Scaling rules for fire regimes

Abstract

Forest fire is a keystone ecological process in coniferous forests of southwestern North America. This dissertation examines a fire regime in the Jemez Mountains of northern New Mexico, USA, based on an original data set collected from Monument Canyon Research Natural Area (MCN). First, I examine scale dependence in the fire regime. Statistical descriptors of the fire regime, such as fire frequency and mean fire interval, are scale-dependent. I describe the theory of the event-area (EA) relationship, analogous to the species-area relationship, for events distributed in space and time; the interval-area (IA) relationship, is a related form for fire intervals. The EA and IA also allow estimation of the annual fire frame (AFF), the area within which fire occurs annually on average. The slope of the EA is a metric of spatio-temporal synchrony of events across multiple spatial scales. The second chapter concerns the temporal distribution of fire events. I outline a theory of fire interval probability from first principles in fire ecology and statistics. Fires are conditional events resulting from interaction of multiple contingent factors that must be satisfied for an event to occur. Outcomes of this kind represent a multiplicative process for which a lognormal model is the limiting distribution. I examine the application of this framework to two probability models, the Weibull and lognormal distributions, which can be used to characterize the distribution of fire intervals over time. The final chapter addresses the theory and effects of sample size in fire history. Analytical methods (including composite fire records) are used in fire history to minimize error in inference. I describe a theory of the collector's curve based on accumulation of sets of discrete events and the probability of recording a fire as a function of sample size. I propose a nonlinear regression method for the Monument Canyon data set to correct for differences in sample size among composite fire records. All measures of the fire regime reflected sensitivity to sample size, but these differences can be corrected in part by applying the regression correction, which can increase confidence in quantitative estimates of the fire regime.