Statistical Mechanics of Network Models of Macroevolution and Extinction

The fossil record of life has been shown to provide evidence for scaling laws in both time series and in some statistical features. This evidence was suggested to be linked with a self-organized critical phenomenon by several authors. In this paper we review some of these models and their specific predictions. It is shown that most of the observed statistical properties of the evolutionary process on the long time scale can be reproduced by means of a simple model involving a network of interactions among species. The model is able to capture the essential features of the extinction and diversification process and gives power law distributions for (i) extinction events, (ii) taxonomy of species-genera data, (iii) lifetime distribution of genus close to those reported from paleontological databases. It also provides a natural decoupling between micro- and macroevolutionary processes. To appear in The Dynamics of Biocomplexity, M. Rubi (ed.). Lecture Notes in Physics. New York: Springer-Verlag.