Stability analysis of the partial selfing selection model

We undertake a detailed study of the one-locus two-allele partial selfing s election model. We show that a polymorphic equilibrium can exist only in th e cases of overdominance and underdominance and only for a certain range of selfing rates. Furthermore, when it exists, we show that the polymorphic e quilibrium is unique. The local stability of the polymorphic equilibrium is investigated and exact analytical conditions are presented. We also carry out an analysis of local stability of the fixation states and then conclude that only overdominance can maintain polymorphism in the population. When the linear local analysis is inconclusive, a quadratic analysis is performe d. For some sets of selective values, we demonstrate global convergence. Fi nally, we compare and discuss results under the partial selfing model and t he random mating model.