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.