The equilibrium and stability for n alleles under the density-dependent selection

The problem of the equilibrium under the density-dependent selection for n-alleles belonging to one locus is considered. The new “measure of quality” of the population φ is introduced and it is shown that the equilibrium points are the constrained stationary points of the function φ and all locally stable equilibriums are its local maximum points. The analoque of the Fisher theorem for density-dependent selection is considered.