Global change research includes an extensive body of literature covering population-environment interactions focusing on the central issues of migration and demography, environmental site and situation, and socio-economic structures. However, rarely are these conditions addressed within a spatially-explicit, temporally dependent form. Quite often this is simply because neither the data nor the modeling methodologies combine well to effectively address uncertainty with spatially defined time-series data. As dynamical systems theory has advanced, the available data and the simulation tools have evolved so that it is now possible to simulate not only general change but also the spatial organization of individual landscape elements and their respective interaction. In this research, a cellular automaton model is proposed as an effective framework for the predictive modeling of landuse/landcover change (LULCC) associated with the spatial pattern and rates of deforestation and agricultural extensification in the Ecuadorian Amazon.

The research study site in the northeastern Ecuadorian Amazon, known regionally as the Northern Oriente, is significant from a social, biophysical, and geographical basis. Settlers in the Napo and Sucumbios provinces are generally poor in-migrants settling on predefined 50 hectare plots, clearing primary forest to grow subsistence crops, coffee, and later, pasture for cattle. Despite its global biodiversity and carbon sequestration significance, agricultural settlement and concurrent deforestation threaten the region. The specific site selected for modeling is an intensive study area (ISA) of approximately 200 km2 located to the northeast of the regional capital and largest central place, Lago Agrio.

Cellular automata (CA) were originally conceived by Ulam and von Neumann in the 1940s to provide a formal framework for investigating the behavior of complex, extended systems. The model presented employs user-defined rules based upon spatially-explicit probabilities derived from both biophysical and social characteristics to produce an output image of the anthropomorphized landscape. The ERDAS Imagine Spatial Modeler, an interactive visual tool, was used for model development and enhanced using the spatial model language (SML).

The primary input data for the model are landuse/landcover layers derived using Landsat Thematic Mapper data ranging temporally from 1986 through 1999 classified using a hybrid unsupervised/supervised classification scheme. Attribution was performed using the results from field work conducted in February 1999 and February/March 2000. Additional data layers include transportation, topography, and hydrography.

Model calibration was conducted through comparison of the model's output to an historical data set with respect to the key variables, agricultural extensification and urbanization. The changing temporal and spatial location/process of tropical development provides insight into the activities that currently encourage land clearing. In this way, spatial patterns point to a set of factors that can explain recent changes in regional rates of landuse/landcover change and provide focused spatial constructions suitable for modeling. This work combines the historically descriptive aspects of society with remote sensing and landscape ecology towards the development of a Geographic Information Science based Northern Oriente analogue. With improved data handling, the modeling scheme presented here is extensible to a variety of tropical environments and regional contexts, making cellular automaton modeling not only a promoter of research into predictive spatial systems but more importantly an effective approach to probabilistic modeling of population-environment interactions.

Environmental modeling often takes the approach that events are static in time and space. The more complex models, attempting to define process over time (e.g. GAP, GCM), rarely if ever include human activity as an integrated process. These human effects are difficult to model and do not follow the mechanistic forms favored by modelers. Further, attempts at mechanistic modeling of human activity have fallen from favor in the scientific literature. The process of land degradation, while in many cases visible to the eye and found throughout human history, has not been modeled to any significant degree (Blaikie and Brookfield, 1987). Redclift (1996) cites three primary flaws in the current paradigm used for the evaluation of landuse and landcover change processes: biological determinism, regionalization (fitting society into tight discrete social units for measure), and avoidance of time and space in the modeling process. In the context of the Ecuadorian Amazon all three flaws will be addressed.

Biological determinism rises from the natural science paradigm of abstraction and deduction. Human activity, under determinism, is a function of epigenetics and other biological mechanical processes. The social sciences with the exception of economics simply avoid making statements of causality. Homo economicus, the rational man or profit maximizer, is a fundamental component of economic studies of land degradation. While this view simplifies model building, it does not support alternatives. It could only be used for normative model building and not stochastic predictive modeling. In the Oriente, the actions of the individuals in terms of landuse decision-making habits often depend upon social and demographic variables entirely unrelated to profit maximization. The differences in the patterns of landuse between the indigenous groups, the long-term colonists, and the late arrivals are quite different though the same forces of capitalism apply to all in some measure though likely less for the remote indigenous communities where cultural accumulation processes are less pronounced (Hiroaka and Yamamoto, 1980).

