ESTIMATION OF TEMPORAL VARIATIONS IN HISTORICAL FIRE FREQUENCY FROM TIME-SINCE-FIRE MAP DATA

This paper describes an improved statistical methodology for estimatin g historical forest fire frequencies from time-since-fire map data. Of particular interest is the question of estimating fire frequency in t emporally distinct epochs. Unlike previous graphical and ad hoc method s, the new methodology is firmly grounded within the established stati stical paradigm of likelihood inference. In addition, in contrast to e arlier methods, it takes into account the fact that surviving stands w hich originated in earlier epochs, have been subject to different haza rds of burning as they have lived through more recent epochs. Neglecti ng this fact leads to overestimates of the fire frequency in the more recent epochs. Procedures for obtaining maximum likelihood estimates a nd likelihood ratio confidence intervals for the fire frequency in eac h epoch are developed, along with a likelihood ratio test to assess wh ether the fire frequencies in distinct epochs were significantly diffe rent. This test is not strictly valid when the change points separatin g epochs are suggested from exploratory data analysis; rather it is de veloped assuming that change points are determined independently of th e data. This distinction, which is necessary to avoid selection bias, has not been noted before. The fact that forest fire is a contagious p rocess, with consequent spatial autocorrelation in time-since-fire obs ervations, is taken into account through the use of an overdispersed m odel, with associated quasi-likelihood function. This aspect has been ignored, by and large, in previous analyses which have implicitly assu med independence of observations. An example is given in which the met hod is applied to published fire history data from the Kananaskis Vall ey. The results indicate that the previous analysis overestimated the fire frequency for the most recent epoch. The conclusions of other stu dies concerning temporal changes in fire frequency may need to be reco nsidered.