Spatially Synchronous Extinction of Species under External Forcing

More than 99% of the species that ever existed on the surface of the Earth are now extinct and their extinction on a global scale has been a puzzle. One may think that a species under an external threat may survive in some isolated locations leading to the revival of the species. Using a general model we show that, under a common external forcing, the species with a quadratic saturation term first undergoes spatial synchronization and then extinction. The effect can be observed even when the external forcing acts only on some locations provided the dynamics contains a synchronizing term. Absence of the quadratic saturation term can help the species to avoid extinction.

Figure 1

The interplay between synchronization and extinction in a simple prey-predator model [18]. (a) and (c) show the populations of different patches as a function of time for $b$ positive and negative, respectively. (b) and (d) show the synchronization and extinction parameters $S$ and $E$ (solid and dotted lines, respectively) as a function of time.

Figure 2

The time evolution of populations in different patches is shown when only 50% of the patches interact with the external forcing. (a) $b=50.0$, (b) $b=-4.0$.