Study area

The state of Hidalgo is located in the central-eastern region of Mexico. Its coordinates are: north 21°24 ‘- 19°36' north; 97°58 '- 99°53' west. It is 20 846.5 km² and stands for 1.1 % of the country's total area. It has 84 municipalities (^{Inegi, 2012a}) (Figure 1).

Figure 1 Location of the study area, municipalities of Hidalgo State, Mexico. 

Generation of the database

The variables that were associated for calculation of the occurrence of fires were identified from bibliographic reviews and consultations with state experts. A database was developed in the Excel program for the 84 municipalities of Hidalgo, with information for the 2000-2011 period (Table 1).

Table 1 Variables used to explain the forest fire incidence in Hidalgo State municipalities. 

¹ IDH = Human development index

The metheorological information was taken from the data base of the surface climatic stations of the México Climate Computing Project (CLICOM) managed by the Servicio Meteorológico Nacional (National Metheorological Service) (^{Cicese, 2015}). The temperature and precipitation data were completed with the method proposed by ^{Gómez et al. (2008)} and the isoyettes and isotherms of ^{Inegi (2015a)} were also taken into account.

The statistical variables (production, number of fires and surface area) and the road network were compiled from the Anuario Estadístico y Geográfico de Hidalgo (Hidalgo Statistical and Geographic Yearbook) (^{Inegi, 2015a}).

Municipal areas and land use were determined by using the Sistema de Información Geográfica ArcGis 10.1 (^{ESRI, 2012}) (Geographic Information System) (^{ESRI, 2012}), based on the Áreas Geoestadísticas Municipales (Geographic Statistics Areas) (^{Inegi, 2012b}) map, which is the result of the Inventario Forestal Nacional 2000 (^{Semarnat, 2001}) (National Forest Inventory 2000) (^{Semarnat, 2001}) and the Cartas de Uso del Suelo y Vegetación de Inegi escala 1:250 000 (Inegi Soil and Vegetation Use Scale scale maps1: 250 000) (^{Inegi, 2015b}) (Table 2).

Table 2 Vegetation and land use maps used to get information of the areas. 

The annual area information was estimated from a rate of change that was assumed linear and was obtained from cartographic products of different years. For example, if between one map and another edited five years apart, there was a reduction of 1 000 ha in forest area, the reduction rate was 200 ha year^-1.

The data about the social variables were consulted from the electronic page of the Departamento de Estadística, Matemática y Cómputo de la Universidad Autónoma Chapingo (Statistics, Mathematics and Computation of Chapingo Autonomous University) (^{DEMYC, 2015}). They were completed with the PNUD reports (²⁰⁰⁶, ²⁰⁰⁹, ²⁰¹²). Since the social indexes were calculated every 5 years (2000, 2005 and 2010), a rate of annual municipal change was determined in a similar way to what was pointed out for the maps.

When working with such a large set of variables, the possibility of multicollinearity increases, in order to reduce its possible effects, the SAS 9.0 statistical package (^{SAS, 2002}) carried out exploratory analyzes and correlation matrices, using the Pearson coefficient among all the variables. The explanatory types that correlated with each other were eliminated.

In addition, since the 22 municipalities did not have fires in record during the study period, and one has not forest area, it was decided to remove them from the analysis. After depuration, the data base was made up by 732 observations and 77 variables: four about the number of fires and the area the affect and response variables and 73 independent variables referring to the sociodemographic and territorial characteristics.

Later, another correlation analysis was made in order to know the relationship between the independent variables and the response ones; as expected, the values of the coefficient were low, in general, even if they were considered the greatest values to select one 10 variables and use them for the logistic regression: mean average temperature of the maximum temperature of the season, number of lambs, number of goats, number of cows, forest area, disturbed areas, life expectancy, length of the roads and Gross Domestic Product per capita. All the variables that were previously selected were significant with an α=0.05.

Statistical model

The logistic model has been used in different analyzes to estimate the occurrence of forest fires at regional or local scales, by generating predictive and explanatory models, by knowing the most important variables in the phenomenon (^{Carvacho, 1998}).

