Ecosystems (1998) 1: 427–430 ECOSYSTEMS ௠ 1998 Springer-Verlag C OMPLEX ADAPTIVE SYSTEMS Use and Analysis of Complex Adaptive Systems in Ecosystem Science: Overview of Special Section Gregg Hartvigsen,1* Ann Kinzig,1 and Garry Peterson2 1Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08544; and 2Department of Zoology, 111 Bartram Hall, University of Florida, Gainesville, Florida 32611, USA INTRODUCTION changes in that variation lead to system-level re- sponses. To introduce this Special Section, we distin- Ecological systems are complex assemblages of inter- guish systems theory and complex adaptive systems acting organisms embedded in an abiotic environ- theory, outline the articles in this Special Section, ment. Complexity arises from interspecific and intra- and suggest new ecological insights that could specific interactions among individuals or agents, emerge from CAS-based approaches. interactions across trophic levels, and the interac- tions of organisms with the abiotic environment over space and time. In addition, interactions can SYSTEMS THEORY range from strong and direct to weak and diffuse and are modified by both positive and negative Systems theory is an analytical approach that repre- feedback with the environment. In our effort to sents the natural world as a set of stocks and flows understand pattern formation at the community or regulated by a variety of feedback processes. These ecosystem level, we are confronted with the daunt- representations are subjected to a variety of math- ing array of processes that function across different ematical analyses in order to gain insight into spatial and temporal scales. We are thus forced to system behavior. Systems theory has been widely address the question of how these different levels of applied in ecology. For example, early work on organization can be integrated, or how mechanisms processes organizing community dynamics and pat- and patterns at one level of organization can be terns, such as predator-prey interaction, used sys- understood in terms of processes operating at a tems concepts. These early analyses were generally different level of organization. deterministically and analytically based. Even so, The goal of this Ecosystems Special Section is to relatively simple models were able to produce com- provide an overview of the relatively new approach plex dynamics [for example, see May (1976)]. With of analyzing ecosystems using complex adaptive increasingly powerful computers, researchers have systems (CAS) theory. CAS theory is an extension of had the opportunity to increase model complexity, traditional systems theory [for example, see von and analyze and replicate simulations at larger Bertalanffy (1968)] but addresses one of the omis- spatial and temporal scales, or conduct simulations sions of systems theory—namely, adaptation—by with greater spatial and temporal resolution. Explic- specifically modeling how individual variation and itly representing space in models, for instance, leads to significantly different model behaviors and out- Received 10 June 1998; accepted 22 June 1998. comes than those resulting from a nonspatial or G. Hartvigsen’s current address: Biology Department, SUNY–Geneseo, 1 College homogeneous model (Huffaker 1958; Turner 1989; Circle, Geneseo, New York 14454, USA. Levin 1992; Durrett and Levin 1994; Tilman and A. Kinzig’s current address: Department of Biology, Arizona State University, Tempe, Arizona 85287, USA. Kareiva 1997; Hartvigsen and Levin 1997; Kinzig *Corresponding author; e-mail: [email protected] and Harte 1998). 427 428 G. Hartvigsen and others One of the main limitations with the traditional ics (that is, numbers of individuals and the relative systems approach to analyzing ecological dynamics abundance of species over time) can be extremely is that it omits the influential process of adaptation. sensitive to variability among individuals and that Clearly, the ability of species to adapt to changing this response depends on the spatial structure of the environmental conditions is likely to be important. interacting populations (Hartvigsen and Levin 1997). The ability of ecologists to incorporate adaptation in This Special Feature is intended to provide a general models has in the past been limited by the inherent introduction to this and other CAS approaches to difficulty of including variability and selection within ecology. the aggregated stocks and flows used in systems The incorporation of variability and adaptation in analysis. Recent advances in both theory and com- CAS allows for a greater understanding of how puting ability have, however, increased our capacity patterns and processes emerge and interact across to incorporate individual-level variability and