  The energy at which cosmic rays from extra-galactic sources begin to dominate
over those from galactic sources is an important open question in astroparticle
physics. A natural candidate is the energy at the 'ankle' in the approximately
power-law energy spectrum which is indicative of a cross-over from a falling
galactic component to a flatter extra-galactic component. The transition can
occur without such flattening but this requires some degree of conspiracy of
the spectral shapes and normalizations of the two components. Nevertheless it
has been argued that extra-galactic sources of cosmic ray protons which undergo
interactions on the CMB can reproduce the energy spectrum below the ankle if
the cross-over energy is as low as the 'second knee' in the spectrum. This low
cross-over model is constrained by direct measurements by the Pierre Auger
Observatory which indicate a heavier composition at these energies. We
demonstrate that upper limits on the cosmic diffuse neutrino flux provide a
complementary constraint on the proton fraction in ultra-high energy
extra-galactic cosmic rays and forthcoming data from IceCube will provide a
definitive test of this model.
