Agent-Based Dynamic Spatial Simulation of Land-Use/Cover Change: Methodological Aspects

1. Introduction

This paper discusses a prototype “Agent-based Dynamic Spatial Simulation” (ADSS) used to explore land-use/cover change.The simulation relies on a conceptual framework that combines research into decision making, socioeconomic institutions, and ecology.Then, by drawing upon recent advances in geographic information science, the ADSS maps the conceptual framework onto an agent-based model and generalized cellular automata within a geographic information system (GIS) framework.This paper uses the example of tropical deforestation and subsequent cultivation in the southern Yucatán peninsular region (SYPR) of Mexico to explore methodological aspects of the ADSS.

The ADSS is a spatial decision support system in that it combines spatial data processing, modeling, and display in order to facilitate decision making in the face of ill-structured problems (Densham 1991).Divining the nature of human-environment interaction requires spatial analysis that can draw out the complexities of these interactions coupled with iterative exploration of their ramifications and nature.This need for iterative exploration of dynamic and complex relationships remains unsatisfied by geographic information systems alone.GIS operations such as overlays and buffering are concerned largely with pattern instead of process.The ability of GIS to store, manipulate, and display patterns, however, is the base upon which further modeling can take place.

The ADSS addresses two key failures of present land-use/cover research.Land-use and land-cover change occurs incrementally in spatially distinct patterns that have different implications for environmental change, yet most models lack a spatial component or are coarse-grained (Lambin 1994).The ADSS has a regional scale of analysis that accommodates a fine temporal and spatial grain.Second, many models do not adequately account for the complexity of, and relationships among, socioeconomic and environmental factors (Turner et al. 1995).The ADSS places human-environment relations such as LUCC at the intersection of theories dealing with land manager decision making, the environment, and socioeconomic institutions.

The next section briefly describes the “actor-institution-environment” conceptual framework that underlies the ADSS.Section 3 then goes on to link this conceptual framework to methods used to model LUCC and justify the choice of methods used by the ADSS.Section 4 offers a description of the ADSS structure and implementation through the example of LUCC in the southern peninsular Yucatán region of Mexico.The paper concludes with Section 5.

2. Conceptual framework

While a full description of the conceptual framework underlying the ADSS is beyond the scope of this paper, it is necessary to explore its key aspects.A major vein of human-environment research lies in global environmental change (GEC).Within the GEC research community, there is general agreement on how to conceive of human-environment issues.Environmental change results from infrastructure development, population pressure, market opportunities, resource institutions, and environmental or resource policies (Stern et al. 1992).The international LUCC Science/Research Plan partitions these causes and their effects among the conceptual foci of social systems, ecological systems, and land managers (Turner et al. 1995)

The ADSS reconfigures these foci as a three-component “actor-institution-environment” conceptual framework (Figure 1).The first part focuses on the decision making of households and other actors.In the context of LUCC in the region explored here, the actors are the farming households, or smallholders, who are often the chief actors of change in tropical forests.The second component, socioeconomic institutions, affect actor decision making.Both actors and institutions interact with the third component of the conceptual framework, the biophysical environment.

The conceptual framework draws on research in decision making, bounded rationality, and the effect of actor resources on decision making.Agrarian and development literature posits household behavior ranging from subsistence to market production.Production decisions may be formulated as an objective function of decision variables such as family labor, household consumption, and market price for goods (Singh et al. 1986).It is possible to reformulate the utility-maximization objective function as a bounded rationality problem to account for satisficing behavior resulting from difficulty in generating choice alternatives and the limits of knowledge and learning (Tversky and Kahneman 1990; Simon 1997). In addition, the number of decision variables may be increased through a “resource profile” that includes access to information, ability to learn, and personal characteristics in addition to standard variables such as land, labor and capital (Sen 1981).

