Ecological Modelling 150 (2002) 239 – 254 Power-law behaviour and parametric models for the size-distribution of forest fires William J. Reed a, *, Kevin S. McKelvey b a Department of Mathematics and Statistics, Uniersity of Victoria, P.O. Box 3045, Victoria, BC, Canada V8W 3P4 b Forestry Sciences Laboratory, USDA Forest Serice, RMRS, P.O. Box 8089, Missoula, MT 59807, USA Received 13 February 2001; received in revised form 6 November 2001; accepted 6 November 2001 Abstract This paper examines the distribution of areas burned in forest fires. Empirical size distributions, derived from extensive fire records, for six regions in North America are presented. While they show some commonalities, it appears that a simple power-law distribution of sizes, as has been suggested by some authors, is too simple to describe the distributions over their full range. A stochastic model for the spread and extinguishment of fires is used to examine conditions for power-law behaviour and deviations from it. The concept of the extinguishment growth rate ratio (EGRR) is developed. A null model with constant EGRR leads to a power-law distribution, but this does not appear to hold empirically for the data sets examined. Some alternative parametric forms for the size distribution are presented, with a four-parameter ‘competing hazards’ model providing the overall best fit. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Fire area; Power-law; Size distribution; Extinguishment growth rate ratio; Self-organized criticality www.elsevier.com/locate/ecolmodel 1. Introduction A number of recent papers have examined the size-distribution of wildfires (Malamud et al., 1998; Ricotta et al., 1999; Cumming, 2001). In all three cases, the claim has been made that empiri- cal size-distributions exhibit power-law behaviour. In the first two papers, it is argued that the observed power-law behaviour is consistent with the self-organized criticality (SOC) arising in sim- ple dynamical systems models. Malamud et al. argue for power-law behaviour from what physi- cists call the ‘forest-fire model’ (Bak et al., 1990) while Ricotta et al. use the ‘sandpile model’ (Bak et al., 1988) as a metaphor. In contrast Cumming makes no claim based on theory—only that the best-fitting parametric distribution that he can find is a truncated exponential distribution for the logarithm of area or, in other words, a truncated power-law (or Pareto) distribution for area. An earlier paper (Baker, 1989) claims that the size- distribution is exponential. In this article, we first examine whether evidence from fire records sup- ports a single form for the size distribution and, if * Corresponding author. Tel.: +1-250-721-7469; fax: +1- 250-721-8962. E-mail addresses: reed@math.uvic.ca (W.J. Reed), kmckelvey@fs.fed.us (K.S. McKelvey). 0304-3800/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII:S0304-3800(01)00483-5