The regionalization flaw focuses on the long-standing process of defining groups using social boundary constructions (Redclift, 1987). The aggregation of social variables into this level is valid in modeling some social issues. However, environmental variables often cross social boundaries: they may be caused in one country, development zone, political system, or industrial region and have no relationship to political boundaries or even cultural ones that affect another region at multiple space-time scales. The fairly recent expansion of transnational industries increases the complexity of the issue. For example, African Palm plantations are now found in many Oriente areas. These plantation products are strictly for export (MAG and ORSTOM, 1978).

Temporal and spatial scale problems may prove the most problematic. Development in poorer countries generally takes precedence over all other concerns. The use of the land to raise the standard of living defined by the developed nations is the dominant pattern. Environmental issues occur over time and space. Slowly developing environmental problems like climate change are the most difficult to quantify and model. Marx (Redclift and Benton, 1994) identified no actual problems with environmental degradation. Any problems were simple inequalities in the allocation of resources. This view tends to overlook social construction of environmental views and differing temporal opinions of nature within the same culture (Keyes, 1976). Amazonian processes of deforestation certainly take center stage and are most easily seen and quantified (O'Brian, 1998). However rapid the actual process, it is unlikely that it is consistent across space or time and subject to only fixed local neighborhood considerations. Exogenous factors include commodity prices, land policies, international relations, and social pressures. These are but some of the issues imposed upon the Oriente and LULCC as a consequence of externalities, multi-thematic dimensions, and space-time variation.

Deforestation activities are often the result of exogenous factors. Global capitalism and the commodification process are inextricably intertwined. In many Latin American countries, the national governments enforce price fixes on regular consumable farm produce and promote the export of beef as a means to increase revenues. The local farmer under this scenario faces either fixed income using standard produce with the only options being the expansion of agricultural land or the clearing of land for pasture. Either scenario results in deforestation while the farmer is predominantly influenced by outside forces. The process of land clearing requires additional labor input that could otherwise be used for the creation of landesque capital (Blaikie and Brookfield, 1987). Many of the Amazonian regions contain fractured and convoluted topography with only adequate soils. Instead of building terraces or rotating crops, the farmer often deforests and converts to pasture or overplants. Once the land is degraded to a level below sustainable levels, the farmer, as part of the peasant-pioneer cycle, is forced to abandon the land and search for new land opportunities including deforestation of additional portions of one's finca or, if not an option, then complete abandonment and emigration (Stearman, 1985.). The investment in resources is lost and the possibility of successful resettlement is reduced. Within the presented research, the activities of individuals and the consequent effects on landuse/landcover dynamics are modeled using a multi-state dynamic simulation model. The use of social survey data, and an assumption regarding the nature of exogenous drivers, are combined within a composite model containing both deterministic and stochastic processes.

It is readily apparent that individual, social, and structural processes occur at different temporal and spatial scales. Individuals choose incorrectly, they decide based upon the decisions of their neighbors, or decide to satisfy the whims of a society far removed from their own. There are in fact many possible routes that an individual might take in making land use decisions. However, those decisions cluster around a common core. By defining the core decisions and modeling stochastically, it is possible to predict the majority of the decisions made by the regional community and their expression upon the landscape.

