# Evolutionary Stability on Graphs

 Title: Evolutionary Stability on Graphs Author: Ohtsuki, Hisashi; Nowak, Martin A. Note: Order does not necessarily reflect citation order of authors. Citation: Ohtsuki, Hisashi, and Martin A. Nowak. 2008. Evolutionary stability on graphs. Journal of Theoretical Biology 251(4): 698-707. Full Text & Related Files: Nowak_EvolutionaryStability.pdf (286.8Kb; PDF) Abstract: Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree $$k > 2$$. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth–death (BD), death–birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs. Published Version: doi:10.1016/j.jtbi.2008.01.005 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:4054433 Downloads of this work: