Various population structures for which σ values are known. (a) For the well-mixed population we have σ = (

*N* - 2)/

*N* for any mutation rate. (b) For the cycle we have σ = (3

*N* - 8)/

*N* (DB) and σ = (

*N* - 2)/

*N* (BD) for low mutation. (c) For DB on the star we have σ = 1 for any mutation rate and any population size,

*N* ≥ 3. For BD on the star we have σ = (

*N*^{3} - 4

*N*^{2} + 8

*N* - 8)/(

*N*^{3} - 2

*N*^{2} + 8), for low mutation. (d) For regular graphs of degree

*k* we have σ = (

*k* + 1)/(

*k* - 1) (DB) and σ = 1 (BD) for low mutation and large population size. (e) If there are different interaction and replacement graphs, we have σ = (

*gh*+

*l*)/(

*gh*-

*l*)(DB) and σ = 1 (BD) for low mutation and large population size. The interaction graph, the replacement graph and the overlap graph between these two are all regular and have degrees,

*g*,

*h* and

*l*, respectively. (f) For `games in phenotype space' we find

(DB or synchronous) for a one dimensional phenotype space, low mutation rates and large population size. (g) For `games on sets' σ is more complicated and is given by (). All results hold for weak selection.

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