  We study evolutionary games on the torus with $N$ points in dimensions $d\ge
3$. The matrices have the form $\bar G = {\bf 1} + w G$, where ${\bf 1}$ is a
matrix that consists of all 1's, and $w$ is small. As in Cox Durrett and
Perkins \cite{CDP} we rescale time and space and take a limit as $N\to\infty$
and $w\to 0$. If (i) $w \gg N^{-2/d}$ then the limit is a PDE on ${\bf R}^d$.
If (ii) $N^{-2/d} \gg w \gg N^{-1}$, then the limit is an ODE. If (iii) $w \ll
N^{-1}$ then the effect of selection vanishes in the limit. In regime (ii) if
we introduce a mutation $\mu$ so that $\mu /w \to \infty$ slowly enough then we
arrive at Tarnita's formula that describes how the equilibrium frequencies are
shifted due to selection.
