Modeling Agricultural Change through Logistic Regression and Cellular Automata: A Case Study on Shifting Cultivation


Agricultural expansion is one of the prime driving forces of global land cover change. Despite the increasing attention to the factors that cause it, the patterns and processes associated with indigenous cultivation systems are not well understood. This study analyzes agricultural change associated with subsistence-based indigenous production systems in the lower Pastaza River Basin in the Ecuadorian Amazon through a spatially explicit dynamic model. The model integrates multiple logistic regression and cellular automata to simulate agricultural expansion at a resolution consistent with small scale agriculture and deal with inherently spatial processes. Data on land use and cultivation practices were collected through remote sensing and field visits, and processed within a geographic information system framework. Results show that the probability of an area of becoming agriculture increases with population pressure, in the vicinity of existing cultivation plots, and proximity to the center of human settlements. The positive association between proximity to cultivation areas and the probability of the presence of agriculture clearly shows the spillover effect and spatial inertia carried by shifting cultivation practices. The model depicts an ideal shifting cultivation system, with a complete cropping-fallow-cropping cycle that shows how agricultural areas expand and contract across space and over time. The model produced relatively accurate spatial outputs, as shown by the results of a spatial comparison between the simulated landscapes and the actual one. The study helped understand local landscape dynamics associated with shifting cultivation systems and their implications for land management.

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Lopez, S. (2014) Modeling Agricultural Change through Logistic Regression and Cellular Automata: A Case Study on Shifting Cultivation. Journal of Geographic Information System, 6, 220-235. doi: 10.4236/jgis.2014.63021.

1. Introduction

Land use and land cover changes (LUCC) are the prime driving forces of transformations in the Earth system [1] . The focus of LUCC studies is generally on the identification of cause-effect relationships to uncover patterns of land uses and land covers and the processes of their change [2] . LUCC studies that concentrate on cause-effect relationships usually point at economic drivers [3] [4] , population dynamics [5] [6] , suburban sprawl factors [7] [8] , household developmental cycles [9] -[11] , transportation infrastructure [12] -[14] , tenure security [15] [16] , environmental conditions [17] [18] , and patterns of commercial agriculture and subsistence swidden land use [14] [19] [20] as major forces impacting the landscape.

Until a couple of decades ago, computational capacity constrained the operation of spatially explicit techniques to characterize human-environment interactions [21] . Advances in spatially oriented techniques that integrate spatially explicit data, as derived from remote sensors and geographic information analysis, provide new opportunities to truly incorporate innovative approaches to address fundamental questions about the relationships between social and ecological systems [22] [23] . These relatively new approaches allow researchers to identify key environmental and social variables that shape the landscape, and also to dynamically (as opposed to statically) model inherently spatial complex processes. Spatially explicit land use change models are not only capable of estimating the quantity of change and where these changes will occur over relatively long periods of time, but also useful to unravel multifaceted pattern-process relationships at different spatial and temporal scales. This study follows such an approach to analyze LUCC associated with agricultural expansion and subsistence-based production systems in tropical environments.

Spatially explicit approaches, such as cellular models, have been successful in analyzing complex spatial phenomena given their relative simplicity and flexibility. In cellular automata (CA), for instance, each cell in a spatial array exists in one of a finite set of states (e.g. a type of land cover or land use), and future states (e.g. the transition from one type of land use/land cover to another) depend on transition rules based on a local spatio-temporal neighborhood. A CA system is homogenous in the sense that the set of possible states is the same for each cell and the same transition rules apply to each cell. Time advances in discrete steps, and updates in the state of each cell may be synchronous (i.e. cells are all updated to their new state simultaneously) or asynchronous (i.e. cells are updated to their new state at different times) [24] . LUCC studies have used CA models to study frontier settlement dynamics [25] , fire spreading [26] , forest dynamics [27] , and urban growth [28] [29] [30] [31] . Most of these studies assume that the probability of change from one state to another at a time step n + 1 depends on two conditions: 1) the current state at time n and not on the sequence of states that preceded it, and 2) the transition potential of cells is determined by the influence that the spatio-temporal neighborhood exerts on a particular location. These two conditions make CA a robust framework to capture the intrinsic spatial and dynamic nature of evolving human-environment interactions.  

