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Mathematical Medicine and Biology 1997 14(1):71-83; doi:10.1093/imammb/14.1.71
© 1997 by Institute of Mathematics and its Applications
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Estimating historical forest-fire frequencies from time-since-last-fire-sample data

WILLIAM J. REED

Department of Mathematics and Statistics, University of victoria PO Box 3045, Victoria BC, Canada V8W 3P4

A method of estimating historical forest-fire frequencies based on time-since-last-fire observations at a simple random sample of points in an area of undisturbed forest is presented. The historical-fire-hazard rate function is assumed to be piecewise constant (constant within distinct epochs separated by change points). The method is based on maximum likelihood, with the likelihood function incorporating two sources of randomness—the random occurrence and spread of fires, and the random selection of sample points. The fire model includes a contagion effect related to the spread of fires and the consequent spatial autocorrelation in the time-since-last-fire. An example using data from Wood Buffalo National Park is presented, and the effects of grouping data is discussed.

Keywords: fire frequency; dendrochronology; fire history; time-since-last-fire sample; contagion; overdispersion; Dirichlet distribution


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