Long-term evolution of an ecosystem with spontaneous periodicity of mass extinctions

Twenty years ago, after analysing palaeontological data, Raup and Sepkoski suggested that mass extinctions on Earth appear cyclically in time with a period of approximately 26 million years (My). To explain the 26 My period, a number of proposals were made involving, e.g., astronomical effects, increased volcanic activity, or the Earth's magnetic field reversal, none of which, however, has been confirmed. Here we study a spatially extended discrete model of an ecosystem and show that the periodicity of mass extinctions might be a natural feature of the ecosystem's dynamics and not the result of a periodic external perturbation. In our model, periodic changes of the diversity of an ecosystem and some of its other characteristics are induced by the coevolution of species. In agreement with some palaeontological data, our results show that the longevity of a species depends on the evolutionary stage at which the species is created. Possible further tests of our model are also discussed.