  A simple model of biological extinction with variable system size is
presented that exhibits a power-law distribution of extinction event sizes. The
model is a generalization of a model recently introduced by Newman (Proc. R.
Soc. Lond. B265, 1605 (1996). Both analytical and numerical analysis show that
the exponent of the power-law distribution depends only marginally on the
growth rate $g$ at which new species enter the system and is equal to the one
of the original model in the limit $g\to\infty$. A critical growth rate $g_c$
can be found below which the system dies out. Under these model assumptions
stable ecosystems can only exist if the regrowth of species is sufficiently
fast.
