  We investigate spatial evolutionary games with death-birth updating in large
finite populations. Within growing spatial structures subject to appropriate
conditions, the density processes of a fixed type are proven to converge to the
Wright-Fisher diffusions with drift. In addition, convergence in the
Wasserstein distance of the laws of their occupation measures holds. The proofs
of these results develop along an equivalence between the laws of the
evolutionary games and certain voter models and rely on the analogous results
of voter models on large finite sets by convergences of the Radon-Nikodym
derivative processes. As another application of this equivalence of laws, we
show that in a general, large population of size $N$, for which the stationary
probabilities of the corresponding voting kernel are comparable to uniform
probabilities, a first-derivative test among the major methods for these
evolutionary games is applicable at least up to weak selection strengths in the
usual biological sense (that is, selection strengths of the order $\mathcal
O(1/N)$).
