The Largest, Smallest, Highest, Lowest, Longest, and Shortest: Extremes in Ecology

Biostatistics channels ecologists into thinking primarily about the mean and variance of a probability distribution. But many problems of biological interest concern the extremes in a variable (e.g., highest temperature, largest force, longest drought, maximum lifespan) rather than its central tendency. Such extremes are not adequately addressed by standard biostatistics. In these cases an alternative approach–the statistics of extremes–can be of value. In the limit of a large number of measurements, the probability structure of extreme values conforms to a generalized distribution described by three parameters. In practice these parameters are estimated using maximum likelihood techniques. Using this estimate of the probability distribution of extreme values, one can predict the expected time between the imposition of extremes of a given magnitude (a return time) and can place confidence limits on this prediction. Using data regarding sea—surface temperature, wave—induced hydrodynamic forces, wind speeds, and human life—spans we show that accurate long—term predictions can at times be made from a surprisingly small number of measurements if appropriate care is taken in the application of the statistics. For example, accurate long—term prediction of sea—surface temperatures can be derived from short—term data that are anomalous in that they contain the effects of an extreme EL Nino. In the cases of wave—induced forces and wind speeds, the probability distribution of extreme values is similar among years and diverse sites, indicating the possible existence of unifying principles governing these phenomena. Limitations and possible misuse of the method are discussed.