ISSN e:2007-4018 / ISSN print: 2007-3828



Vol. XXIV, issue 1 January - April 2018

ISSN: ppub: 2007-3828 epub: 2007-4018

Scientific article

Projection and probability of land use change in Zoquiapan, Mexico: considerations for forest management

Paredes-Gonzalez, Adriana 1 ; Monterroso-Rivas, Alejandro I. 2 * ; Rodríguez-Esparza, Luz J. 1 ; Zamudio-Sánchez, Francisco J. 3

  • 1Universidad Autónoma Chapingo, División de Ciencias Forestales. km 38.5 carretera México-Texcoco. C. P. 56230. Chapingo, Texcoco, Estado de México, México.
  • 2Universidad Autónoma Chapingo, Departamento de Suelos. km 38.5 carretera México-Texcoco. C. P. 56230. Chapingo, Texcoco, Estado de México, México.
  • 3Universidad Autónoma Chapingo, Departamento de Estadística, Matemática y Cómputo. km 38.5 carretera México-Texcoco. C. P. 56230. Chapingo, Texcoco, Estado de México, México.

Corresponding author:, tel.: +52 (595) 952 1500 ext. 6178.

Received: July 12, 2017; Accepted: November 09, 2017

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The dynamics of land use and changes in vegetation cover is essential for natural resource management.


To analyze the land use change in the micro-watersed of Zoquiapan, between 1989 and 2009, and to estimate the change trend for the year 2020.

Materials and methods:

Two satellite images (March 21, 2009 and March 7, 1989) were taken, corresponding to the Landsat sensor, and were processed using the software IDRISI©. The classes studied were forest, grassland and agricultural use. The Márkov-Markovian transition estimator command was applied to estimate the stationary vector of the chain between the years of study and to know the future trends of vegetation cover.

Results and discussion:

Between 1989 and 2009, the agricultural and grassland area decreased 1.86 and 88.63 ha, respectively; the forest area increased 90.5 ha. By 2020, the micro-watershed of Zoquiapan will have a low probability of change. The probabilities of permanence are 94 % for forest, 88 % for grassland and 91 % for agricultural activities.


The micro-watershed of Zoquiapan has not had any significant land use change. The areas covered by forests have a low probability of change, as long as the conservation efforts carried out so far continue.

Keywords:Vegetation cover; Márkov chains; IDRISI; stable state


Land use studies and change of vegetation cover, as well as its dynamics over time, are essential for the sustainable management of natural resources (Memarian et al., 2012). Vegetation cover is essential in the global dynamics of the planet: plants absorb and recycle nutrients such as carbon dioxide, nitrogen, sulfur and phosphorus that are in the atmosphere, retain water and transpire. Forests play an important role in the conservation of the environment, since they regulate water currents, have a moderating effect on the global and local climate, and favor the conservation of soils preventing erosion; in addition, they are home to numerous species of plants and animals (Secretaría de Medio Ambiente y Recursos Naturales [SEMARNAT], 2009) . However, human activities have altered the original uses of the land, modifying the natural landscape and, consequently, the functioning of the ecosystems (Zepeda, Nemiga, Helgueras, & Madrigal, 2012). The land uses associated with anthropic activities, such as agriculture and grazing, have a deep influence on the change of the ecological, hydrological and atmospheric regulation processes of the planet. Therefore, the study of spatial and temporal dynamics of land uses is important (Martínez-Santiago, Alvarado-Segura, Zamudio-Sánchez, & Cristobal-Acevedo, 2017), but even more, to know their trends and projections to suggest interventions that reduce or slow down degradation.

A useful tool for modeling projection and trends of land use change are the Márkov chains (Eastman, 2012; Levin, Peres, & Wilmer, 2009; Memarian et al., 2012). In these, the transition to a next state depends on the current state of the system, regardless of the route to achieve it. The model considers the random variable of states and the parameter t (time) as discrete variables; in this way, it is possible to determine the probability with which the process can enter a certain state (Bedoya & Barrera, 2006). The method is convenient for modeling the change in land use when changes and processes in the landscape are difficult to describe.

