Statistics of extremes: Modeling ecological disturbances

The potential advantage of extreme value theory in modeling ecological disturbances is the central theme of this paper. The statistics of extremes have played only a very limited role in ecological modeling, despite the disproportionate influence of unusual disturbances on ecosystems. An overview of this theory is provided, with emphasis on recent developments that both make more efficient use of the available data on extremes and enable applications that are more ecologically realistic. Consistent with the emphasis on scale in ecology, scaling properties of extremes are emphasized. It is argued that the existence of distributions whose extreme upper tail is "heavy" (i.e., decreases at a relatively slow rate) implies that ecological disturbances are sometimes regarded as more "surprising" than they ought to be. The application focuses on modeling disturbances in paleoecology. Two examples are considered: the first, a sediment yield time series for Nicolay Lake in the high Arctic, reflects only the influence of hydrologic disturbances; the second, a sediment rate time series in the Chesapeake Bay, includes both climatic and anthropogenic influences. Strong evidence supports a heavy-tailed distribution for the Nicolay Lake sediment yield, but not necessarily for the Chesapeake Bay sediment rates. For each example, it is demonstrated how the statistics of extremes can readily incorporate information about covariates, such as large-scale atmospheric-oceanic circulation patterns or land use.