  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 26My 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.
