We analyze a popular model of the evolution of traits related to perfo
rmance in exploitative competition. This model has previously been use
d to explain a mechanism by which interspecific competition can cause
taxon cycles. We show that purely intraspecific competition can cause
evolution of extreme competitive abilities that ultimately result in e
xtinction, without any influence from other species. The only change i
n the model required for this outcome is the assumption of a nonnormal
distribution of resources of different sizes measured on a logarithmi
c scale. This suggests that taxon cycles, if they exist, may be driven
by within- rather than between-species competition. Self-extinction d
oes not occur when the advantage conferred by a large value of the com
petitive trait (e.g., size) is relatively small, or when the carrying
capacity decreases at a comparatively rapid rate with increases in tra
it value. The evidence regarding these assumptions is discussed. The r
esults suggest a need for more data on resource distributions and size
-advantage in order to understand the evolution of competitive traits
such as body size.