For the statistical analysis of forest fire probability, the logistic regression model of ^{Hosmer and Lemeshow (2000)} was used:

P =1(1+e-(α+β1X1+β2X2+β3X3+...+βnXn))

This method requires a binomial dependent variable; therefore, the continuous variable number of forest fires was transformed, assigning the value 0 when a fire did not occur and 1 when there was at least one during the year. The analysis was performed using the logistic procedure (Proc logistic) of the SAS 9.0 program (^{SAS, 2002}) for microcomputers.

To evaluate if the parameters were significant, the estimated parameters were examined, in addition to using the values of the χ² test and the Wald statistic. The 10 previously selected variables were "backward" stepwise and alternated one by one, until they were found to have no statistically significant differences (p ≤ 0.05) in the model. Finally, four variables were selected: two of land use, disturbed area (apertur) and forest area (supbosq); in addition, two social, longcarr and GDP per capita (pib_p_c). Few variables were chosen because it was intended to achieve a meaningful model, but that its use was not complex.

The apertur, supbosq and pib_p_c variables were categorized from a cut-off point, 10 000 for the three variables (Table 3). The value chosen for the cut corresponds to its proximity to the averages of the explanatory variables: area with forest (11 481 ha), disturbed area (13 531 ha) and GDP per capita (US$ 7795). The variable longcarr remained continuous.

Table 3 Categories made up from the study variables. 

Construction of the fire occurrence model for Hidalgo State

A scale of fire occurrence was made (Table 4), in regard to the obtained values for the probability of forest fire occurrence (P); and they were included in a map.

Table 4 The categories of occurrence that were used. 

Logistic model

The best model included four variables: forest area (supbosq), GDP per capita (pib_p_c), length of the roads (longcarr), with positive influence and disturbed areas surface (apertur), with negative influence; Table 5 shows the estimated coefficients and variables in the model.

Table 5 Variables included in the model and regression coefficients and confidence intervals. 

g.l. = Degrees of freedom; p = Probability

P =1(1+e-(-0.6190+1.1825(supbosq)+0.785(pib_p_c)+0.00299(longcarr)-1.531(apertur))) 

Most of the signs of the coefficients for each variable are logical, according to the previous knowledge that exists about the causes of forest fires in Mexico. For the disturbed area, the relation is not what was expected, whose coefficient is negative. ^{Rodríguez et al. (2008)} recorded a positive relation between the disturbed areas and the affected area, at a national scale.

The significant variables in this study, in part, confirm what other studies have documented for some federative entities, for example: ^{Román and Martínez (2006)}, ^{Carrillo et al. (2012)} and ^{Pérez-Verdín et al. (2013)} state that the density of roads is one of the anthropic factors related to the incidence, distribution and size of the fire in Chiapas, Puebla and Durango States, respectively.

At the global level, there are also coincidences with the results of the present study: ^{Guo et al. (2015)}, through logistic regression analysis, indicate that the heterogeneity of the distribution of forest fires is caused by altitude, nearness to train tracks, forest type and temperature in the Daxing'an Mountains, China. ^{Chas et al. (2012)} studied the spatial pattern of fires in the region of Galicia, Spain. They observed that high demographic pressure, communal property, large number of roads and access roads to the forest increase the likelihood of a conflagration; while with the establishment of forest plantations the risk decreases.

^{Cardille et al. (2001}) applied generalized linear regression to abiotic, biotic, and human variables to determine which best explain the fire activity in the midwest region of the United States of America. Their results evidenced that the combination of the three groups of variables was related to the spatial distribution of fire, but they emphasized that the areas with greater population density, of roads and with the shortest distance to non-forest areas were more prone to conflagrations.

The forest area variable was positively related to the occurrence of forest fires, partly due to the presence of forest fuels that exist in woods, which increases the fire hazard. Among the works that have reported similar trends, is that of ^{Guo et al. (2015)}.

The center and south of Hidalgo has the highest concentration of population and economic development above the rest of the state, coincidentally, in that area the highest number of fires is recorded. The development of the region implies the promotion of programs of productive activities that are better remunerated and generate enough income for families to have access to higher levels of consumption that also lead to more dynamic economies.