In the past couple of decades, statistical methods such a multiple logistic regression (MLR) have been increasingly used in land cover transformation studies to analyze forest dynamics and fire dispersal [32] , agricultural and land use change [20] [33] [34] , and deforestation [12] [13] [35] . Generally, this kind of statistical studies are based on empirically parameterized static models that compute land cover change probabilities, indicating the likelihood of occurrence of a specific land use at a specific location [36] . MLR identifies the explanatory power of factors on the probability of the presence or absence of a phenomenon (e.g. agriculture), which is generally defined as a categorical variable [37] . If the observations used to generate the MLR model are spatially explicit (i.e. geolocated), the technique yields coefficients that can be used to generate maps depicting the probability of a particular location to change to a certain state or remain un-changed.

The integration of techniques such as MLR and CA, within a geographic information system (GIS) framework, is an efficient option to dynamically and spatially model LUCC. This type of synergism is suited for developing LUCC scenarios, which are themselves models of how a spatial system functions and, like other types of models, they allow explorations of understanding. At fine spatial resolutions, this type of integration allows quantifying and predicting land cover changes associated with local level spatial processes [43] . MLR/CA models of LUCC, for instance, have been successfully applied to model urban growth [38] , land changes in colonization frontiers [39] , and land use allocation in rural areas [40] -[42] . Despite the increasing popularity of MLR/CA models to study landscape dynamics, there has been only very limited research on the patterns and processes associated with subsistence based cultivation systems using this approach. Thus, this study tries to fill this gap in research and addresses the following research question: What are the patterns and processes associated with agricultural expansion in subsistence-based cultivation systems in the lower Pastaza River Basin in the Ecuadorian Amazon (PRBEA)? The emphasis is on the analytical model, presented here as an efficient alternative to simulate local landscape scenarios at fine resolutions and to illustrate its application and interpretation.

2. Study Area

This study focuses on the lower PRBEA region in Western Amazonia, which is predominantly occupied by indigenous populations. The modeling framework is applied to the case of the lowland Jívaros (the Achuar) and the Jívaro-Kichwa (the Shiwiar). Their territories encompass approximately a combined area of 930,000 ha (Figure 1) with an average population density of 0.7 persons per km2. The annual population growth rate is approximately 3.6 percent [44] . Agricultural production is limited to an area of less than 5% of the total territory and is mostly oriented towards subsistence purposes. The rate of agricultural expansion in the PRBEA is approximately 0.2 percent per annum (Figure 2, Table 1). Patterns of land use and land cover are consistent with traditional resource management practices. Indigenous families congregate around airstrips to form small semi-permanent villages. Landing strips are the only type of accessibility infrastructure in the area and constitute the centers of the communities where most families reside. Residential areas are followed by cultivation, foraging, and hunting zones [45] . The lower PRBEA is a mega bio diverse region and is currently located in the center of a variety of conservation and development projects given the region’s rich natural and cultural resources.

Figure 1. Study area—The Pastaza River Basin in the Ecuadorian Amazon.                                         

Figure 2. Post-classification comparison of agricultural and forested areas between years 1987 and 2002.    

Table 1. Change detection matrix between years 1987 and 2002. Land cover changes are reported in km2 and percentages.   

a: year 1987; b: year 2002; Annual conversion rate from forest to agriculture = 0.2%.

3. Methods and Materials

3.1. Data Collection and Processing

To characterize current spatial conditions in the area, a series of RGB images with a spatial resolution of < 1 m and video graphy were collected in year 2006 with the aid of an aircraft, a GPS enabled digital camera, and a video mapping system (VMS 2.0). These data were processed using digital remote sensing techniques such as image geometric correction, mosaicking, interpretation, and on-screen digitizing. With these data, a land use/land cover geo data base of 101 production units was generated that comprised residential, agricultural, and foraging areas of seven communities in the region (Figure 1). From this set, 66 were surveyed in the field to obtain not only socio-economic and demographic attributes, but also information about the structural characteristics of the production system (e.g. fallow periods, land allocation practices, production strategies). These data were processed within a GIS framework (ArcGIS v. 9.3), linking household surveyed and land use and land cover information. The vector data were transformed to raster grids and resampled to a spatial resolution of 20 m (i.e. a fourth of the minimum agricultural plot in the surveyed communities) to characterize the cultivation system. Official maps at scales of 1:25000 and 1:50000 from the Ecuadorian Military Geographic Institute were used to help describe spatial conditions (i.e. hydrography and the presence of infrastructure) in the area. Topographic conditions were derived from ASTER Global Digital Elevation Map (GDEM) data [46] . Transition rates from forest to agriculture for the region were obtained from classifications of Land sat TM and ETM satellite images of years 1987 and 2002 respectively. The data were analyzed through the integration of MLR and CA to explain landscape patterns due to variations in population numbers and environmental conditions.

