Mexican journals. The brochures have been created by government institutions (Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias [INIFAP] and State of Hidalgo Government), aimed at forest service providers. Technical reports, in turn, have been created by firms backed by a renowned researcher and under CONAFOR funding. This scenario shows that the information is only generated and disseminated locally, in Spanish language and to a reduced scientific community sector. Thus, it is important to promote institutional strategies so that future documents will be published in journals, because journals have greater spread spectrum. The results of the research should be aimed at finding general principles that rule and describe the processes occurring in forest areas.
Species studied. The most studied species belong to the Pinus genus, whose importance based on the number of studies that used it as an object of study are: P. patula Schltdl. & Cham. (17), P. teocote Schltdl. & Cham. (7), P. greggii Engelm. ex Parl. (5), P. montezumae Lamb. (5), P. cembroides Gordon (1), P. ayacahuite C. Ehrenb. ex Schltdl. (1), P. pseudostrobus Lindl. (1) and P. rudis Endl. (1). Other species such as Abies religiosa (Kunth) Schltdl. & Cham. (3), Alnus sp. (4), Clethra sp. (3), Quercus sp. (3), Cedrela odorata L. (1), Inga spuria Humb.
& Bonpl. ex Willd. (1), Cupania dentata Moc. et Sessé ex D.C. (1), Bursera simaruba (L.) Sarg. (1), Juniperus flaccida Schltdl. (1), Platanus sp. (1), Liquidambar styraciflua L.
(1), Psidium guajava L. (1) and Dendropanax arboreus (L.) Decne. & Planch. (1) are less frequent (Tables 3, 4 and 5). The species P. patula, besides being the most studied, it is reported since 1976.
Current state of biometric models in the study area
Distribution of models per species. Figure 2 outlines the importance of the species studied and types of biometric models developed in the state of Hidalgo. A total of 289 models were found, which are distributed among the genera Pinus, Abies, Quercus and other broadleaf trees. Pinus concentrated 86 % of the fitted equations (249) distributed in the following species: 148 in P. patula, 58 in P. montezumae, 23 in P. teocote, 13 in P. greggii, four in P. rudis and one in P. cembroides. Meanwhile, A. religiosa concentrated 5 % (16) and Quercus only 1 % (3); the remaining 8 % of equations (22) distributed in 18 species.
The economic importance of some species from the genera Pinus and Abies in the study area coincides with the number of studies carried out. On the other hand, the genus Quercus has been little studied despite the exploited wood volume, perhaps because of the difficulty of their taxonomic identification, high morphological variability (Bárcenas, 2011) and the ability to form hybrids (Zúñiga, Sánchez-González, & Granados, 2009). Moreover, there are other species of Pinus, conifers and broadleaf trees that despite of being exploited, are not reported in research studies (Pinus leiophylla Schiede ex Schltdl. & Cham., P. michoacana Martínez, P. oocarpa Schiede ex Schltdl., Cupressus lindleyi Klotzsch ex Endl. and Arbutus xalapensis Kunth), so it is suggested to extend the base of models for these forest species.
No models developed for the mixed pine-oak or oak-pine forests were reported, which together occupy 17 % of the state wooded area (INEGI, 2015; Figure 1). However, the forest inventory of the state of Hidalgo (SAG, 1976) contains volume equations for two pine species groups: for the group of P. montezumae, P. patula and P. ayacahuite, and for the group P. teocote, P. greggii and P. pseudostrobus. Since models were fitted for mixed forests, it is necessary to validate if they make good estimates for monospecific masses of the corresponding species. Models for pine-oak forest start to develop for other Mexican forests, using the diameter growth dynamics (Návar, 2014).
With regard to increment and yield models, it is recommended to develop at individual tree level, diameter classes, groups of species or stand-level to meet different purposes as obtaining roundwood or logs used for cellulose or poles; individual tree models are important especially in processes of validation of models used in an area (Návar-Chaidez & Domínguez-Calleros, 2013).
Classification of models. Of all models, forest management studies are those that have received greater attention: 116 growth, 82 of volume, 23 of site index, seven of density and one of mortality models. Volume models were the most reported in research studies. The studies’ approach shows two major groups, on the one hand, the logging and on the other hand, the environmental services (estimation of biomass and carbon) (Figure 2). From 2007, models of biomass (44) and carbon estimation (16) have become more frequent; also from the same year, the genus Pinus was incorporated to the studies on environmental services in the study area. Under this approach, A. religiosa. and broadleaved trees are the most frequent species.
Most models use mainly diameter at breast height (d) and total height (h) as input variables. The models have been fitted with data from established silvicultural sites, so the use of national forest inventory sites as permanent sample plots is proposed to understand the behavior of forests.