Márkov chains simulate the prediction of the state of a system for a given time, from two preceding states (Eastman, 2012). This means that the modeling does not take into account the explanatory and descriptive variables, but is based exclusively on the analysis of the system internal dynamics. One limitation of the algorithm is the need to have the same categories in the time series, so that the disappearance or appearance of some class prevents applying the method (Paegelow, Teresa, & Minor, 2003). Markov models have been widely used in studies on land cover change at various spatial scales (Sanchayeeta & Southworth, 2012); according to Memarian et al. (2012), models are easy to create with minimum data requirements and are based on a transition matrix.

In the case of Mexico, Markov chains have been used in migration studies (Garrocho, Jiménez-López, & Álvarez-Lobato, 2016), demographic projections (Partida, 1989), financial investments (Torres, Gaytán, & Tinoco, 2017), livestock diseases (Rojas, Barajas, Riemann, & Franti, 1993) and air quality (Hoyos, Lara, Ortíz, López, & González, 2009). In the case of land use change studies, recent cases are known in Texcoco (Pérez, Valdez, Moreno, González, & Valdez, 2012), Morelia (López, Bocco, & Mendoza, 2001) and Hidalgo (Reynoso, Valdez, Escalona, de los Santos, & Pérez, 2016). The purpose of the present study was to analyze the land use change in the micro-watershed of Zoquiapan in the period 1989-2009, through the Stochastic Márkov chains process, to estimate the trend of land use change in the year 2020 and find the transition matrix of the stable state. According to the proposed territorial ecological order made by Lomas-Barrié, Terrazas-Domínguez, and Tchikoué-Maga (2005), Zoquiapan covers a portion of the Park known as Parque Nacional Zoquiapan y Anexas, which has serious problems of ecological imbalance, environmental degradation, as well as a low sustainability of the environment.

Materials and methods

Study area

The study area included the micro-watershed of Zoquiapan of the Parque Nacional Zoquiapan, located in the 18th hydrographic region of the river Balsas over the watershed of the river Atoyac. The micro-watershed is located at the extreme UTM coordinates 2137115 to the North, 2122190 to the South, 544888 to the East and 532075 to the West; it has an area of 8 087 ha in the municipalities of Ixtapaluca, Chalco and Tlalmanalco in Estado de México, as well as in Tlahuapan and San Salvador el Verde in Puebla.

The micro-watershed has complex relief and heights that vary from 2 400 to 4 642 m, which means a gradient of more than 2 000 m. The volcanic origin is dominant with extrusive igneous class deriving in deep andosol soils, but it is possible to find very thin soils like lithosols in some small surfaces. The dominant climates are semi-cold of the temperate group with fresh and long summer. The annual rainfall varies from 1 000 to 1 500 mm, while the mean temperature ranges between 10 and 14 °C, although it is possible to find places with 5 to 10 °C (Instituto Nacional de Estadística y Geografía [INEGI], 2009 , 2013, 2014).

The above characteristics are reflected in the dominant land uses. According to the Instituto Nacional de Estadística, Geografía e Informática (INEGI, 2005) there are seven categories: fir forest, pine forest, pine-oak forest, induced grassland, fir forest with secondary vegetation, montane grasslands and agricultural uses. The management program of the same year shows that four vegetation associations predominate: association of fir Abies religiosa (Kunth) Schltdl. & Cham., association of Alnus firmifolia Fernald, association of Pinus hartwegii Lindl. and association of P. hartwegii-A. firmifolia.

