  We study the multi-strategy stochastic evolutionary game with death-birth
updating in expanding spatial populations of size $N\to \infty$. The model is a
voter model perturbation. For typical populations, we require perturbation
strengths satisfying $1/N\ll w\ll 1$. Under appropriate conditions on the
space, the limiting density processes of strategy are proven to obey the
replicator equation, and the normalized fluctuations converge to a Gaussian
process with the Wright-Fisher covariance function in the limiting densities.
As an application, we resolve in the positive a conjecture from the biological
literature that the expected density processes approximate the replicator
equation on many non-regular graphs.