Most used models. Table 6 shows the forest biometric models used in the state of Hidalgo. The most commonly used model is the Schumacher’s model for growth curves and site index (Schumacher, 1939) and that of Schumacher and Hall to estimate volume (Schumacher & Hall, 1933). Given the large number of models fitted so far, it is suggested to create growth simulators (Santiago-García, de los Santos-Posadas, Ángeles-Pérez, Valdéz-Lazalde, & Ramírez-Valverde, 2013), that bring together mathematical models in a program to predict and calculate different growth scenarios (Salas & Real, 2013; Santiago-García et al., 2013). It is appropriate to verify, validate and update existing models to assess whether they are valid and can spread to other areas with similar conditions.
On the other hand, it is highly recommended the use of models for sustainable management of forest communities of Hidalgo, especially those focused on forest protection. Some studies with this approach have been developed in Durango, the state with greater timber production in Mexico (SEMARNAT, 2013), where fire behavior and magnitude have been studied regarding the anthropogenic factor, the ecological role of forest fires, climatic and soil variables, socioeconomic conditions of the area, population density and access roads (Návar-Chaidez, 2011; Pérez-Verdín, Márquez-Linares, Cortés-Ortiz, & Salmerón-Macías, 2013; Rodríguez-Trejo & Fulé, 2003).
Validation and model selection. Different authors used criteria such as the coefficient of determination (R2), root mean square error (RMSE), coefficient of variation, number of parameters of the equation and number of variables to validate and select a model. The parsimony criterion has been included in recent studies (Akaike Information Criterion [AIC], Bayesian information criterion [BIC] and Schwarz selection criteria). Graphical adjustment and of the model were used as secondary selection criterion. No values of R2, RMSE, range in diameter and height range were reported in many of the models fitted in the study area, information that would facilitate the subsequent verification and validation of the models.
Sample size. Sample sizes used in fitting models vary according to the purpose of the study. Logging modeling was carried out with larger destructive samples compared to the modeling of biomass and carbon content (Tables 3, 4 and 5).
Analysis of the documentary references
In the 32 studies reviewed (Appendix 1), a total of 1,547 cited references were found, which corresponded to 1,022 documents. This means that about 34 % of the references were cited in two or more articles.
Regarding the origin of documentary references, 19.2 % comes from the main forestry journals with an impact factor the JCR (Journal Citation Report): Forest Ecology and Management (7.4 %), Forest Science (3.8 %), Agrociencia (2.7 %), Canadian Journal of Forest Research (2.7 %) and Madera y Bosques (2.6 %). About 10.2 % of the references comes from UACh and ColPos (6.8 % and 3.4 %, respectively). Approximately 7.2 % of the sources comes from sourcebooks. Another 3.4 % came from conference proceedings or union meetings. The remaining information (60 %) derived from articles published in journals of lower impact, brochures, technical reports, theses in other institutions and unpublished documents. According to the language of publication, 56.7 % of the documents are in Spanish (580), 42.4 % in English (434 documents) and less than 1 % in German (5) and Portuguese (3).
The 10 most frequent citations reported within the 32 studies reviewed are: Clutter, Fortson, Pienaar, Brister, and Bailey (1983) in 13 articles; Romahn de la Vega, Ramírez, and Treviño (1994) in nine; Spurr (1952) and Figueroa (2010) in eight; Acosta Vargas, Velázquez, and Etchevers (2002), Aguirre et al. (2008), Caballero (1972), Díaz et al. (2007), Perry (1991) and Torres and Magaña (2001), in seven each. References come from a small number of institutions and authors that cited each other, so the link with academic groups at national and international level as well as networks of scientists related to the forestry area should be searched. The interaction between different disciplines related to the forestry sector favor the increase of information with inter and multidisciplinary approach, which is of vital importance in modern science (Borut, Levnajic, Povh, & Perc, 2014).
Biometric models in Hidalgo, Mexico, have been fitted mainly for the genus Pinus. It is proposed to expand the base of models for other economically important genera such as Abies, Quercus, Arbutus and Cupressus, and verify, validate and update existing models. Reported models based their reliability by the coefficient of determination (R2) but more studies using selection criteria with biological, economic and management significance are needed. In the studies reviewed, it is not mentioned if the fitted models are valid or have managed to meet user demand. Studies are restricted to local use and have been carried out by a small group of authors. It is recommended that forestry research will focus on identifying general principles that describe the factors underlying processes inherent to the forest, and have importance for forest management. In practical terms, the focus must be that volume models reduce economic losses as a result of underestimation or overestimation. Finally, it is suggested to integrate a state or regional forestry information system.