THE LARGEST, SMALLEST, HIGHEST, LOWEST, LONGEST, AND SHORTEST - EXTREMES IN ECOLOGY

Biostatistics channels ecologists into thinking primarily about the me an and variance of a probability distribution. But many problems of bi ological interest concern the extremes in a variable (e.g., highest te mperature, largest force, longest drought, maximum lifespan) rather th an its central tendency. Such extremes are not adequately addressed by standard biostatistics. In these cases an alternative approach-the st atistics of extremes-can be of value. In the limit of a large number o f measurements, the probability structure of extreme values conforms t o a generalized distribution described by three parameters. In practic e 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 o n 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 al times be made from a surpr isingly small number of measurements if appropriate care is taken in t he application of the statistics. For example, accurate long-term pred iction 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 probabi lity distribution of extreme values is similar among years and diverse sites, indicating the possible existence of underlying unifying princ iples governing these phenomena. Limitations and possible misuse of th e method are discussed.