Projection and probability of land use change in Zoquiapan

The analysis began with two satellite images of different dates, corresponding to the Landsat sensor (available at The images with the best quality and low cloudiness were those of March 21, 2009 and March 7, 1989, both with a resolution of 25 m. The images were processed with the software IDRISI© (Eastman, 2012), where a false color combination was first made using bands 1, 2 and 3. Later, an unsupervised classification was made with the same number of previously known classes: forest, grassland and agricultural use. The process was repeated for both images with the care of having the same area of the studied area, resolution and number of classes. The forest class consisted of tree species such as fir, pine, oak and their associations. The grassland class refers to vegetation communities predominating pastures with few trees and shrubs that can be produced by the clearing of wooded land. It is also possible to find montane grasslands, predominating Lupinus montanus Kunth, Agrostis, Festuca and Muhlenbergia. The agricultural class refers to rain-dependent agricultural activities for annual production, known mainly as maize under rainfed conditions.

Following the methodology of Eastman (2012) the Markovian transition estimator was applied in the software IDRISI© in order to know the transition matrix of land uses in the micro-watershed of Zoquiapan, regarding the period 1989-2009, to project the use of soil in the year 2020 with an error of 5 %. According to Levin et al. (2009), when i and j are two states of a Markov chain, the probability will be given by P(X n+1) = j(X n = 1), denoted by pij(n, n+1) which represents the transition probability from state i at time n, to state j at time n+1. These probabilities are known as one-step transition probabilities. When the probabilities pij(n, n+1) do not depend on n, it is said that the chain is stationary or homogeneous in time. For simplicity, such situation is assumed so that the one-step transition probabilities are written as pij. For example, by varying the indices i and j over the set of states {0, 1, 2} we obtain the transition probability matrix as follows:

P = p 00 p 01 p 02     p 10 p 11 p 12 p 20   p 21 p 22

The input (i, j) of this matrix is the transition probability (ij); in other words, the probability of moving from state i to state j in a unit of time. A state is stable when there are no changes in the system; that is, equilibrium is reached. A possible way to obtain the stable state of the system is to repeat the calculations iteratively for each period in order to find the one that has those probabilities that remain constant or do not change .

When the Markov chains are applied, first we have to check whether the chain reaches the steady state. Since the observations that are generated are dependent, we have to wait for the chain to stabilize. This means that a certain number of iterations must be run as a “warm-up period” in the chain and then estimate their seasonality and convergence. In order to have an idea of a stationary state is being reached; the simplest thing is to make some graphs. For example, averages of some function of interest could be plotted, such as 1 k i = 1 k h ( x i ) , which by the ergodic theorem, should be placed around E(h(X)) as n grows. In this case, the transition matrix was generated for the year 2010 to find the stationary distribution, and we obtained the initial probabilities (pi) with the land use data of 2009 and 10 000 iterations of a Markov chain were made at discrete time using the program R (R Development Core Team, 2016). Then the ergodic mean of this process (dimensionless) was estimated. Once the stationary vector was obtained, by means of the ergodic mean, as has been discussed in other studies (Bouchard-Côté, Vollmer, & Doucet, 2017; Saldi, Linder, & Yüksel, 2013), a random data was taken by every 10 observations to obtain a sample of 1 000 and estimate their respective transition matrix using the program IDRISI©. As a result, the analyzed period comprised 20 years and three categories of land use: forest, grassland and agricultural use, and a one-year estimate with an error range of 0.05. That is, the transition matrix for the year 2010 has as reference data the land use classifications for the year 2009, to achieve an error prediction of 5 %.

Results and discussion

Projection and probability of land use change in Zoquiapan

Figure 1 shows the satellite images of the years 1989 and 2009, where it is observed that the dominant land use is forest followed by grassland and agricultural use. This was also found by Virgen-Cobos (2016), who points out that the associations of species in the Zoquiapan Forest Station are fir, pine, pine-Alnus firmifolia, pine-oak and pine-fir.

Figure 1. Classification of land use and vegetation in the micro-watershed of Zoquiapan, based on the satellite images of 1989 (top image) and 2009 (bottom image).

