• hemp3quilt posted an update 4 months ago

    They satisfy the symmetry relations V arα(S1A)=V arβ(S2A) and V arα(S2A)=V arβ(S1A), are concave in mm, and vanish at m=0m=0 and m=mna(SA). In addition, V arα(S1A)≥V arα(S2A) holds and the maxima Sirtuin inhibitor of V arα(S1A) and V arα(S2A) are equation(8.6) 1(1+κ)2and  1(1+κ)2P−κ+κPP+κ+κP, respectively. They can be realized when these equilibria are stable (e.g. Fig. 11(c)). As Fig. 11 also shows, the genetic variance maintained at a SLP may be higher or lower than at a fully polymorphic equilibrium. If selection is directional and P>1/(1+κ)P>1/(1+κ), I0 is the unique stable equilibrium for weak migration. From (8.1) and  we obtain equation(8.7) V arγ(I0)=Dˆ0,γ(4+rs1+κ2−P(1+κ)2(1−P−κP)(P−κ+κP))+O(m2), where Dˆ0,γ=m/(r+4Ps)>0 is the LD. It is readily shown that for strong recombination, V arγ(I0) may increase or decrease in κκ and PP, whereas in the limit r→0r→0, V arγ(I0) is independent of κκ and decreases in PP. In addition, it is easy to show that V arγ(I0) increases in rr if P>1/2P>1/2, hence, whenever P>1/(1+κ)P>1/(1+κ). Near P=1P=1, and if all other parameters are fixed, V arγ(I0) decreases in PP, hence it is maximized for some intermediate value of PP. If P=1P=1, (8.7) simplifies to equation(8.8) V arγ(I0)=2ms(1−2sr+4s)+O(m2), which to first order in mm is independent of κκ and increases in rr. Fig. 11(c) indicates that the influence of κκ on the genetic variance is also negligible for intermediate migration rates. For higher migration rates, V arγ(I0) may decrease as rr increases (e.g. Fig. 12(a)). In the limits of weak or strong recombination, (8.8) yields equation(8.9) V arγ(I0)={ms+mr4s2+O(r2)+O(m2)if  r  is small ,2ms−4mr+O(1r2)+O(m2)if  r  is large . It seems remarkable that in these limiting cases essentially the same amount of variance is maintained under strong divergent selection as in the special case leading to (8.5), in which divergent selection is weak (if κ>1/2κ>1/2) or moderate (if κ<1/2κ<1/2). Nevertheless, there is a substantial difference between these cases, because under stabilizing selection, variance will be maintained only for appropriate initial conditions (i.e., sufficient initial differentiation between the subpopulations). Since  and (8.7) assume that mm is sufficiently small for given κ,Pκ,P, and rr, the limit P→1/(1+κ)P→1/(1+κ) cannot be performed in (8.7). If P=1/(1+κ)P=1/(1+κ) and κ<1κ<1, the internal equilibrium I0 is unstable. The SLPs S1A and S2A are asymptotically stable for weak migration (Section  6.2.2). The variances in deme αα and ββ at S1A are approximately m/[s(1+κ)]m/[s(1+κ)] and m/[s(1−κ)]m/[s(1−κ)], respectively. At S2A, these are the variances in deme ββ and αα. Some of the approximations given above do not apply if recombination is weak.