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.