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.

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.

Figure 2 Importance of biometric models and forest species studied in the state of Hidalgo. The most important genera by the number of studies carried out are Pinus, Abies and Quercus. The rest of the studies (8 %) is distributed in 18 species. Most models are focused on logging (growth: 116, volume: 82, site index: 23, density: 7, mortality: 1) and a few others on models of biomass (44) and estimation of carbon content (16). The number of models reported in the research work is shown in the middle of the figure, volume and growth models are most relevant. 

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}).