Evolution and extinction dynamics in rugged fitness landscapes

After an introductory section summarizing the paleontological data and some of their theoretical descriptions, we describe the "reset" model and its (in part analytically soluble) mean field version, which have been briefly introduced in Letters.(1,2) Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness landscapes. As a consequence, the average fitness 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 field version, analytically. We also consider the effect of externally added "mass" extinctions. The predictions for various quantities of paleontological interest (life-time distribution, distribution of event sizes and behavior of the rate of extinction) are robust and in good agreement with available data.