In Figure 1, the use of bare soil refers to the area without vegetation cover (203 ha), near the Iztaccíhuatl volcano. According to the results, in the 20 years studied, the agricultural area was reduced 1.86 ha; that is to say, it remained practically the same in the period 1989-2009. It should be noted that in the first year there were 522 hectares that corresponded to 6.45 % of the surface area. In terms of grassland, the surface area was also reduced 88.63 ha, going from 208.3 ha, which corresponded to 2.5 % of the micro-watershed of Zoquiapan, to 119.7 ha. The use of forest land, consequently, increased its surface area by practically 90.5 ha, as shown in Table 1.

Table 1. Surface occupied by land use and vegetation in the micro-watershed of Zoquiapan in the years 1989 and 2009.

Soil use 1989 2009 Difference 1989-2009%
ha % ha % ha %
Agricultural use 523.78 6.47 521.91 6.45 -1.86 -0.02
Grassland 208.39 2.57 119.76 1.48 -88.63 -1.09
Forest 7 052.37 87.22 7 142.87 88.32 90.49 1.11
Bare soil 302.60 3.74 302.60 3.75 0 0
Total 8 087.16 100.00 8 087.16 100.00 0 0

The results are similar to those obtained a few years ago. According to the analysis on land use change carried out by Lomas-Barrié et al. (2005), in general, the vegetation cover remained unchanged during the period from 1977 to 2000. The vegetation covers that were best maintained were the mixed forest, grassland and Abies forest. For its part, the Mexican Civil Council for Sustainable Silviculture (CCMSS, 2008) indicated that, in the period 2000-2007, agriculture in the area of influence of the park Izta-Popo lost 28 hectares of agricultural area, approximately, and that changes in land use were detected in only 1.35 % of the surface. In this way, with the results obtained in this study, it is possible to point out that the area of Zoquiapan has not had any aggressive change in land use since 1977, year of the first studies with satellite images.

According to Villegas, Muñoz, Muñoz, Gallo, and Ponce (2011), due to the legal practices of conservation of protected natural areas, transformation rates are low compared to unprotected areas. The micro-watershed of Zoquiapan is located within two subzones of management of the National Park: recovery subzone and preservation subzone (SEMARNAT, 2013). In these subzones, some of the unauthorized activities related to the modification of vegetation cover are the following: opening trails, gaps or roads; forest harvesting, except for scientific collection and domestic use; build public and private works; damage, cut and mark trees, except for scientific research activities; extract living or dead flora and fauna, as well as other biogenetic elements, except for self-consumption or scientific collection; livestock, including grazing; carry out hunting or exploitation activities of wild flora and fauna species without authorization, except for the use of natural resources for self-consumption purposes.

Another factor for which there is a low probability of land use change is the constant reforestations during the analysis period. According to the Manifestation of Environmental Impact of the Management Program for the Harvesting of Dead Trees, a reforestation was done in the year 2004 of the order of 10 ha and it was proposed to reforest 65.4 ha for the year 2006 (Universidad Autónoma Chapingo, 2005). Subsequently, in April 2010, and following a technical study due to the environmental contingency of the National Park Izta-Popo, Zoquiapan y Anexas, the SEMARNAT indicated the execution of reforestation work. This was done with native species at random, with homogeneous distancing that avoided competition between them and with forest density of 1 600 plants·ha-1; the clearings smaller than 100 m2 were also reforested. It is worth mentioning that this study proposed reforestation for three consecutive years in 325 ha (Tejada-Nichols, 2010).

Table 2 shows the results of the transition by type of dominant land use. The transition matrix analyzes the information of the years 1989 and 2009, to be used later in the projection for the year 2020. The above regarding that the conditions external to the analysis remain similar to those observed. According to the matrix, it is observed that the probability of the forest remaining as such by 2020 is 94 % (in 5 613 ha). The probability that grassland is maintained is 88 % (in 874 ha), while that of the agricultural area is 91 % (in 284 ha). That suggests that there are high probabilities that current uses will remain; that is, if we continue with the current trend, we can expect that the dominant vegetation covers will be maintained by the year 2020.

