  The average of the ratio of powers of the spectral determinants of the Dirac
operator in the $\epsilon$-regime of QCD is shown to satisfy a Toda lattice
equation. The quenched limit of this Toda lattice equation is obtained using
the supersymmetric method. This super symmetric approach is then shown to be
equivalent to taking the replica limit of the Toda lattice equation. Among
other, the factorization of the microscopic spectral correlation functions of
the QCD Dirac operator into fermionic and bosonic partition functions follows
naturally from both approaches. While the replica approach relies on an
analytic continuation in the number of flavors no such assumptions are made in
the present approach where the numbers of flavors in the Toda lattice equation
are strictly integer.
