Cross-scale Structure and Scale Breaks in Ecosystems and Other Complex Systems

Abstract

The five articles in this special feature extend the discovery of regular patterns of deviation from scaling laws and from continuous distributions of attributes in ecosystems and other complex systems. These patterns suggest that these systems organize over discrete ranges of scale and that organization abruptly shifts with changes in scale. If this is so, scaling laws (for example, see West 1997, 1999; Zipf 1949) serve only as the baseline from which to measure those departures, and those departures indicate “scale breaks” (transitions) between scales of structure in complex systems. Patterns in the deviations from a scaling-law baseline may provide hints of the processes that cause the emergence of the scaling relationships themselves. At minimum, the investigation of departures from scaling laws gives us a clue into the nature of structure and process in ecological systems. Ecosystems may be structured by relatively few key processes, each operating at specific temporal and spatial scales (Carpenter and Leavitt 1991; Levin 1992). The distinct temporal frequencies and spatial scale characterizing these processes creates landscape structures with scale-specific pattern (Burrough 1981; O’Neill and others 1991; Milne and others 1992). This may in turn entrain attributes of animals residing on the landscape (Holling 1992) because different-sized animals living upon the same landscape perceive their environment at different scales (Milne and others 1989; Holling 1992; Peterson and others 1998) (Figure 1). Holling (1992) suggested that this entrainment reflects adaptations to the discontinuous pattern of resource distribution acting through animal community assembly and evolution, both by sorting species and by providing a specific set of evolutionary opportunities and constraints. On the animal community level, this should be expressed by a discontinuous distribution of species body masses (Holling 1992). Within a system, aggregations of species body masses are separated by discrete breaks (or discontinuities) separating different ranges of scale. Animals within a particular body mass aggregation perceive and exploit the environment at the same range of scale (Peterson and others 1998) (Figure 2). Holling’s proposition that ecosystem structure entrains attributes of animals—such as body mass distributions (the textural discontinuity hypothesis)—was received with some skepticism, but also with interest. It is now generally accepted that many attributes of ecosystems are discontinuously distributed, but mechanisms other than entrainment by ecological structure (Brown 1995) have been proposed. However, most of the disagreements with Holling’s proposition have been technical, focusing on the methods used to detect discontinuities (Manly 1996; Siemann and Brown 1999). New evidence for a link between landscape structure at different scales and body mass distributions has provided support for the textural discontinuity hypothesis. Discontinuous body mass patterns have been documented in many systems (see for example, Holling 1992; Restrepo and others 1997; Lambert and Holling 1998; Allen and others 1999; RafReceived 25 January 2002; accepted 28 January 2002. *Corresponding author; e-mail: allencr@clemson.edu Ecosystems (2002) 5: 315–318 DOI: 10.1007/s10021-001-0075-3 ECOSYSTEMS