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Ecosystems (1998) 1: 427–430 ௠ 1998 Springer-Verlag

C OMPLEX ADAPTIVE

Use and Analysis of Complex Adaptive Systems in : Overview of Special Section

Gregg Hartvigsen,1* Ann Kinzig,1 and Garry Peterson2

1Department of and Evolutionary , Princeton University, Princeton, New Jersey 08544; and 2Department of , 111 Bartram Hall, University of Florida, Gainesville, Florida 32611, USA INTRODUCTION changes in that variation lead to -level re- sponses. To introduce this Special Section, we distin- Ecological systems are complex assemblages of inter- guish systems and complex adaptive systems acting embedded in an abiotic environ- theory, outline the articles in this Special Section, ment. arises from interspecific and intra- and suggest new ecological insights that could specific among or agents, emerge from CAS-based approaches. interactions across trophic levels, and the interac- tions of organisms with the abiotic over and . In addition, interactions can 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- with the environment. In our effort to sents the natural as a of and flows understand formation at the or regulated by a 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 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 can be integrated, or how mechanisms processes organizing community dynamics and pat- and at one level of organization can be terns, such as predator-prey , used sys- understood in terms of processes operating at a tems . 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 , 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 at larger Bertalanffy (1968)] but addresses one of the omis- spatial and temporal scales, or conduct simulations sions of systems theory—namely, —by with greater spatial and temporal resolution. Explic- specifically modeling how 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).

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One of the main limitations with the traditional ics (that is, numbers of individuals and the relative systems approach to analyzing ecological dynamics of 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 of the environmental conditions is likely to be important. interacting (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 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 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 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 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 . 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 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 ) 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 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 , with particular reference to should improve our ability to manage complex colonies. Social colonies are composed of ecological systems. For example, of hundreds to millions of genetically similar individu- salmon in the Pacific Northwest has focused on the als. These individuals interact locally yet collectively absolute number of salmon rather than the hetero- produce large-scale patterns of colony dynamics. geneity within salmon populations, despite the well- Researchers since at least Darwin have been fasci- known importance of this behavioral and genetic nated by how large colonies appear to have orga- heterogeneity (Gross 1991). While maintaining some nized behavior. Reintroducing the con- populations, this policy has lead to the of cept of ‘‘,’’ Bonabeau discusses ant-colony many stocks and the endangerment of hundreds of behavior as an emergent property of self-organiza- others. CAS-based management models that explic- tion based on local among indi- itly consider variability among and across salmon vidual . Through his discussion of ant-colony populations have the potential to improve salmon behavior, he illustrates the role of self-organization management greatly (Volkman and McConnaha as a defining property of CAS and how this ap- 1993; Jager and others 1997; Policansky and Magnu- proach to understanding self-organization can be son 1998). applied to other dynamic, interacting populations. The ability of ecosystems and the as a Large-scale patterns also emerge in human societ- whole to respond to perturbations such as changes ies from the interaction and cooperation of indi- in , declines in , and disruption of vidual people. Specifying only the rules governing regional and global biogeochemical cycles is difficult interactions among individuals can produce societal- to predict. Understanding how change at one level level patterns of behavior (Axelrod 1984, 1997). of biological organization will alter emergent pat- Karl Sigmund (in this issue) uses to terns or mechanisms at another level of biological discuss the role of reciprocity in the interactions organization is one of the most pressing problems in among individuals and makes the important point ecology. CAS approaches offer insights into these that cooperation can be adaptive in the formation cross-scale interactions and enable analysis of the and maintenance of groups or . role of adaptation in governing system dynamics Complexity also arises at the community and and response to novel situations. An extension and ecosystem levels. Bruce Milne (in this issue) dis- challenge is to use our understanding of ecosystems cusses the application of integrative analysis tech- as complex adaptive systems in our management niques such as renormalization group analysis, bor- efforts. Clearly, our ability to manipulate and reha- rowed from , to understanding pattern bilitate damaged ecosystems rests with our under- formation at the level. He suggests that standing of how these complex systems adapt, the use of these types of approaches may lead to a respond, and change over time. synthesis within ecology to understand scaling pat- terns across hierarchical levels of organization. REFERENCES The final article discusses the application of CAS Arthur WB, Durlauf SN, Lane DA, editors. 1997a. The economy to the management of interacting and coevolving as an evolving II. Reading (MA): Addison- social and ecological systems. Janssen (in this issue) Wesley. uses genetic to model adaptation in two Arthur WB, Durlauf SN, Lane DA, editors. 1997b. Introduction. management situations: how the of drug In: Arthur, WB, Durlauf SN, Lane DA, editors. 1997. The alters malaria dynamics, and how indi- economy as an evolving complex system II. 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