Concepts of scale and scaling

The relationship between pattern and process is of great interest in all natural and social sciences, and scale is an integral part of this relationship. It is now well documented that biophysical and socioeconomic patterns and processes operate on a wide range of spatial and temporal scales. In particular, the scale multiplicity and scale dependence of pattern, process, and their relationships have become a central topic in ecology (Levin 1992, Wu and Loucks 1995, Peterson and Parker 1998). Perspectives centering on scale and scaling began to surge in the mid-1980's and are pervasive in all areas of ecology today (Figure 1.1). A similar trend of increasing emphasis on scale and scaling is also evident in other natural and social sciences (e.g., Bl?schl and Sivapalan 1995, Marceau 1999, Meadowcroft 2002). Scale usually refers to the spatial or temporal dimension of a phenomenon, and scaling is the transfer of information between scales (more detail below). Three distinctive but interrelated issues of scale have frequently been discussed in the literature: (1) characteristic scales, (2) scale effects, and (3) scaling (and associated uncertainty analysis and accuracy assessment). The concept of characteristic scale implies that many, if not most, natural phenomena have their own distinctive scales (or ranges of scales) that characterize their behavior (e.g., typical spatial extent or event frequency). Characteristic scales are intrinsic to the phenomena of concern, but detected characteristic scales with the involvement of the observer may be tinted with subjectivity (Wu 1999). Conceptually, characteristic scales may be perceived as the levels in a hierarchy, and associated with scale breaks (O'Neill et al. 1991, Wu 1999). Ecological patterns and processes have been shown to have distinctive characteristic scales on which their dynamics can be most effectively studied (Clark 1985, Delcourt and Delcourt 1988, Wu 1999). Thus, identifying characteristic scales provides a key to profound understanding and enlightened scaling. Scale effects usually refer to the changes in the result of a study due to a change in the scale at which the study is conducted. Effects of changing scale on sampling and experimental design, statistical analyses, and modeling have been well documented in ecology and geography (e.g., Turner et al. 1989b, White and Running 1994, Wu and Levin 1994, Pierce and Running 1995, Jelinski and Wu 1996, Dungan et al. 2002, Wu 2004). In geography, scale effects have been studied for several decades in the context of the modifiable areal unit problem or MAUP (Openshaw 1984, Jelinski and Wu 1996, Marceau 1999). Scale effects may be explained in terms of scale-multiplicity, characteristic scales, and hierarchy, but may also be artifacts due to errors in sampling and measurements, distortions in data resampling, and flaws in statistical analysis and modeling (Jelinski and Wu 1996, Wu 2004). Characteristic scales and scale effects are inherently related to the issue of scaling. While characteristic scales provide a conceptual basis and practical guidelines for scaling, quantitative descriptions of scale effects can directly lead to scaling relations (Wu 2004). With the recent burst of interest in the issues of scale, the terms scale and scaling have become buzzwords in ecology. However, because these terms have been used in diverse disciplines, both have acquired a number of different connotations and expressions. Good science starts with clear definitions. The development of a science of scale or scaling may be hampered if the concepts of scale and scaling are used without any consistency. In this section, we review the main usages of these terms, propose a three-tiered scale conceptualization framework, and discuss their relevance to the issue of ecological scaling.