  The ratio of anti-electron to total neutrino flux,
$\Phi_{\bar{\nu}_e}:\Phi_\nu$, expected from $p\gamma$ interactions in
astrophysical sources is $\le1:15$. We point out that this ratio is enhanced by
the decay of $\mu^+\mu^-$ pairs, created by the annihilation of secondary high
energy photons from the decay of the neutral pions produced in $p\gamma$
interactions. We show that, under certain conditions, the
$\Phi_{\bar{\nu}_e}:\Phi_\nu$ ratio may be significantly enhanced in gamma-ray
burst (GRB) fireballs, and that detection at the Glashow resonance of
$\bar{\nu}_e$ in kilometer scale neutrino detectors may constrain GRB fireball
model parameters, such as the magnetic field and energy dissipation radius.
