  We study evolutionary game dynamics in a well-mixed populations of finite
size, N. A well-mixed population means that any two individuals are equally
likely to interact. In particular we consider the average abundances of two
strategies, A and B, under mutation and selection. The game dynamical
interaction between the two strategies is given by the 2x2 payoff matrix
[(a,b), (c,d)]. It has previously been shown that A is more abundant than B, if
(N-2)a+Nb>Nc+(N-2)d. This result has been derived for particular stochastic
processes that operate either in the limit of asymptotically small mutation
rates or in the limit of weak selection. Here we show that this result holds in
fact for a wide class of stochastic birth-death processes for arbitrary
mutation rate and for any intensity of selection.
