  A mathematical model of interacting species filling ecological niches left by
the extinction of others is introduced. Species organize themselves into genera
of all sizes. The size of a genus on average grows linearly with its age,
confirming a general relation between Age and Area proposed by Willis. The
ecology exhibits punctuated equilibrium. Analytic and numerical results show
that the probability distribution of genera sizes, genera lifetimes, and
extinction event sizes are the same power law $P(x) \sim 1/x^2$, consistent
with paleontological data.