Table 2. Probability of change or permanence between land uses in the micro-watershed of Zoquiapan for the year 2020.

Soil use Forest Grassland Agricultural
Forest 0.9454 0.0546 0.0000
Grassland 0.0556 0.8875 0.0569
Agricultural use 0.0000 0.0900 0.9100

With respect to the changes, they are not projected from an agricultural use to the forest or vice versa. This can be attributed to the conservation of the majority of the surface analyzed. The population near the area of Zoquiapan recognizes the value of forest ecosystems in the provision of environmental services. On the other hand, the change of use from agricultural land to grassland is the most likely, with 9 % for 324 ha. This may be explained when an agricultural plot is abandoned, because a process of ecological succession begins and the land is initially covered by grass.

Figure 2 shows the behavior of the ergodic average; it is observed that the stable period is reached after the 400 iterations. The estimation of the ergodic average averages the states of the Márkov chain (forest, grassland or agriculture) every 10 iterations and graphs them to make visible the moment in which these states converge and stop changing. The values shown in Table 2 come from the stable state, which was reached after 600 iterations in the ergodic average.

Figure 2. Ergodic average of 1 000 iterations of a Márkov chain at discrete time.

As pointed out a few years ago by Orantes and Musálem (1982), who considered 50-year-old trees in their study, the experimental field of Zoquiapan has trees of medium to high quality with heights of more than 20 m. Over the years and in accordance with the conservation efforts made in the area, in this study it was found that the vegetation covers have remained practically unchanged. However, the region is susceptible to forest fires (Castañeda, Endara, Villers, & Nava, 2015; Rodríguez Trejo, 2001) and even to clandestine logging and pest attacks (SEMARNAT, 2013).

Considerations for forest management of the micro-watershed of Zoquiapan

The forest area analyzed is within the subzones of preservation and public use of the National Park Iztaccíhuatl-Popocatépetl, where forest harvesting is not allowed, except for scientific collection and domestic use. However, there is a manifestation of environmental impact that allows selective felling of dead trees with the purpose of maintaining phytosanitary conditions of the forest (Universidad Autónoma Chapingo, 2005). In this sense, it is recommended to reforest with native species to maintain the vegetation cover, because it is an area susceptible to water erosion due to the factor that is pending that is higher than 26 %. It is also recommended to make firebreaks and implement forest cleanup and sanitation plans. The conservation of the area is a priority, since in the ravines the blue juniper (Juniperus monticola fo. compacta Martínez), is distributed, a species under special protection in accordance with the NOM-059-SEMARNAT-2010 (SEMARNAT, 2010).

The grassland area is located in the public use subzone of the National Park Iztaccíhuatl-Popocatépetl, where livestock is not allowed. However, this activity, although of low impact, it is carried out, so it is necessary to establish a grassland management program by means of restoration and recovery of the vegetation cover.

In the agricultural areas, the slope is moderate so it is recommended to implement soil and water conservation practices, such as conservation tillage, terraces, contour furrowing and rotation of crops. It should be noted that the agricultural area is not within the limits of the National Park Iztaccíhuatl-Popocatépetl .

A problem that has not been eradicated is the extensive livestock farming that causes overgrazing, affecting natural regeneration. An alternative could be the definition of suitable agroforestry areas for such activity and promote a sustainable management that considers the carrying capacity. The exclusion of grazing areas requires enclosing areas conducive to natural regeneration. According to Serrada (2003), soil compaction is a factor that hinders natural regeneration, since it prevents contact of the seed with the mineral soil and proper rooting. The presence of organic waste, leaf litter and twigs also avoid the contact of the seed with soil, as well as the presence of the dense herbaceous cover that, in addition, causes competition between species. The favorable conditions for natural regeneration can be created by soil improvement actions that reduce their compaction, such as scarification and controlled burning.

