Use of scaling terminology and concepts in ecology evolved rapidly from rare occurrences in the early 1980s to a central idea by the early 1990s (Allen and Hoekstra 1992; Levin 1992; Peterson and Parker 1998). In landscape ecology, use of "scale" frequently connotes explicitly spatial considerations (Dungan et al. 2002), notably grain and extent. More generally though, scaling refers to the systematic change of some biological variable with time, space, mass, or energy. Schneider (2001) further specifies ecological scaling sensu Calder (1983) and Peters (1983) as "the use of power laws that scale a variable (e.g., respiration) to body size, usually according to a nonintegral exponent" while noting that this is one of many equally common technical definitions. He further notes that "the concept of scale is evolving from verbal expression to quantitative expression" (p. 545), and will continue to do so as mathematical theory matures along with quantitative methods for extrapolating across scales. In what follows, we operate mainly with this quoted definition, noting that other variables can replace "body size", but we also use such expressions as "small scales" and "large scales" somewhat loosely where we expect confusion to be minimal. We examine the idea of contagious disturbance, how it influences our cross-scale understanding of landscape processes, leading to explicit quantitative relationships we call scaling laws. We look at four types of scaling laws in fire regimes and present a detailed example of one type, associated with correlated spatial patterns of fire occurrence. We conclude briefly with thoughts on the implications of scaling laws in fire regimes for ecological processes and landscape memory.
McKenzie, Donald; Kennedy, Maureen. 2011. Scaling laws and complexity in fire regimes [Chapter 2]. In: McKenzie, Donald; Miller, Carol; Falk, Donald A., eds. The landscape ecology of fire. Ecological Studies 213. New York, NY: Springer Science and Media. p. 27-50.