Coevolution of nodes and links: Diversity-driven coexistence in cyclic competition of three species

When three species compete cyclically in a well-mixed, stochastic system of N individuals, extinction is known to typically occur at times scaling as the system size N. This happens, for example, in rock-paper-scissors games or conserved Lotka-Volterra models in which every pair of individuals can interact on a complete graph. Here we show that if the competing individuals also have a "social temperament" to be either introverted or extroverted, leading them to cut or add links, respectively, then long-living states in which all species coexist can occur. These nonequilibrium quasisteady states only occur when both introverts and extroverts are present, thus showing that diversity can lead to stability in complex systems. In this case, it enables a subtle balance between species competition and network dynamics to be maintained.