Table 2.

Thresholds for cooperation on infinite graphs with low mutation

Graph	b/c threshold
1D lattice	$2+\sqrt{8u}+\mathcal{O}\left(u\right)$
2D lattice	$4-\frac{24}{\pi }u\ln u+\mathcal{O}\left(u\right)$
k-Cayley tree (k ≥ 3)	$k+\frac{k^2}{k-2}u+\mathcal{O}\left(k{u}^2\right)$