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Dimensions of ecosystem complexity: Heterogeneity, connectivity, and history

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Abstract

Biocomplexity was introduced to most ecologists through the National Science Foundation's grant program, and the literature intended to introduce that program. The generalities of that literature contrast with the abstract and mathematical sophistication of literature from physics, systems theory, and indeed even of pioneering ecologists who have translated the concept into ecology. This situation leaves a middle ground, that is both accessible to ecologists in general, and cognizant of the fundamentals of complexity, to be more completely explored. To help scope this middle ground, and to promote empirical explorations that may be located there, we propose a non-exclusive framework for the conceptual territory. While recognizing the deep foundations in the studies of complex behavior, we take ecological structure as the entry point for framework development. This framework is based on a definition of biocomplexity as the degree to which ecological systems comprising biological, social and physical components incorporate spatially explicit heterogeneity, organizational connectivity, and historical contingency through time. These three dimensions of biocomplexity – heterogeneity, connectivity, and history – will be explored as axes of increasing complexity. Basing the description of spatial heterogeneity on either patch or continuous quantification, complexity of spatial structure increases as quantification moves from simple discrimination of patch types and the number of each type to assessment of configuration and the change in the mosaic through time. Organizational complexity reflects the increasing connectivity of the basic units that control system dynamics. At the simple end of the axis, the functional connectivity between units is low, and the processes within a unit are determined by structures or other processes within that unit. At the highest level of complexity along this axis, units in a mosaic interact through fluxes of energy, matter, organisms, or information, and the structure and dynamics of the mosaic can be altered by those fluxes. Temporal relationships in the system range from direct contemporary ones to indirect and historically contingent ones. The influence of indirect effects, legacies, the existence of lagged effects, and the presence of slowly appearing indirect effects constitute increasing temporal complexity. This framework embodies some features of both the structural approach to complexity and the approach of complexity of explanations that we extracted from the literature. It leaves the issue of what levels of each axis result in complex behavior as an important question for further research.

Introduction

Ecologists have long been aware of the importance of complexity, but few have explicitly adopted it into their research programs. The opportunity to incorporate complexity came to the attention of most ecologists primarily through the National Science Foundation's granting program focusing on biocomplexity. This program spurred a burst of literature targeted at ecologists in general (Colwell, 1998, Michener et al., 2001, Cottingham, 2002). In an attempt to be accessible, this recent literature leaves much of the concept of biocomplexity, and its application and adoption, to be explored. In spite of the relatively recent general increase of interest in complexity, the theory and associated concepts such as non-linear dynamics, self-organization, emergence, criticality, etc., have been a rich topic for study in physics, thermodynamics and systems theory (Kay and Schneider, 1994, Bak, 1996, Auyang, 1998, Milne, 1998). Some ecologists familiar with these fields have applied these concepts successfully to ecological systems (Ulanowicz, 1997, Milne, 1998, Medvinsky et al., 2001, Li, 2002a). These applications are sophisticated and mathematically advanced, but their abstraction may make it difficult for empirical ecologists in general to appreciate or apply the formal concepts of complexity in their own research (Kay and Schneider, 1994, Anselin and Tam Cho, 2002). Therefore, a middle ground is needed between the very accessible and consequently general introductions (Colwell, 1998, Michener et al., 2001), and the sophisticated mathematical abstractions (Li, 2000, Bruggeman et al., 2002, Li, 2002b, Ulanowicz, 2004). This middle ground would relate biocomplexity to concepts and issues that ecologists are concerned about and familiar with but would show clear links to the general ideas of complexity. The purpose of this paper is to explore this middle ground and is under taken in the spirit of recognizing a need for a diversity of ways to conceive and apply complexity in ecology (Milne, 1998, Li, 2004, Loehle, 2004).