Socioeconomic institutions, the conceptual framework’s second component, affect actor decision making.Simultaneously artifacts and dynamic processes, institutions constitute, and are constituted by, regularized behavior (Ostrom 1990).Institutions influence actor decision making by modifying actor resource profiles and decision variables.For example, introduction of new land tenure rules changes access to land in actor profiles and affects decision variables such as crop prices by changing production regimes(Bohle 1993).

Completion of the actor-institution-environment conceptual framework hinges on environmental relationships.Land manager production strategies in forested areas balance the benefits of agriculture, timber, and nontimber forest products (Galletti 1998).These are subject to alternative biophysical configurations of precipitation, soil characteristics, secondary growth, pest infestations, and disturbances such as fire or hurricanes.Complex relationships result when production strategies affect these biophysical forces and lead to changes such as cover conversion, soil erosion, or nutrient depletion (Uhl 1987)

Although this paper concerns deforestation and cultivation, the actor-institution-environment framework, as it is derived from the larger body of GEC research, offers a general view on human-environment situations (although certainly not the only one).The iterative nature of human-environment interaction highlights the need for all three components of the actor-institution-environment conceptual framework.Actor decision making influences, and is affected by, the environment and is subject to institutions that modify actor decision making.Actor-institution relationships are the means by which institutions impact the environment.Finally, actors are not merely beholden to institutions, but are active participants that form much of what makes institutions.

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Figure 1.ADSS conceptual framework

There are a limited number of spatiotemporally explicit LUCC modeling techniques and few suitable for implementation of the actor-institution-environment framework.Traditional approaches, which include cellular automata, spatial statistical techniques, and Markov models, downplay decision making and institutions (e.g., Li and Reynolds 1997; Mertens and Lambin 1997; Moran and Brondizio 1998).Spatial econometrics linked to ecological theory is promising but not amenable to the conceptual framework used here (e.g., Geoghegan et al. 1998).

Dynamic spatial simulation (DSS) portrays the landscape as a two-dimensional grid where rules based on factors such as agricultural suitability determine which cells are deforested (e.g., Wilkie and Finn 1988; Southworth et al. 1991; Gilruth et al. 1995).These simulations typically lack heterogeneous actors, institution-actor relations, and multiple production activities.In an exhaustive review of deforestation models, however, Lambin recommends DSS as the “most advanced modelling approach for a complex, dynamic and spatial problem such as tropical deforestation” (1994: 92)

The shortcomings of DSS can be ameliorated by coupling an agent-based model (ABM) and generalized cellular automata (GCA) to create an agent-based DSS, or ADSS.Agent-based approaches combine empirical and theoretical models of actor behavior in resource-use situations (Conte et al. 1997).Here they embody the actor and institution components of the conceptual framework.The use of cellular automata in ecological models suggests the use of generalized cellular automata to represent the environment (Smith and Bull 1997).By coupling generalized cellular automata and agent-based models, the ADSS is a novel means of operationalizing the actor-institution-environment framework and offers a powerful approach to understanding and projecting land-use/cover change.

Cellular automata are two-dimensional grids where cell values, representing land-use/ cover (or some other states), change in time according to rules based on the value of adjacent cells.GCA models offer greater realism through rules independent of adjacency (Couclelis 1997).A forest succession model, for instance, could have a non-adjacent rule for precipitation in addition to adjacent rules to account for the effect of neighboring timber stands.

An agent-based model is a system of software agents described by variables that store information about the agent and processes that represent agent behavior.This research uses agent variables to represent actor characteristics, especially household resources, and those of institutions, such as spatial extent of land tenure.Agent processes represent actor behavior and institutional effects.An actor’s locational decision for a particular crop, for instance, may be formulated as smallholder-agent processes that link plot choice to agricultural suitability.ADSS agents also use processes based on genetic programs (GP), software representations of strategies that evolve according to their fitness in meeting measurable goals (Koza 1992).In particular, GP are a bounded rationality approach to the decision-making component of the conceptual framework (Edmonds 1999).In view of common property research, institutions translated as agent processes that represent institutional rules (Bousquet et al. 1994).Institution-agent processes may represent crop subsidies, for instance, that affect the decisions of smallholder-agents.

