A Simple Model of Evolution with Variable System Size

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. 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.