Much ecology considers only the typical size of a population, yet extr
eme values may be of particular importance. Unusually low numbers may
doom a population to extinction and unusually high numbers may pose an
economic threat. Extreme values may also determine the evolutionary t
raits that predominate. Obviously, even for a fixed variance in annual
numbers, the observed maximum and minimum population size will increa
se the more years that we count the population. Interestingly, over th
e time scales of available data (<100 years), most animal populations
have an observed variance in annual numbers that increases the more co
nsecutive years we use in its calculation. Consequently, populations w
ill meet extreme values more quickly than if the variance were constan
t. We quantify the increases in variance for diatoms, insects, and ver
tebrates, first correcting the data for overall differences in varianc
e. Short- and long-lived species are not consistently different. Speci
es that cycle in density have relatively small increases relative to t
hose that do not cycle. Species in marine ecosystems have larger incre
ases than those in terrestrial and freshwater systems. All these resul
ts suggest that the system in which a species is embedded - rather the
species' own characteristics - plays the crucial role in determining
the nature of population extremes.