Scaling rules and probability models for surface fire regimes in ponderosa pine forests

Statistical descriptors of the fire regime in ponderosa pine forests of the Jemez Mountains, New Mexico, are spatially scale-dependent. Thus, quantification of fire regimes must be undertaken in a spatially explicit framework. We apply a variety of analytical tests adapted from species-area relationships to demonstrate an analytical framework for understanding scaling of disturbance regimes. A new spatio-temporal scaling index, the slope of the event-area function, can provide a useful measure of the synchrony of events within watersheds (where fire spread regulates the distribution of events) as well as among mountain ranges. We propose two alternative mathematical models of fire interval distributions based on inherent properties of the fire record and the ecology of frequent-fire disturbance regimes; a discrete probability model, and a probabilistic application of the lognormal distribution. Because they involve distribution of energy and matter, these spatial and temporal scaling rules indicate more general disturbance event-area relationships that can facilitate the analysis of disturbance regimes in a broader ecological framework.