  Punctuated equilibrium is a mode of evolution in which phenetic change occurs
in rapid bursts that are separated by much longer intervals of stasis during
which mutations accumulate but no major phenotypic change occurs. Punctuated
equilibrium has been originally proposed within the framework of paleobiology,
to explain the lack of transitional forms that is typical of the fossil record.
Theoretically, punctuated equilibrium has been linked to self-organized
criticality (SOC), a model in which the size of avalanches in an evolving
system is power-law distributed, resulting in increasing rarity of major
events. We show here that, under the weak-mutation limit, a large population
would spend most of the time in stasis in the vicinity of saddle points in the
fitness landscape. The periods of stasis are punctuated by fast transitions, in
lnNe time (Ne, effective population size), when a new beneficial mutation is
fixed in the evolving population, which moves to a different saddle, or on much
rarer occasions, from a saddle to a local peak. Thus, punctuated equilibrium is
the default mode of evolution under a simple model that does not involve SOC or
other special conditions.
