Bifurcation Analysis in Population Genetics Model with Partial Selfing

Figure 1

𝑢₁₁=1, 𝑢₁₂=0.5, 𝑢₂₂=0, and 𝜉=0.85. If 𝛾<0, then all interior trajectories evolve to the stable monomorphic equilibria (𝑝^∗=0 and 𝑝^∗=1). (a) For 𝛽=0, there is unique polymorphic phenotypic equilibrium (𝑝^∗,𝐹^∗)=(0.85,0.25), which is stable for 0<𝛾<𝛾_𝑐𝛾2=31.37254902. (b) For 𝛽=0.4, there is unique polymorphic phenotypic equilibrium (𝑝^∗,𝐹^∗)=(0.85,0.25), which is stable for 0<𝛾<𝛾^′_𝑐𝛾2=25.09803922.

(a)

(b)