In summary, this research implements the actor-institution-environment conceptual framework by coupling an agent-based model and generalized cellular automata (Figure 2).Smallholder-agent processes based on household resources, environmental information from GCA cells, and decision variables such as crop prices, represent actor decision making.Agent behavior feeds back on GCA cells to allow continual interaction that simulates actor-environment relationships.Institution-agents modify smallholder-agent resources and decision variables to affect actor decision making.Subsequent agent decisions are the means by which institution-agents influence the environment.

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Figure 2.ADSS model structure

4. Implementation

4.1 ADSS framework

The ADSS consists of the ABM and GCA linked to a program shell and user interface.The shell, guided by user-provided scripts, controls the ABM and GCA, conducts tests, and derives statistics.The interface and scripts specify exogenous simulation parameters and model configurations.ADSS is written in the object oriented programming language C++ as a stand-alone program on the Microsoft Windows platform.The ADSS is a close-coupled GIS model (Goodchild et al. 1992), where the user of the ADSS can employ the full functionality and strengths of the other programs without concern for the mechanics of different software programs.It is seamlessly integrated with the Idrisi32 GIS system and the Microsoft Access relational database product through a component object model (COM) conduit and data access object (DAO) respectively.

The ADSS offers the user a script language with which to specify agents, specify GCA grids, enact calibration/validation routines, make general operating system calls, and make direct calls to Idrisi32 or Microsoft Access.The script language also provides a means of storing and changing variables and control structures of a simulation.The ADSS per se provides the shell, GCA, ABM (including the GP framework), and several validation techniques not typically available to commercial GIS (detailed more fully in Section 4.4).Idrisi32 supports the functionality of the ABM and GCA components in addition to providing graphical output, statistical analysis, and validation techniques.ADSS uses Microsoft Access as a relational database to store, query, and update aspatial data.The user in turn can use Access to perform advanced database queries.

For a single simulation, the ADSS shell conducts Monte Carlo runs, extracts the simulated environment from each run, and combines the results for a probabilistic measure of land-use/cover change.A single simulation run iterates through five stages once a year for time intervals ranging up to forty model ‘years’ (1970-2010) as follows:

The shell updates exogenous parameters
Institution-agents change smallholder-agent resource profiles
Smallholder-agents choose production activities with decision making models that combines household resources, exogenous parameters, and environmental characteristics
Agent results are registered in agent resources and as a LUCC impact in the GCA
GCA environment updates

4.2 Generalized Cellular Automata

The environmental component of the model is specified and calibrated as seven sets of GCA grids, denoted E_x.Grids update through endogenous transitions or non-adjacent transition rules that result from actor behavior.For a deeper discussion of GCA and its underlying principles, the reader is directed elsewhere (Couclelis 1997)

GCA are calibrated in a top-down or bottom-up manner.Top-down calibration lies in defining rules from theory and assigning likely parameters for these rules.Bottom-up methods are inductive in that they search for likely candidate rules through repeated runs of a GCA. Work with cellular automata in geography can combine these methods {White, 1994 #1991; Clarke, 1996 #1252}.GCA rules for the ADSS application explored here are derived from ecological theory and field work and then tested with repeated runs that allow for introduction of rules that reproduce the behavior of land-cover outside the influence of human intervention.A simple set of rules, for example, can correlate forest cover in a cell with the state of its neighbors to represent secondary succession.