On the other hand, it is suggested to reforest with native species those areas with low forest density, to increase it up to 1 600 plants per hectare. The growth of forests leads to an increase in interception rates and a greater infiltration of moisture in soils; also, a balanced structure of the stands provides habitat for wildlife, contributing to the increase in biodiversity.

According to Aguirre (1997) it is important to keep dying trees, dead trees and large fallen trees to preserve the species associated with them, which can be distributed in a fraction of the stand forming copses. It also indicates the prevention of forest fires by reducing the accumulation of combustible materials and the use of firebreaks, black lines, pruning, clearing, thinning or prescribed burns.

Finally, it is important that the Forest Station of Zoquiapan continues with its fundamental objectives of teaching, research, conservation and, above all, sustainable management of natural resources.


According to the results, for 2020, the areas covered by forests within the micro-basin of Zoquiapan will have a low probability of land use change. The aforementioned as long as the efforts that so far are made to conserve the site continue. Areas covered with grassland and used for agricultural activities also have a low probability of change. Specifically, and considering the results of the transition matrix as stable state, the probabilities of permanence of land uses are 94 % for forest, 88 % for grassland and 91 % for agricultural activities. The method applied is able to capture the behavior of land uses in recent years for the study region.


  • The authors thank for the financial support of CONACYT for the student scholarship granted through the Program of Master of Science in Forest Sciences and thank the Centro de Investigación en Recursos Naturales y Medio Ambiente (CIRENAM) of the Universidad Autónoma Chapingo. In the same way, we thank the anonymous reviewers whose suggestions improved the manuscript.


Aguirre, C. O. (1997). Hacia el manejo de ecosistemas forestales. Madera y Bosques, 3(2), 3-11. doi: 10.21829/myb.1997.321369

Bedoya, J. C., & Barrera, M. (2006). Convergencia de las cadenas de Markov. Scientia Et Technica, 12, 73-78. doi: 10.22517/issn.2344-7214

Bouchard-Côté, A., Vollmer, S. J., & Doucet, A. (2017). The bouncy particle sampler: A non-reversible rejection-free Markov chain Monte Carlo method. Journal of the American Statistical Association. doi: 10.1080/01621459.2017.1294075

Castañeda, R. M. F., Endara, A. A. R., Villers, R. M. de L., & Nava, B. E. G. (2015). Evaluación forestal y de combustibles en bosques de Pinus hartwegii en el Estado de México según densidades de cobertura y vulnerabilidad a incendios. Madera y Bosques, 21(2), 45-58. doi: 10.21829/myb.2015.212444

Consejo Civil Mexicano para la Silvicultura Sostenible (CCMSS). (2008). Estudio de las condiciones territoriales y su percepción del Parque Nacional Iztaccíhuatl-Popocatépetl, Zoquiapan y Anexas. Retrieved from

Eastman, R. (2012). IDRISI Selva. GIS and image processing software version 17.0. Massachusetts, USA: Clark Labs.

Garrocho, C., Jiménez-López, E., & Álvarez-Lobato, J. (2016). Modelando la migración interestatal de México: cadenas de Markov estáticas versus cadenas de Markov dinámicas con medias móviles. Papeles de Población, 22(90), 109-144. doi: 10.22185/24487147.2016.90.036

Hoyos, L., Lara, P., Ortíz, E., López, R., & González, J. (2009). Evaluation of air pollution control policies in Mexico City using finite markov chain observation model. Revista de Matemática: Teoría y Aplicaciones, 16(2), 255-266. Retrieved from

Instituto Nacional de Estadística, Geografía e Informática (INEGI). (2005). Uso de suelo y vegetación a escala 1:250000, Serie III (conjunto nacional). Retrieved July 1, 2016 from

