How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open question in science; attracting attention from different fields, from Theoretical Ecology to Mathematics and Physics. In this context, modeling the stable coexistence of species competing for limited resources is a particularly challenging task. From a mathemati- cal point of view, coexistence in competitive dynamics can be achieved when dominance among species forms intransitive loops. However, these relationships usually lead to species’ relative abundances neutrally cycling without converging to a stable equilibrium and, although in recent years several mechanisms have been pro- posed, models able to explain the robust persistence of competitive ecosystems are still lacking. Here we show that stable coexistence can be achieved when the locality of interactions is taken into account. We consider a simplified ecosystem where individuals of each species lay on a spatial network and interactions are possible only between nodes at a certain distance. Varying such distance allows to interpolate between local and global competition. Our results demonstrate that when two conditions are met: individuals are embedded in space and can only interact with other individuals within a short distance, species coexist reaching a stable equilibrium. On the contrary, when one of these ingredients is missing large oscillations and neutral cycles emerge.
Violeta Calleja-Solanas, Nagi Khalil, Jesús Gómez-Gardeñes, Emilio Hernández-García, and Sandro Meloni Phys. Rev. E 106, 064307
And finally, my research institute (IFISC) celebrates every year a poster party. I adapted this work to study… POKEMON!