3.2. A MLR/CA Land Use Change Modeling Framework

This study employs two main modeling techniques. First, it employs a MLR approach to model the presence (1) or absence (0) of agriculture in the region based on a stratified random sample of 2948 cells separated at least 60 m from each other (i.e. three times the cell resolution). A random sample may help minimize issues associated with spatial autocorrelation and obtain more efficient coefficients [13] . The model accounts for agricultural variability (La) that could be explained by a series of environmental and demographic factors [20] . The MLR model is formalized as:



where Logit (Pa(x, y)) is the logit of the probability (Pa) of the presence of agriculture at location (x, y), α is the intercept, and βn are the slope parameters estimated via a maximum likelihood iterative procedure. The slope parameters represent how variations of the predictor affect the propensity towards agriculture. Soil is a dummy variable that depicts “good” or “bad” soil conditions and estimated from soils maps created by Ecuador’s Ministry of the Environment [47] and soil observations from the field. PopPre is the ratio between total household size and total cultivated land and estimated from household surveys and land use maps. DstLdn is the Euclidean distance from the edge of the closest landing strip to any site. NstNbr is the Euclidean distance to the nearest agricultural area. Slope is an estimate of on-site conversion costs and depicts terrain steepness or flatness and determined based on a 30 m resolution digital elevation model of the area. CstDstHo is the least accumulative cost of moving through different surfaces and terrain conditions.

Second, this study relies on a CA mechanism that simulates a decision making process, in which key and random unknown factors affect personal decisions on whether or not to expand agriculture. Some events appear to be random because agricultural expansion is a complex phenomenon and not all driving factors are known. Since all the variables are spatially explicit, the coefficients of the MLR model are used to generate a probability raster (employing Equations (1) and (2)) that is the basis for the CA model. The probability map depicts the likelihood of the presence of agriculture at every location. The CA rules determine which cells will transition from forest to agriculture based on the cell’s probability and of its eight closest neighbors. The CA algorithm was implemented in ArcGIS using Python language and is formally defined as follows:

Line 1: If then else

Line 2:

Line 3: If then else

Line 4: Go to Line 2 where Pa(x, y) is the propensity towards agriculture at location x,y at time T and estimated through MLR and extrapolated to other cells via map algebra; is the average probability of observed agricultural areas;

is the probability of a cell of being agriculture at location x, y at time T + 1; Nij is the average probability in a window of 3 × 3 pixels. At the beginning of the very first iteration (Line 1), the algorithm assigns a value of one (presence of agricultural area) to those cells that have a value equal or higher than the cut-off probability value (i.e. the average probability of observed cultivation areas [value = 0.6] and entered as a parameter in the model). Otherwise, the probability of the cell remains the same. If most of the area surrounding a forest patch has been transformed to agricultural use, it is likely that the patch of forest will also be cleared in the near future (based on the assumptions of the model). Line 2 takes into consideration the spatial context to update a cell’s probability based on the characteristics of the eight closest neighboring cells and its own. Line 3 compares the average probability to the cut-off probability and assigns a value of one to those cells that are equal or higher. Line 4 creates a loop in the algorithm that allows agricultural areas to expand until there are no more possible transitions utilizing the most current set of variables. The new landscape map primarily shows the presence (value = 1) or absence (values < 1) of agriculture in N years (Figure 3).

The total number of cells to change from forest to agriculture in an N-year simulation depends mostly on the cell’s probability (obtained from the probability map and modified by the influence of its spatio-temporal neighborhood) and on the transition rate from forest to agriculture for the region. Each iteration in the model represents a time step of one year since population and agricultural growth estimates are annual. The mechanism continues until there are no more possible transitions. If the extent of agriculture at a particular time step is less than the expected area, a new set of randomly chosen cells will go through the CA mechanism to determine the size and shape of agricultural areas. The system stops if the agricultural area is larger than or equal to the expected agricultural extent in N years.

Conceptually, the variables in the model can be classified as state dynamic or static. State dynamic variables are those that change over time, whereas static variables (or parameters) remain the same (Figure 4). For in-


Figure 3. Probability maps before (a) and after (d) the convolution of the cellular automata engine using an average probability of 0.6. (b) and (c) show intermediate steps in the transition process.                                     


Figure 4. Conceptual logistic multipleregression/cellular automata (MLR/CA)model of shifting cultivation.        

Conflicts of Interest

The authors declare no conflicts of interest.


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