Before revision:  The first main result proves that the density processes of strategy converge to the replicator equation in the limit of a large finite population subject to appropriate, but general, conditions. Multiple strategies and mutations are allowed. Moreover, after normalization, the limiting fluctuations are shown to be Gaussian with a covariance function in the replicator equation's solution through the Wright--Fisher noise coefficient.
After revision:  The first main result proves that the density processes of strategy converge to the replicator equation , and the normalized fluctuations converge to a Gaussian process with the Wright-Fisher covariance function in the replicator equation's solution through the Wright--Fisher noise coefficient.