A Simple Model of Evolution with Variable System Size
C. Wilke, T. Martinetz
Abstract
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∞. A critical growth rate gc 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.
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