We study the stochastic dynamics of evolutionary games, and focus on the
so-called `stochastic slowdown' effect, previously observed in (Altrock et. al,
2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a
beneficial mutation may take longer to fixate than a neutral one. More
precisely, the fixation time conditioned on the mutant taking over can show a
maximum at intermediate selection strength. We show that this phenomenon is
present in the prisoner's dilemma, and also discuss counterintuitive slowdown
and speedup in coexistence games. In order to establish the microscopic origins
of these phenomena, we calculate the average sojourn times. This allows us to
identify the transient states which contribute most to the slowdown effect, and
enables us to provide an understanding of slowdown in the takeover of a small
group of cooperators by defectors: Defection spreads quickly initially, but the
final steps to takeover can be delayed substantially. The analysis of
coexistence games reveals even more intricate behavior. In small populations,
the conditional average fixation time can show multiple extrema as a function
of the selection strength, e.g., slowdown, speedup, and slowdown again. We
classify two-player games with respect to the possibility to observe
non-monotonic behavior of the conditional average fixation time as a function
of selection strength.Comment: Accepted for publication in the Journal of Theoretical Biology.
Includes changes after peer revie
