We present a simple theoretical model of evolution featuring a decreasing extinction rate due to an increasing average fitness of the species. The dynamics is based on a random walk on a rugged fitness landscape, with evolutionary jumps for each species triggered by the achievement of fitness records during the walk. We analyze two different rules for extinction. In the first, an evolutionary jump leads to an extinction with a given probability, while in the second a specific competition mechanism is considered. In both cases temporal power laws are found to describe the evolution. Extensive simulation results from our second model are in reasonable agreement with paleontological data, showing that the background extinction rate has decreased since Cambrian time.

• Received 22 February 1995

DOI:https://doi.org/10.1103/PhysRevLett.75.2055