Cellular automata (CA) were originally conceived by Ulam and von Neumann in the 1940s to provide a formal framework for investigating the behavior of complex, extended systems (von Neumann 1966). Cellular automata are dynamic, discrete space and time systems. A cellular automaton system consists of a regular grid of cells, each of which can be in one of a finite number of k possible states, updated synchronously in discrete time steps according to a local, identical interaction rule. The state of a cell is determined by the previous states of a surrounding neighborhood of cells (Wolfram 1984; Toffoli and Margolus 1987). The infinite or finite cellular array (grid) is n-dimensional, where n=1,2,3 is used. The identical rule contained in each cell is essentially a finite state machine, usually specified in the form of a transition function or growth rule that addresses every possible neighborhood configuration of states. The neighborhood of a cell consists of the surrounding (adjacent) cells. For 1-D (one-dimensional) CA models, a cell is connected to r local neighbors (cells) on either side, where r is a parameter referred to as the radius (e.g. each cell has 2r+1 neighbors, including itself). The increasing application of cellular automata in general phenomenological modeling is an important indicator of the developmental potential of CA. The ability of a system to grow and then alter its rate of growth and possibly reverse or "die" is a fundamental goal in biological or human system CA modeling. Ermentrout and Edelstein-Keshet (1993) performed CA applications in biological modeling. The systems modeled by Clarke et al. (1996, 1997) and the example presented here both attempt to follow biological patterns of development. The difficulty in modeling population-environment interactions has historically been the necessary dual simulation mode of model construction. Human systems are necessarily stochastic while many natural systems are adequately modeled deterministically. Combining the two methodologically polar components into an effective approximation of reality requires the use of alternative modeling techniques. The model employs the user-defined rules to produce an output image of the anthropomorphized landscape. In order to minimize IO issues, the ERDAS Imagine Spatial Modeler, an interactive visual tool, was used for model development and implementation. In order to better parameterize the image dynamics of the model, the individual growth rules were assembled and tested as discrete elements.

The input data for the model include landuse/landcover data layers organized as binary data structures and derived from Landsat Thematic Mapper data ranging temporally from 1986 through 1996 (Figures 1,2). These layers were classified using a hybrid unsupervised/supervised classification scheme and the ERDAS Imagine software package. Class validation and accuracy assessments were performed using transformed divergence and random class fields. Field campaigns conducted in the spring of 1999 and 2000 provided control information. Additional data layers include roads digitized from 1:50,000 topographic maps and slope data. Soils data are included but have not been tested for accuracy. These data are rescaled (1 bit to 2 byte) in order to optimize space and computing efficiency. Finally, social survey data collected in both 1990 and 1999 were used in qualitative CA rule evaluation.

The first model component written creates a random number image. The random number generation procedure is vital to successful CA modeling. While CA purists will insist that only local neighborhood rules are necessary for CA modeling, the use of the stochastic component permits growth more closely mimicking reality. By design, the total number must be low, but the low number of random pixels selected necessitates an additive set of rules. In modeling the Oriente, the random number generator creates a random number field by selecting each pixel by row and column, and then applying a random number as a pixel digital number. This pixel digital number is then altered via an adjustable scalar value. The adjustability of the scalar value allows for iterative adjustments in increased or decreased growth rate conditions.

Organic growth spreads outward from existing urban centers and agricultural areas, representing the tendency of the humanized landscape to expand. Spontaneous growth occurs when a randomly chosen cell falls nearby an already urbanized cell, simulating the influence urban areas have on their surroundings (Clarke et al. 1997). Both organic and spontaneous growth rules are modeled in the first phase of the Oriente model. Focal filters are used to create a field of neighbor effect in order to approximate urban influence and allow the development to expand based upon the location of the random cell. By combining the two components into one section, the random effect is modeled as an additive component to the organic urbanization as a whole. Diffusive growth promotes the random dispersed development of agricultural plots regardless of proximity functions (Clarke et al. 1996). This type of growth component is handled later in the Oriente model with the second application of the random number field. In the Oriente model, the diffusion component is modeled using its own adjustable random number field and by modifying the organic growth routine by applying the focal filter using the maximum value criteria rather than the mean. Random dispersiveness is modeled by using a random number generator: identifying an intermediate image and applying a search function, or by applying a random number table to the focal filter to vary field characteristics. Random non-isotropic spreading is possible with the spreading center assignment acting randomly.

