|Title||Does the Web Have a Weaver? Mechanisms Behind Scaling Laws in Fire Regimes|
|Affiliation||US Forest Service|
|Authors||Donald McKenzie, Maureen Kennedy|
|Keywords||composite fire interval, fire scars, power laws, Sorensen variogram, topographic controls|
Scaling relationships abound in natural phenomena, but it can be difficult to determine whether they arise from physical mechanisms or are simply numerical artifacts of the way data are quantified. In fire regimes, scaling laws appear in frequency distributions of fire sizes, wherein power laws -- linear relationships of two variables in double-logarithmic space -- are common, though not ubiquitous. Fire-size distributions have received the most attention, but we have documented spatial scaling laws in other components of fire regimes, using a spatially explicit fire-scar database from eastern Washington, USA, for which direct measurement of fire sizes is problematic. Specifically, composite fire intervals (CFIs) and the shape parameters of hazard functions (measuring the changing probability of fire over time since the previous fire) scale with sample area. The similarity between two fire-scar time series scales with the distance between them, producing variogram-like relationships. Power laws fit to CFI vs. sample area, and to fire-history similarity vs. distance, are stronger on more topographically complex landscapes, as is the qualitative behavior of the hazard function parameter across scales. In all three cases, we propose that topographic controls on fire spread are the underlying driver for more proximate mechanisms that govern the observed scaling relationships, even though in one case, CFIs, geometric arguments alone are sufficient to explain the existence of a power law per se. We further suggest that the search for mechanisms behind scaling laws in landscape ecology may be fruitful only when the scope of observed phenomena is sufficiently local to be in the domain of a contagious process -- in this case fire propagation. Power laws and other scaling relationships at broader scales, even if not simply numerical artifacts, are likely to be phenomenological in nature rather than governed by identifiable mechanisms.