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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.
