Fig 13. Fan.

(A) The Fan F_n,m (or Windmill [56]) consists of one hub and n blades containing m vertices each. We consider a weighted version, with edge weights as shown. Pictured here is the case n = m = 3. (B,C) The neutral fixation probability ρ^∘ and weak selection coefficient ρ′, plotted as ϵ varies from 0 to infinity, for all Fan graphs of sizes N = 13 and N = 101. As ϵ increases, the behavior changes from absolute and relative suppressor, to absolute and relative amplifier, to relative amplifier but absolute suppressor. For ϵ → ∞, the ρ^∘ and ρ′ values approach those of the Star graph S_nm (marked by a red star). (D) As n → ∞, there are three regimes of behavior, depending whether ϵ is held constant (blue line) or scales as n⁻¹ (purple line), or as n⁻² (green line). The maximal ρ′ for fixed m is ρ′ = (m + 1)/(2m), achieved for n → ∞ with $ϵ=(m-1)/\left(m\sqrt{n}\right)$.