Modeling complex ecological systems: an introduction

The world is replete with all kinds of complex systems, be they ecological, social, economic, or political. Nevertheless, complex systems share several common characteristics. First, they are thermodynamically open, meaning that they exchange energy and/or mass with their environment. Second, they are often composed of a large number of diverse components. Third, system components interact with each other nonlinearly, and frequently have response delays and feedback loops among them. Fourth, complex systems exhibit a high degree of heterogeneity in both time and space. Consequently, complex systems are often characterized by emergent properties, multiscale interactions, unexpected behaviors, and self-organization (Jørgensen, 1995; Prigogine, 1997; Levin, 1999; Wu, 1999). Furthermore, a comprehensive concept of complexity not only needs to include the inherent system properties, but also the role of the observer (Allen and Starr, 1982; Flood, 1987; Wu, 1999). While the term ‘complexity’ has become a buzzword across many fields in science, it has various meanings. For example, structural complexity may refer to the compositional diversity and configurational intricacy of a system; functional complexity emphasizes the heterogeneity and nonlinearity in system dynamics; and self-organizing complexity hinges on the emergent properties of systems co-evolving with their environment primarily through local interactions and feedbacks at different spatiotemporal scales. Such self-organizing systems have often been referred to as ‘complex adaptive systems’ (Cowan et al., 1994). According to Levin (1999), a complex adaptive system is ‘ a system composed of a heterogeneous assemblage of types, in which structure and functioning emerge from the balance between the constant production of diversity, due to various forces, and the winnowing of that diversity through a selection process mediated by local interactions’. Most ecological and socioeconomic systems exhibit different degrees of self-organizing complexity, and thus may be considered as complex adaptive systems (Cowan et al., 1994; Levin, 1999). Scientists have long been interested in unraveling the problem of complexity. The late Noble Laureate Herbert A. Simon (Simon, 1996) identified three bursts of interest in the study of complexity in the 20th century. The post-World War I period was characterized by such terms as ‘holism’, ‘Gestalts’, and ‘creative evolution’. The post-World War II period was signified primarily by general systems theory, information theory, and cybernetics, focusing primarily on the roles of feedback and homeostasis in maintaining system stability. The current period of complexity research has focused mainly on causes, mechanisms and methods, and a diversity of views can be identified with terms such as ‘chaos’, ‘catastrophe’, ‘fractal’, ‘cellular automata (CA)’, ‘genetic algorithms (GA)’, ‘neural networks’, ‘hierarchy’, ‘self-organization’, and ‘complex adaptive systems (CAS)’ (Wu, 1999). Different concepts and theories entail different approaches to modeling complex systems. In many cases, however, they are more complementary than contradictory. It is in-