The sets of GCA grids are as follows:

E_use - A repository for simulated land-use by actors.
E_cover - State of land cover as a function of land-use (E_use) and extant cover.
E_soil - Stores soil fertility as a function cover (E_cover), past soil fertility (E_soil at the last timestep), and duration of the cell’s present land-use (E_use).
E_env - Environmental attributes: hydrology, soil type, slope, and aspect.
E_suit - Suitability for three production activities: agriculture, forestry, and nontimber forest products. Based on land use (E_use), land-cover (E_cover), soil quality (E_soil) and biophysical attributes (E_env).
E_econ - Distance to market and transportation infrastructure.
E_lucc - Actual land-use and land-cover for model verification and calibration.

4.3 Agent-Based Model

The ABM is composed of smallholder and institution agents.The latter communicate institutional rules to smallholder-agents, specifically land tenure and market characteristics such as crop and fuel prices or governmental subsidies.Institutions have rules, an implementation region, duration, economic value, and targeted producers (Young 1994).The ADSS converts these characteristics into: 1) GIS layers of spatial extent over time for use by institution-agent processes in directing the focus of institutions towards particular smallholder-agents; 2) institution-agent processes for land tenure rules; and 3) exogenous shell production functions that incorporate subsidies.

The agents that represent smallholder actors are invested with one of three different decision making models.The first is a set of heuristic processes that link site selection to agricultural suitability (E_suit) and distance to roads (E_econ), similar to those used by other dynamic spatial simulations (e.g., Southworth et al. 1991; Gilruth et al. 1995).While quite simple, in many respects these rules can capture more complex relationships or practices when they reflect key aspects of smallholder behavior without recourse to complex combinations of data.As such, they are applicable to data-poor situations, such as when the sole source of spatial data is remotely sensed imagery that provides only information on land-cover and infrastructure (e.g., roads, settlements).

The second form of decision making is a relatively simple economic decision making model.It has the form of a multicriteria evaluation that uses household variables (e.g., labor availability), agricultural suitability (E_suit), and accessibility measures (E_econ) to determine the location of production activities.This is a basic model with a number of restrictive assumptions, such as risk-taking behavior and lack of labor market participation (Sadoulet and deJanvry 1995).This model is a weighted linear average of the form:

where suitability is a function of factor weight , criterion scores , and constraints

The third form of decision making invested in agents is an inductive alternative-oriented model (Carroll and Johnson 1990).Sets of GP are calibrated by matching surveyed actor land-use histories to an array of decision variables from the actor survey and other considerations (E_econ, E_env, E_suit, and E_lucc).GP creation is analogous to the evolution of genomes in living organisms, whereby a population of genes, or candidate solutions, is repeatedly mutated, recombined and selected for desirable features.GP experiment with a whole range of functional forms by building equations from functions, symbols and arithmetic operations.The GP algorithm finds structures that produce the best performance given these criteria.

When applied to agents, GP are bounded-rationality representations of decision making.When using the ADSS to examine LUCC in the SYPR study region, agents equipped with GP strategies and train on samples taken from spatial data and smallholder household surveys.In one sense, GP strategies may be treated as inductive black-boxes for use in projection of land-use change. One selects GPs that have a high fitness and that are best able to match actual land-use histories to land-use change.In a less instrumental sense, GP represent different agent production strategies that evolve over the course of the simulation (Beckenbach 1999).Frequency counts of spatial and aspatial factors in GP can indicate the relative importance of factors, as can detailed examination of where key branch points in a strategy have a ‘tipping’ effect on the eventual outcome of the strategy.

4.4 ADSS Output and Validation

The ADSS validation suite measures the difference in accuracy between projected LUCC (as expressed by summing Monte Carlo runs, SE_cover and SE_use) and observed land-use/cover change (E_lucc).An example ofSE_cover is shown in Figure 3 for the example of projected secondary forest succession.The complexity inherent to spatial simulation demands several different approaches to validating the model (Turner et al. 1989).The ADSS uses a set of five different tests to measure projection accuracy.The first test is standard error matrix analyses that yields relative Kappa Index of Agreement (KIA) coefficients calculated in Idrisi32.The second and third tests measure differences in land-use/cover fragmentation (Frohn et al. 1996).The ADSS derives indices of fractal dimension (D₁) a measure of land-use patch complexity and contagion (D₂) the extent to which land-uses are clumped or fragmented (O'Neill et al. 1988).The fourth test is a multi-resolution goodness of fit (F_t) procedure built into the ADSS shell (Costanza 1989).Finally, the ADSS applies a Monte Carlo uncertainty (MCU) analysis that compares probabilities assigned to land-use choices (Ogneva-Himmelberger 1998).

