  A popular approximation in lattice gauge theory is an extrapolation in the
number of fermion species away from the four fold degeneracy natural with the
staggered fermions formulation. I show that at finite lattice spacing and for
an odd number of flavors this extrapolation misses terms which, on general
principles, must be present in the continuum theory. For a correct continuum
limit, this forces unphysical singularities in parameter regions where
continuum physics is smooth and all physical particles are massive. These
singularities are not expected with other lattice regulators. Finally, I argue
that unnatural constraints on certain correlation functions appear even when
all quarks are massive.