Road influenced growth, the most important driver of landscape alteration in the Oriente, encourages change cells to develop along the transportation network replicating the effects of increased accessibility. The likelihood of settlement and consequent deforestation along a road is high yet variable depending upon access to markets. Road accessibility growth is currently modeled with another random number image, an adjustable search function, and an adjustable conditional statement. The model component outputs a "roadgrowth" image for visual validation. A corollary to road growth is river influenced growth. In many cases, the initial settlement push into a region is via river system transportation. As such, river growth is modeled using hydrography information and the same routine as the road growth process. The physical element, slope, is iteratively applied. All the pixels at each step are analyzed with respect to the slope layer. This method seems unnecessarily repetitive, as the slope values themselves do not change, though the effect varies whereby slope constraints can and do change among growth rules. The Oriente model incorporates slope as a separate layer with an adjustable scalar function to modify the slope desirability over time as demand for land changes. In the final phases of model execution, excluded areas are removed, and the original urban extent image is added. It is inevitable that pixels will be incorrectly urbanized during the model run, as water areas and other types of features are not initially removed from consideration; therefore the excluded image is subtracted from the whole. Second, the original seed image is added back into the growth image to account for areas erroneously removed due to slope constraints and topographical data errors (Figure 3).

Self-modification is necessary, as the model would otherwise produce linear or exponential growth (Clarke et al. 1997). The self-modification design element was included in order to better approximate the S-curve growth rate of urban and agricultural expansion; however, considering the artificial and non-rule based component of this implementation of self-modification, the resulting growth becomes temporally scale dependent. The self-modification criteria can be adjusted interactively; however, the annual iterative decrease is hard-coded. By limiting the areal extent of the region, the model is forced to slow down in order to maintain equivalency in growth functionality. Over the course of multiple model runs, the boom and bust cycles likely cancel each other out, minimizing the effect. The agricultural versus urban growth modes vary according to both initial complexity and areal extent.

This initial calibration follows a comparative model of predicted versus actual change. The actual change is measured through the LULCC data sets created from the remotely sensed data. While the output from the Oriente model is certainly suitable for this type of analysis, the summary correlations by class tend to be more appropriate. As the complexity of the seed image directly influences the shape and pace of growth, complexity may ultimately be the best measure of similarity (Messina et al 2000). Most existing CA models, after multiple iteration, tend to produce smooth, isotropically consistent output. Standard measures of spatial autocorrelation are not used as they tend to provide false confidence in the results.


Total Area in Hectares				Summary Correlations
	1986	1996 Predicted	1996 actual	Forested	Urbanized	Agriculture
Forested	48036	30015	31853	70.95%	7.80%	23.08%
Urbanized	1050	3591	3774	2.15%	54.50%	3.94%
Agriculture	27158	45072	43029	26.90%	37.70%	72.98%

Upon initial examination, the two images appear quite different (Figures 4,5). However, by comparing the model output with landuse/landcover data of the finest resolution, both the successes and the flaws of the model become apparent. The model predicts the total landscape change within the intensive study area region reasonably well with slight overprediction of agricultural expansion and slight underprediction of urban expansion. The summary correlations are lower than would be seen in a less complex environment due in part to the author's intent in selecting a subset area of maximum spatial and quantitative change and in part to the diffusive growth limitations of the model. Specifically, the low urban correlation is due in large part to the effects of both roads (only one date of road coverage was used) and random oil exploration activities. The relative regional homogeneity of the biophysical and climatic regimes permits the wider application of the model to multiple social and physical scales. However, one cannot avoid the fact that the spatial fit is less than ideal. The true measure of spatial complexity as applied in a CA context is one not yet fully realized in the literature and is like the next phase in this research. The tools exist to build complex (in the complicated not complexity sense) models to predict LULCC in a variety of environments and time periods. Without further development of the theoretical underpinnings of complexity theory and spatial pattern - what is a good fit - the models run the very real risk of over-specification.

The Oriente, like most places, is surprisingly complex. As snapshots in time, images provide the raw material to assist in the derivation of complex environmental and human processes: in effect, to see patterns instead of isolated points and relationships between different distributions. The challenge of modeling population-environment interactions closely parallels the methodological concerns of much of social science. With improved data handling, the modeling scheme presented here is extensible to a variety of tropical environments and regional contexts, making cellular automata modeling not only a promoter of research into predictive spatial systems but more importantly an effective approach to modeling population-environment interactions.

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