Using Size-Frequency Distributions to Analyze Fire Regimes in Florida

Wildfire regimes in natural forest ecosystems have been characterized with power–law distributions. In this paper, we evalu­ ated whether wildfire regimes in a human-dominated landscape were also consistent with power–law distributions. Our case study focused on wildfires in Florida, a state with rapid population growth and consequent rapid alteration of forest ecosys­ tems and natural fire regimes. We found that all fire size–frequency distributions evaluated in this study were consistent with power–law distributions, but the power–law distributions were piece-wise linear. A kink in the power–law distributions occurred at about 640 ha for flatwoods fires and at about 290 ha for swamp fires. Above these levels, fires “exploded” into a catastrophic regime. If the kink represents the level at which fires become immune to fire suppression effort, we would expect that the location of the kink would occur at smaller fire sizes during extreme fire years due to the increased flammability of fuels and the relative scarcity of fire suppression resources. We found this result for three of four extreme fire years in flatwoods ecosystems and for all four extreme fire years in swamps. These results suggest that catastrophic fires may not be pos­ sible to prevent and that suppression efforts during extreme fire years may be best applied to strategic areas that decrease the connectivity of fuels. keywords: fire regime, fire suppression, Florida, power–law distributions, self-organization, size–frequency distribution. Citation: Holmes, T.P., J.P. Prestemon, J.M. Pye, D.T. Butry, D.E. Mercer, and K.L. Abt. 2004. Using size–frequency distri­ butions to analyze fire regimes in Florida. Pages 88–94 in R.T. Engstrom, K.E.M. Galley, and W.J. de Groot (eds.). Proceed­ ings of the 22nd Tall Timbers Fire Ecology Conference: Fire in Temperate, Boreal, and Montane Ecosystems. Tall Timbers Research Station, Tallahassee, FL. INTRODUCTION dynamics of large interactive natural systems such as The catastrophic wildfires that occurred in Florida avalanches and earthquakes (Bak and Chen 1991). during the summer of 1998 were the worst in terms Self-organized criticality is a holistic theory that explains the global features of a dynamic system with of area burned in at least a half-century (Barnett and parameters that summarize the relative number of Brenner 1992). In northeast Florida alone, approxismall and large events. A key feature of self-orga­ mately 202,430 ha burned and produced economic nized systems is that the small-scale properties of a losses of at least $600 million (Butry et al. 2001). system cannot be used to predict large-scale behavAlthough there is some recent empirical evidence ior. Rather, large-scale behavior emerges over time that catastrophic wildfire seasons in Florida are relatand space, resulting from the dynamic interactions ed to the El Niño–Southern Oscillation phenomenon between parts of the system. (Brenner 1991, Prestemon et al. 2002), the broadA widely cited example of self-organized critical scale characteristics of fire regimes over time and behavior is the “sandpile model” (e.g., see Kauffman space are not well understood. As human populations 1995). In this model, grains of sand are persistently increase in the urban–wildland interface, it becomes placed in a pile on the top of a table. Over time, the increasingly important to understand the nature of sandpile grows and avalanches of many sizes occur, wildland fire regimes and how they are affected by with an occasional catastrophic avalanche that carhuman actions such as fragmentation of wildlands, ries sand off the table to the floor below. However, prescribed burning, and fire suppression. catastrophic avalanches are initiated by the same Recent attempts to characterize forest fire regimes event that causes smaller avalanches—the addition of have been developed using a theory known as “selfa grain of sand. In this model, a catastrophic cause is organized criticality” (Drossal and Schwabl 1992). not required to induce a catastrophic effect. This theory has also been used to describe the An avalanche is a branching process that causes