On Mar 13, 2007, PED Seminar Series Presents

Rock-Paper-Scissors Games and Biodiversity

by Professor Erwin Frey

Counterintuitive to a naive understanding of Darwinian evolution, where among two interacting species one is expected to be fitter than the other and therefore outcompetes it, a surprising biodiversity exists within the earth's ecosystems. Evolutionary game theory, where the success of one species depends on what the others are doing, provides a promising framework to theoretically investigate coevolving populations. In this context, rock-paper-scissors games, where three strategies cyclically dominate each other, have emerged as a fruitful metaphor for the explanation of biodiversity. In this talk we discuss populations spatially coevolving with local cyclic dominance, and show that they are capable of preserving coexistence of all subpopulations, and in this way ensuring biodiversity. We find that the individuals' mobility competes with the locality of interactions (cyclic dominance) such that biodiversity gets lost above a certain mobility threshold. Below this critical value, all subpopulations coexist forming fascinating moving patterns composed of entangled spirals, which we describe analytically. The potential implications range from population dynamics and cell signaling in biology to spreading of epidemics and arrythmia in medicine.

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