  Without mutation and migration, evolutionary dynamics ultimately leads to the
extinction of all but one species. Such fixation processes are well understood
and can be characterized analytically with methods from statistical physics.
However, many biological arguments focus on stationary distributions in a
mutation-selection equilibrium. Here, we address the equilibration time
required to reach stationarity in the presence of mutation, this is known as
the mixing time in the theory of Markov processes. We show that mixing times in
evolutionary games have the opposite behaviour from fixation times when the
intensity of selection increases: In coordination games with bistabilities, the
fixation time decreases, but the mixing time increases. In coexistence games
with metastable states, the fixation time increases, but the mixing time
decreases. Our results are based on simulations and the WKB approximation of
the master equation.
