Theory in a complex world
Geographic systems are inherently problems of organized complexity, which too often have been inappropriately modeled as problems of simplicity (following physics) or as problems of disorganized complexity (statistical generalization) (Jacobs, 1961, p 429). Recent advances in computing power and in computational modelling techniques such as agent-based simulations finally supply us with the means to model and understand these more difficult problems of organized complexity (Openshaw, 1995). Yet the computing power to develop such models has already outstripped our understanding of their most effective use; there is a deep need for theory which "provides the maps that turn an uncoordinated set of experiments or computer simulations into a cumulative exploration."
What is required for such computational models to constitute a rigorous and cumulative exploration of important phenomena?
This question is explored by building and testing a family of agent-based simulations (ABS) to model regional settlement patterns on the basis of the individual local choices of many agents interacting with one another and with their landscape. The simulations are built using the Santa Fe Institute's Swarm simulation platform, which is developing as an interdisciplinary standard platform for agent-based simulation modeling (Langton et al., 1995). Swarm supports the specification of a virtual universe with explicit space and time; both objects and agents have locations in space and time, and the universe provides the context within which large numbers of each interact and "live their lives." Swarm execution is both distributed (across explicitly-specified spatial landscapes, objects, and agents) and concurrent (many things happening at the same time).
The geographic systems addressed here are settlement patterns, modelled as an emergent property of individual locational choices, as agents seek access to resources and other agents. Yet the underlying computational modelling and theoretical issues addressed are likely to be of interest to anyone modeling geographic systems characterized by:
Agent-based simulations
Agent-based simulations are especially useful because they allow us to explore relationships between micro-level individual actions and emergent macro-level phenomena. We can frame our hypotheses at the individual level, directly in terms of individual preferences, abilities, and imperfect information, and explore the implications of each for the patterns and properties that emerge at macro levels. In addition, hypotheses can be related not merely to specific properties of individuals, but also to both proportional and spatial distributions of such properties within a particular population. This can have especially important consequences in spatial models, since the distribution of agent characteristics can vary across space in patterns that are relevant to the behavior of the system as a whole. This becomes especially interesting when the emergent macro phenomena (e.g. settlement patterns, environmental impacts) in turn feed back to affect micro-level individual decisions.
The Swarm (Langton et al., 1995) agent-based simulation platform serves as the foundation for exploring these models. Swarm is designed to serve as a generic platform for agent-based simulation models in a wide range of fields. It allows for the specification of large classes ("swarms") of individual agents with particular properties and capabilities for interaction in both time and space. Agent interactions can be restricted to a particular spatial neighborhood, but also may span considerable distances, and can be inhibited or facilitated by landscape structures such as barriers or spatial technologies. Swarm is especially appropriate for exploring geographic models of agent interactions since it provides a selection of explicit spatial structures in which its agents interact (cellular grids, lattices, networks), and allows for the addition of customized landscape structures, including landscape layers imported from Geographic Information Systems.
Geographic systems: settlement patterns example
The sizes and distribution of cities within a nation or large region are strongly influenced by changes in economic structure such as the transition toward an information-based economy, and by improvements in the complementary transportation and communication spatial technologies (Couclelis, 1994). Such changes have potential policy implications in terms of appropriate infrastructure, economic, social, and environmental interventions or accommodations for the likely growth or decline of cities with different characteristics.
These settlement pattern models divide the population of agents into several economic sectors, where agents in each sector are assigned a sector-specific profile of access requirements (to other agents from their own or different sectors, and possibly to resources) and access capabilities (ability to make use of various spatial technologies to facilitate interaction). Sectors are interpreted as an economic differentiation among agents, and are not necessarily spatially correlated a priori.
This paper introduces results from early members of a family of models designed as part of a cumulative exploration of the joint influences of economic sector proportions and spatial technologies on human settlement patterns. This systematic exploration begins with a few simple sectors and a universal transportation technology, and investigates the influence of different sector proportions (thus, different proportions of access requirements) on settlement pattern characteristics that coalesce from initial random distributions of agents. A second set of models holds sector proportions fixed and explores the effects of differential access to and improvements in spatial technologies. The final set allows for changes in both sector proportions and spatial technologies. Each includes evaluation of the robustness of the results, sensitivity analysis with respect to the components, and development of relevant pattern metrics and analytical characterizations.
References
Booker, L. B., Goldberg, D.E. and J. Holland, J.H. 1989. "Classifier Systems and Genetic Algorithms", Artificial Intelligence, 40, 235-282.
Couclelis, H. 1994. "Spatial Technologies" (Editorial), Environment and Planning B: Planning and Design, 21(2),142-143.
Jacobs, J. 1961. The Death and Life of Great American Cities, New York: Vintage Books.
Langton, C. , Minar, N. and Burkhart. R. 1995. The Swarm Simulation System: A Tool for Studying Complex Systems, Santa Fe Institute, www.santafe.edu/projects/swarm
Openshaw, S. 1995. "Commentary: Human systems modelling as a new grand challenge area in science", Environment and Planning A, 27, 159-164.