title: Evolutionary games on cycles with strong selection.
abstract: Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the well-mixed case, can act as amplifiers or suppressors of selection by increasing or decreasing the fixation probability of a beneficial mutant. Properties of the associated mean fixation times can be more intricate, especially when selection is strong. The intuition is that fixation of a beneficial mutant happens fast in a dominance game, that fixation takes very long in a coexistence game, and that strong selection eliminates demographic noise. Here we show that these intuitions can be misleading in structured populations. We analyze mean fixation times on the cycle graph under strong frequency-dependent selection for two different microscopic evolutionary update rules (death-birth and birth-death). We establish exact analytical results for fixation times under strong selection and show that there are coexistence games in which fixation occurs in time polynomial in population size. Depending on the underlying game, we observe inherence of demographic noise even under strong selection if the process is driven by random death before selection for birth of an offspring (death-birth update). In contrast, if selection for an offspring occurs before random removal (birth-death update), then strong selection can remove demographic noise almost entirely.
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, USA.|Dana-Farber Cancer Institute, Boston, Massachusetts, USA.|Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA.
authors.forename: P M
authors.initials: PM
authors.lastname: Altrock
authors.affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Plön, Germany.
authors.forename: A
authors.initials: A
authors.lastname: Traulsen
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, USA.
authors.forename: M A
authors.initials: MA
authors.lastname: Nowak
mesh_terms: D000818:Animals; D005075:Biological Evolution; D005716:Game Theory; D005717:Games, Experimental; D008962:Models, Theoretical; D009026:Mortality; D009154:Mutation; D036801:Parturition; D011157:Population Dynamics; D013269:Stochastic Processes; D013997:Time Factors