Evolution and extinction dynamics in

After an introductory section summarizing the paleontological data and some of their theoretical descriptions, we describe thèreset' model and its (in part analytically soluble) mean eld version, which have been brieey introduced in Letterss1, 2]. Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by tness records found by random exploration of the agents' tness landscapes. As a consequence, the average tness in the system increases logarithmically with time, while the rate of extinction steadily decreases. This non-stationary dynamics is studied by numerical simulations and, in a simpler mean eld version, analytically. We also consider the eeect of externally added`mass' extinctions. The predictions for various quantities of paleontological interest (lifetime distribution, distribution of event sizes and behavior of the rate of extinction) are robust and in good agreement with available data.