Periodicity of mass extinctions without an extraterrestrial cause

We study a lattice model of a multispecies 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 [Proc. Natl. Acad. Sci. 81, 801 (1984)], but thus far is lacking a satisfactory explanation. Our model indicates that this might be a natural consequence of the ecosystem dynamics and not the result of any extraterrestrial cause.

Figure 1

Average size $m$, fraction of a dominant predator species $f$, and the number of species $s$ as a function of update rate $r$. Results of simulations do not depend on an initial configuration, and usually it was a random distribution of prey and predators.

Figure 2

Time dependence of the number of species $s$ (to superpose with other data it was divided by 40), average size $m$, density of prey ${\rho }_0$, and density of predators $\rho$.

Figure 3

Time dependence of the number of species for (from top) $p=0.00001$, 0.0001, 0.001, and 0.01. To superpose the data on a graph the actual values of $s$ were divided by some factors. Such an operation does not change a characteristic period of fluctuations and their relative amplitude. Inset shows the period of oscillation $\tau$ as a function of mutation probability $p$ obtained from the maximum of the Fourier transform of the time dependence of the number of species $(N=1000)$.

Figure 4

Logarithmic plot of the probability distribution of lifetimes of predator species.