Instituto Nacional de Estadística y Geografía (INEGI). (2009). Vegetación y uso de suelo a escala 1:250000, serie IV (conjunto nacional). Retrieved July 1, 2016 from

Instituto Nacional de Estadística y Geografía (INEGI). (2013). Continuo de elevaciones mexicano 3.0. Retrieved July 1, 2016 from

Instituto Nacional de Estadística y Geografía (INEGI). (2014). Conjunto de datos vectoriales edafológicos, escala 1:250,000, Serie II. Retrieved from

Levin, D. A., Peres, Y., & Wilmer, E. L. (2009). Markov chains and mixing times. USA: American Mathematical Society. Retrieved from

Lomas-Barrié, C. T., Terrazas-Domínguez, S., & Tchikoué-Maga, H. (2005). Proposal of territorial ecological ordering for the National Park Zoquiapan and annex. Revista Chapingo Serie Ciencias Forestales y del Ambiente, 11(1), 57-71. Retrieved from

López, E., Bocco, G., & Mendoza, M. (2001). Predicción del cambio de cobertura y uso del suelo: el caso de la ciudad de Morelia. Investigaciones Geográficas, 45, 39-55. doi: 10.14350/rig.59145

Martínez-Santiago, S., Alvarado-Segura, A., Zamudio-Sánchez, F., & Cristobal-Acevedo, D. (2017). Spatio-temporal analysis of forest modeling in Mexico. Revista Chapingo Serie Ciencias Forestales y del Ambiente, 23(1), 5-22. doi: 10.5154/r.rchscfa.2016.01.003

Memarian, H., Balasundram, S. K., Talib, J. B., Sung, C. T. B., Sood, A. M., & Abbaspour, K. (2012). Validation of CA-Markov for simulation of land use and cover change in the Langat Basin, Malaysia. Journal of Geographic Information System, 4(6), 542-554. doi: 10.4236/jgis.2012.46059

Orantes, G. F., & Musálem, S. M. (1982). Determinación de calidad de estación Pinus hartwegii Lind. Zoquiapan México. Revista Mexicana de Ciencias Forestales, 35(7), 3-20. Retrieved from

Paegelow, M., Teresa, M., & Menor, J. (2003). Cadenas de Markov, evaluación multicriterio y evaluación multiobjetivo para la modelización prospectiva del paisaje. GeoFocus, 3, 22-44. Retrieved from

Partida, V. (1989). Aplicación de cadenas de Markov para proyecciones demográficas en áreas geopolíticas menores. Estudios Demográficos y Urbanos, 4(3), 549-571. Retrieved from

Pérez, R., Valdez, R., Moreno, F., González, A., & Valdez, J. (2012). Predicción espacial de cambios del uso de suelos en Texcoco, Estado de México. Revista Mexicana de Ciencias Forestales, 2(5), 59-72. Retrieved from

R Development Core Team. (2016). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.

Reynoso, R., Valdez, J., Escalona, M., de los Santos, H., & Pérez, M. (2016). Cadenas de Markov y autómatas celulares para la modelación de cambio de uso de suelo. Ingeniería Hidráulica y Ambiental, 37(1), 72-81. Retrieved from

Rodríguez Trejo, D. (2001). La ecología del fuego en el ecosistema de Pinus hartwegii. Revista Chapingo Serie Ciencias Forestales y del Ambiente, 7(2), 145-151. Retrieved from

Rojas, J., Barajas, A., Riemann, H., & Franti, C. (1993). Markov chain modeling of endemic cattle diseases in the tropics of Mexico. Ciencia Rural, 23, 325-328. doi: 10.1590/S0103-84781993000300014

Saldi, N., Linder, T., & Yüksel, S. (2013). Quantized stationary control policies in Markov decision processes. Retrieved from

Sanchayeeta, A., & Southworth, J. (2012). Simulating forest cover changes of bannerghatta national park based on a CA-Markov model: A remote sensing approach. Remote Sensing, 4(10), 3215-3243. doi: 10.3390/rs4103215

Secretaría de Medio Ambiente y Recursos Naturales (SEMARNAT). (2009). Impacto del cambio climático en las tierras y sus características. México: Autor.

