The expected Shannon entropy 1H, heterozygosity 2H, for the equilibrium allele distribution at a neutral locus under IAM and SMM for an isolated population, and for a total population (subscript T) composed of n subpopulations (subscript S).

N = population size, m = dispersal rate, μ = mutation rate, m* = nm/(n–1), NT = effective population size in the total population, and ψ(x) = digamma function. See S1 and S2 Appendices for all derivations. For an isolated population, when α tends to 0, all formulas for SMM reduce to those for IAM. For the total population, when αT tend to 0, all formulas for SMM reduce to those for IAM. For subpopulation, when both αT and αS tend to 0, all formulas for SMM reduce to those for IAM.(Notation for IAM) θ = 4Nμ, θT=4NTμ=4Nnμ+(n−1)μm*+μ.(Notation for SMM) θ = 4Nμ, α = [(1 + 2θ)1/2−1]/2, θT = [1/(1−2HT)2−1]/2, αT = [1/(1−2HT)−1]/2 = [(1+2θT)1/2−1]/2. αS=4(Nm*)(H2T−H2S)H2S+4(Nμ)(1−H2S)H2S−1, where 2HT and 2HS are shown in Eqs 8A and 8B. B(x,y) = Γ(x)Γ(y)/Γ(x+y): beta function, Γ(x): gamma function.The expected Shannon entropy 1H, heterozygosity 2H, for the equilibrium allele distribution at a neutral locus under IAM and SMM for an isolated population, and for a total population (subscript T) composed of n subpopulations (subscript S).