  We study a lattice model of a multi-species prey-predator system. Numerical
results show that for a small mutation rate the model develops irregular
long-period oscillatory behavior with sizeable changes in a number of species.
The periodicity of extinctions on Earth was suggested by Raup and Sepkoski but
so far is lacking a satisfactory explanation. Our model indicates that this is
a natural consequence of the ecosystem dynamics, not the result of any
extraterrestrial cause.
