The replicator equation in stochastic spatial evolutionary games

We study the multi-type stochastic evolutionary game with death–birth updating in expanding spatial populations of size N??. The model is a voter perturbation. For typical eligible populations, we require perturbation strengths satisfying 1/N?w?1. Under these conditions, main results prove that vector density processes type obey an extended replicator equation limit, and normalized fluctuations converge to Gaussian process subject Wright–Fisher covariance function. In particular, obtain positive resolution conjecture from [34] extends many non-regular graphs.