3a. Actual secondary succession	3b. Secondary succession predicted by agents using genetic programming
3c. Secondary succession predicted by agents using heuristics	3d. Secondary succession predicted by agents using weighted linear averaging

Figure 3.Probabilistic projection of secondary growth with alternate actor decision making models

Given the differing nature of the validation tests, support varies across the five tests.This variation, instead of being an unfortunate failure of measuring model quality, is potentially quite useful.Figure 4 illustrates the difference across validation techniques for the examples ofSE_cover shown in Figure 3 for the example of projected secondary forest succession.In attempting to predict the location of secondary succession in a small subset of the study-site, for instance, the GP-based model generally fairs better than the others do, as indicated by the ‘Rank’ column.The differences between the model results, however, provide another kind of information.The heuristic and economic models have greater ability to replicate parcel structure, as indicated by their lower difference in contagion (D₂) from the validation data.For applications where this measure is important, such as assessing the effects of ecological structure on biodiversity (Skole and Tucker 1993), a particular incarnation of a heuristic or economic model may be better even if their overall predictive power does not match those of other models or the same models with different inputs.

Model	Heuristic		WLA		Genetic Program
Test	Metric	Rank	Metric	Rank	Metric	Rank
KIA	0.173	3	0.194	2	0.223	1
Difference in D₁	0.024	3	0.0106	2	0.008	1
Difference in D₂	0.00149	2	0.0002	1	0.00306	3
F_t (1 = perfect)	0.770	2	0.767	3	0.783	1
MCU (0 = perfect)	0.8772	1	0.9039	2	0.9116	3

Figure 4.ADSS validation examples

5. Conclusion

The ADSS is a general research tool in that it is a means of modeling the complexity of human-environment relationships.By facilitating the management of complex information and relationships, the ADSS improves understanding of environmental change, especially in light of decision making theory and conceptualization of institutions (Liverman 1994).It also allows examination of the impacts of policy alternatives that often cannot be easily explored in reality.The ADSS is also an example of “computational human geography” that bridges theoretical and empirical conceptions of what constitutes geographical information science and geography in general (cf. Openshaw 1998; Philip 1998).This research speaks to actor-structure debates by explicitly combining micro-scale phenomena (ABM actors and GCA neighborhood transition functions) with those at larger scales (ABM institutions and GCA non-contiguous transition functions) (Couclelis 1985).As such, and in conjunction with the ADSS’s explicit embodiment of the conceptual framework, the research serves as a point of communication between GIS and its critics.Finally, ABM and GCA combined address the problem of surface/entity integration in GIS (Rhind 1988), answer the call for artificial intelligence in GIS-based modeling (Openshaw 1992), and further the use of GIS for dynamic environmental modeling (Steyaert and Goodchild 1994).

Acknowledgements

The author would like to acknowledge the support of the following organizations: Carnegie Mellon University Center for Integrated Study of the Human Dimensions of Global Change National Science Foundation Grant NSF-SB95-21914; US National Aeronautics and Space Administration Earth System Science Fellowship Program; US National Science Foundation Decision, Risk, and Management Science Doctoral Dissertation Improvement Grant Program; Geography and Regional Science Doctoral Dissertation Improvement Grant Program; and El Colegio de la Frontera Sur (ECOSUR), Campeche, Mexico.

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Agent-Based Dynamic Spatial Simulation of Land-Use/Cover Change: Methodological Aspects

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