  We reformulate the eigenvalue problem for the selection--mutation equilibrium
distribution in the case of a haploid asexually reproduced population in the
form of an equation for an unknown probability generating function of this
distribution. The special form of this equation in the infinite sequence limit
allows us to obtain analytically the steady state distributions for a number of
particular cases of the fitness landscape. The general approach is illustrated
by examples; theoretical findings are compared with numerical calculations.