Ecology has long been concerned with structure–function relationships (Watt, 1947). Therefore, many ecological studies begin from a structural perspective. Even functional ecological studies which may not explicitly measure structure may implicitly use structure to frame the contrasts they investigate. The richness of ways in which ecological systems can be structured suggests a backdrop against which complex behavior can be measured. Scientists who study complexity theory often focus on understanding the behavior of systems (Li, 2002b). One of the guiding questions in complexity theory is how simple structures lead to complex behaviors (Bak and Chen, 1991, Bruggeman et al., 2002). From the formal complexity perspective, behavior refers to an entire system, which incorporates both ecological structure and function. Thus in this paper, we use “structure” in two ways. One is the complexity perspective that addresses the behavior of combined structure–function systems, and the other is the traditional ecological perspective of structure constituting system architecture and composition (Noss and Cooperrider, 1994). Understanding structural contrasts may contribute to the conceptual middle ground between complexity theory and empirical ecology.

To explore the potential middle ground, this paper articulates an empirically oriented conceptual framework. Because the concept of biocomplexity is relatively new to many ecologists, we review definitions from the literature and assess their contribution to a general ecological approach. While recognizing the deep foundations in the studies of complex behavior, we take ecological structure as the entry point for the development of this middle ground and suggest a structural definition for biocomplexity that forms the foundation of an organizing framework. This framework links to the growing interest in heterogeneity as a key driver in ecological systems (Huston, 1994) while also incorporating the increasing appreciation of historical and indirect effects (Brown, 1994) and organizational hierarchies (Allen and Hoekstra, 1992). The framework is intended to help guide the empirical quantification of structures that can yield complex behaviors. The framework can also be used to integrate social and ecological sciences and an example from the Baltimore Ecosystem Study will explore this linkage. We will demonstrate how the framework can be used to organize research and generate hypotheses across disciplinary boundaries in an effort to understand the complexity of an urban ecosystem.

Section snippets

Definitions: biocomplexity for ecology

Complexity theory (Auyang, 1998, Milne, 1998) is a precursor to the concept of biocomplexity. This theory is driven primarily by approaches from physics and mathematics and has assigned several properties to complex systems (Costanza et al., 1993, Milne, 1998, Li, 2002a). It may be better to say that these properties characterize complex behavior rather than systems, because simple systems can in some cases exhibit complex outcomes. Thus, the real issue is how simple systems produce complex

Goals of an empirically motivated framework

Our use of a framework, and the characteristics of frameworks, make clear that our attempt to establish some of the middle ground between complexity theory and empirical ecology is a preliminary one. A framework is a conceptual construct that articulates what is included in the conceptual arena under discussion, and what is not (Cadenasso et al., 2003b). It is inclusive of various systems, processes, and scales. The job of the framework is to provide a roster of components, and to suggest how

Framework for biocomplexity in ecology

The structural framework for biocomplexity that we propose consists of three axes: heterogeneity, connectedness, and historical contingency (Fig. 1). These three axes represent a convergence of differing perspectives of system structure. For example, Frost et al. (1988) and Cottingham (2002) recognize space, organization, and time as necessary components for modeling and understanding ecological systems. Hierarchy theory (Allen and Starr, 1982) also embodies how entities are organized and how

Application of the framework

Metropolitan areas are structured by multiple factors (Gottdiener and Hutchison, 2000, Berry, 2001, Vasishth and Sloane, 2002). For example, patch maps can be created based on population density, zoning, time of development, the distribution of income, race, or education levels of people, and land use. Each map shows a snapshot of the system structured by one variable or a suite of variables. A suite of variables is frequently converted into an index or categorization. Comparing the patch

Conclusion

We have proposed a conceptual framework to promote the assessment of structural biocomplexity in ecological systems. This framework draws on two of the approaches to complexity we have discovered through a review of definitions of the concept. These two are: (1) structure of complex systems, and (2) complexity of explanatory model. The third concern of complexity definitions, that of emergent, non-linear, or self organized behavior is beyond our scope here. This framework is intended to help

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