  We present a stochastic model for the size of a taxon in paleobiology, in
which we allow for the evolution of new taxon members, and both individual and
catastrophic extinction events. The model uses ideas from the theory of birth
and death processes. Some general properties of the model are developed, and a
fuller discussion is given for specific distributions of the time between
catastrophic extinction events. Long tails in the taxon size distribution arise
naturally from the model.