adap- levels of biological organization, and across spatial tation. These advances have enabled ecologists to and temporal scales. In addition, other systems, create simple models of adaptive and selective pro- such as economies, also function as complex adap- cesses in ecological systems. tive systems (Arthur and others 1997a; Brock forth- coming). These systems share the property that self-organization produces macroscopic patterns that COMPLEX ADAPTIVE SYSTEMS emerge through local, small-scale interactions. Our Complex adaptive systems theory builds upon sys- understanding and ability to predict large-scale eco- tems theory by explicitly representing the diversity system dynamics have been and continue to be and heterogeneity that systems theory tended to dependent on our understanding of small-scale aggregate within homogeneous stocks and flows. In properties that we are able to test experimentally; other fields, CAS approaches have been particularly CAS offers a method for using the insights and data useful in analyzing situations in which individuals from small-scale experimental manipulations to in a population are governed by nonlinear dynamics understand and predict larger-scale patterns and (Rodrı´guez-Iturbe and Rinaldo 1997). Treating such processes. a population as an aggregate—rather than an inter- acting and heterogeneous set of individuals—may AN INTRODUCTION TO COMPLEX hide a rich set of dynamics, or even lead to incorrect ADAPTIVE SYSTEMS IN ECOLOGY predictions or insights regarding probable popula- tion-level and community-level behavior. Nonlinear- Recently, the Australian ecologist Brian Walker ity and individual heterogeneity are ubiquitous in observed that CAS appeared to have a lot to offer ecology, and we must find ways to capture their with respect to improving our understanding of the importance in our analysis of ecological systems; the dynamics of ecological systems, but he had yet to use of CAS offers methods and approaches for see a demonstration of what that offering might capturing heterogeneity. contain. He suggested that Ecosystems develop a CAS differs from traditional systems theory be- Special Section on complex adaptive systems, to cause it explicitly incorporates the role of adaptation explain how this approach could be applied to in governing the dynamics and responses of these understanding and managing ecological systems. now heterogeneous reservoirs. One increasingly We solicited the following articles in an attempt to common and powerful CAS approach to incorporat- provide a stimulating and diverse overview on the ing individual-level or agent-level variability and use of CAS in the field of ecology. adaptation in models involves using genetic algo- Simon Levin (in this issue) provided the first rithms (Goldberg 1989; Mitchell 1996). The CAS article, which outlines the structure of complex approach enables ecologists to analyze how pro- adaptive systems and provides guidance for apply- cesses at lower levels of organization (for example, ing our understanding of such systems to ecological genes) produce patterns at higher levels of organiza- problems. He defines complex adaptive systems to tion (for instance, ecosystems). Hartvigsen and Levin be systems with interacting individuals that vary, (1997) developed a model of plant–herbivore inter- are spatially discrete, and change in response to actions that incorporated individual-level genetic selection. This definition is a simplification from variability in plant defense and herbivore response previous work (Arthur and others 1997b) and to investigate the influence of adaptation on popula- facilitates our identification of those systems that tion and community dynamics. Their work suggests exhibit emergent properties from small-scale pro- that large-scale population and community dynam- cesses. CAS do not depend, per se, on the presence Complex Adaptive Systems in Ecosystem Science 429 of genetic-level variability. They do, however, de- THE POTENTIAL OF COMPLEX ADAPTIVE pend on a population of interacting agents that SYSTEMS APPROACHES varies either due to their intrinsic attributes, their environmental context, or their pattern of interac- Complex adaptive systems offer ecologists tools to tions with other agents. analyze how large-scale organization arises and is Bonabeau (in this issue) discusses the formation maintained and reorganized by processes occurring and maintenance of self-organized patterns in colo- at smaller scales of organization. This understanding nies of social insects, with particular reference to ant should improve our ability to manage complex colonies. Social insect colonies are composed of ecological systems. For example, management of hundreds to millions of genetically similar