In this regard, the region has a high degree of human development on average (associated with high GDP per capita) (^{PNUD, 2014}). It is possible that the direct relationship between fire probability and GDP per capita can be explained because this variable may also involve a wider range of activities, including the use of fire in or near the forest, as part of agricultural practices.

Apparently, the GDP per capita variable had not been recorded as significant in a fire probability model; Although they have contributed in this sense variables such as the human development index by gender, which at national level ^{Rodríguez et al (2008)} indicate an inverse relation with respect to the area affected by fires and the total forest area. It emphasizes that more economic development can increase the fires, but a greater human development has an opposite effect.

Forest fires are mainly recorded during the months of March to May, possibly because of the lack of precaution during the use of fire in agricultural activities, which coincide with the dry season, as well as the negligence of walkers and hikers during their visits to the woods. Under these circumstances, the length of roads and highways becomes highly relevant, as it can be linked both to the increase in the accessibility of different areas to start a fire by accident or negligence, as well as to the burning of vegetation that is carried out on the roads.

The same thing happens in pinewoods located on roadsides, where from vehicles are thrown butts (^{Rodríguez, 2014}). An example of this happens in the road of the tourist corridor of Pachuca and the one of Pachuca to Real del Monte, where it is common to see areas burned in its edges.

In Hidalgo, Conafor and the State Government provide support in different areas to rehabilitate areas with fire disturbances and other factors (^{Semarnat, 2016}). Such is the case today, during the years covered by this research, policies were developed to recover the forest area for the prevention and awareness of the importance of conserving forest ecosystems.

Thus, during 2003-2010, the Mexican government allocated $ 5 289 000 000.00 under the Environmental Services scheme in an area of 2 767 000 ha (^{Iglesias et al., 2010}). The amount for payment of environmental services in the state of Hidalgo in the 2005-2011 period itwas $ 46,656,674 (^{Conafor, 2017a}, ^2017b), for an approved area of 22 180 ha (^{Semarnat, 2011}); in 2003 and 2004 no such benefit was granted.

These actions partially explain the negative influence of the area of disturbed areas variable in the occurrence of forest fires, since there are other options such as community forest management, whereby many rural communities care for reforested areas and actively participate to reduce the probability of being burned by a fire, and the one that is being explored in Mexico, is the integral fire management (^{Rodríguez, 2000}, ²⁰¹⁵).

Degree of forest fire occurrence

In Figure 2 are shown the degrees of forest fire occurrence for the municipalities of Hidalgo, in regard to the area per class and to the forest area of the state.

Figure 2 Degree of forest fire occurrence for the municipalities of Hidalgo. 

Figure 3 shows a map that expresses, on a probabilistic scale between 0 and 1, the estimated possibility of a fire occurring in a municipality, based on the historical variables of the model. The municipalities that appear in white are those that were not considered in the analysis because they did not have records of fires in the period of study or lack forest area, as it is the case of Tizayuca.

Figure 3 Probability of forest fire occurrence for the municipalities of Hidalgo. 

It is noteworthy that 39 municipalities are classified in a medium category and 10 in the high category; these areas are of interest in fire management strategies. It is observed that the municipalities with the highest probability of fires are located in the southeast of the state, in the regions of Apan, Tulancingo and Pachuca, mainly, but also in the municipalities Actopan, Tula de Allende, Zacualtipán de Ángeles and Zimapán.

The logistic model was plotted to better appreciate the effect of its explanatory variables (Figure 4). In the first case the value of the variable pib_p_c was set at 0 (low GDP), in the second example, the same variable had the value 1 (high GDP). The legend of the graph refers to a degree of occurrence of fire according to the color of the municipalities.

Figure 4 Probability of occurrence of fires. a) pib_p_c bajo and b) pib_p_c alto. 

The values corresponding to forest area and disturbed area, 0 or 1 (low or high), respectively, are indicated in brackets. The probability of fires has a positive influence of the forest area, GDP per capita, length of roads variables; and negative effect of the disturbed area. It is suggested that each variable has an additive effect to the others to explain the phenomenon.