Modelling the Dynamics of Biological Systems, 1995, Volume 65 ISBN : 978-3-642-79292-2 H. Flyvbjerg, P. Bak, M. H. Jensen, K. Sneppen
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A simple mathematical model of biological macroevolution is presented. It describes an ecology of adapting, interacting species. Species evolve to maximize their individual fitness in their environment. The environment of any given species is affected by other evolving species; hence it is not constant in time. The ecology evolves to a “self-organized critical” state where periods of stasis alternate with avalanches of causally connected evolutionary changes. This characteristic intermittent behaviour of natural history, known as “punctuated equilibrium,” thus finds a theoretical explanation as a self-organized critical phenomenon. In particular, large bursts of apparently simultaneous evolutionary activity require no external cause. They occur as the less frequent result of the very same dynamics that governs the more frequent small-scale evolutionary activity. Our results are compared with data from the fossil record collected by J. Sepkoski, Jr., and others.