Secretaría de Medio Ambiente y Recursos Naturales (SEMARNAT). (2010). NOM-059-SEMARNAT. Protección ambiental-Especies nativas de México de flora y fauna silvestre-Categorías de riesgo y especificaciones para su inclusión, exclusión o cambio-Lista de especies en riesgo. México: Diario Oficial de la Federación. Retrieved from

Secretaría de Medio Ambiente y Recursos Naturales (SEMARNAT). (2013). Acuerdo por el que se da a conocer el resumen del Programa de Manejo del Parque Nacional Iztaccíhuatl Popocatépetl. México: Diario Oficial de la Federación. Retrieved from

Serrada, R. (2003). Regeneración natural: situaciones, concepto, factores y evaluación. Cuadernos de la Sociedad Española de Ciencias Forestales, 15, 11-16. Retrieved from

Tejada-Nichols, R. (2010). Estudio técnico por contingencia ambiental del Parque Nacional Izta-Popo, Zoquiapan y Anexas. Amecameca, Estado de México, México: Parque Nacional Izta-Popo Zoquiapan, CONANP-SEMARNAT.

Torres, P. V. H., Gaytán, M., & Tinoco, Z. M. A. (2017). Dinámica de la inversión extranjera directa en los estados de México: un análisis de cadenas de Markov espaciales. Contaduría y Administración, 62(1), 141-162. doi: 10.1016/j.cya.2016.07.001

Universidad Autónoma Chapingo. (2005). Programa de manejo para el aprovechameinto de arbolado muerto en la Estación Forestal Experimental Zoquiapan. Texcoco, México. Retrieved from

Villegas, P. R., Muñoz, R. C., Muñoz, J., Gallo, G. C. A., & Ponce, R. J. (2011). Tasa de cambio de uso del suelo en el Parque Nacional Pico de Orizaba, Veracruz, México en el periodo 2003-2011. Retrieved from

Virgen-Cobos, G. (2016). Establecimiento de una red de monitoreo meteorológico en la Estacion Forestal Experimental Zoquiapan. Chapingo, Texcoco, México: Universidad Autónoma Chapingo

Zepeda, G. C., Nemiga, X. A., Helgueras, A. L., & Madrigal, U. D. (2012). Análisis del cambio del uso del suelo en las ciénegas de Lerma (1973-2008) y su impacto en la vegetación acuática. Investigaciones Geográficas, 78, 48-61. doi: 10.14350/rig.32469


Figure 1. Classification of land use and vegetation in the micro-watershed of Zoquiapan, based on the satellite images of 1989 (top image) and 2009 (bottom image).
Figure 2. Ergodic average of 1 000 iterations of a Márkov chain at discrete time.


Table 1. Surface occupied by land use and vegetation in the micro-watershed of Zoquiapan in the years 1989 and 2009.
Soil use 1989 2009 Difference 1989-2009%
ha % ha % ha %
Agricultural use 523.78 6.47 521.91 6.45 -1.86 -0.02
Grassland 208.39 2.57 119.76 1.48 -88.63 -1.09
Forest 7 052.37 87.22 7 142.87 88.32 90.49 1.11
Bare soil 302.60 3.74 302.60 3.75 0 0
Total 8 087.16 100.00 8 087.16 100.00 0 0
Table 2. Probability of change or permanence between land uses in the micro-watershed of Zoquiapan for the year 2020.
Soil use Forest Grassland Agricultural
Forest 0.9454 0.0546 0.0000
Grassland 0.0556 0.8875 0.0569
Agricultural use 0.0000 0.0900 0.9100