  We quantify to what extent tidal erosion of globular clusters (GCs) has
contributed to the observed u-shaped relation between GC specific frequencies
S_N and host galaxy luminosity M_V. We used our MUESLI code to calculate GC
survival rates for typical early-type galaxy potentials covering a wide range
of observed galaxy properties. We do this for isotropic and radially
anisotropic GC velocity distributions. We find that the calculated GC survival
fraction, f_s, depends linearly on the logarithm of the 3D mass density,
rho_3D, within the galaxy's half light radius, with f_s proportional to
(rho_3D)^(-0.17). For a given galaxy, survival rates are lower for radially
anisotropic configurations than for the isotropic GC cases. We apply these
relations to a literature sample of 219 early-type galaxies from Harris et al.
(2013) in the range M_V=[-24.5:-15.5] mag. The expected GC survival fraction
ranges from ~50% for the most massive galaxies with the largest radii to ~10%
for the most compact galaxies. We find that intermediate luminosity galaxies
M_V=[-20.5:-17.5] mag have the strongest expected GC erosion. Within the
considered literature sample, the predicted GC survival fraction therefore
defines a u-shaped relation with M_V, similar to the relation between specific
frequency S_N and M_V. As a consequence, the u-shape of S_N vs. M_V gets erased
almost entirely when correcting the S_N values for the effect of GC erosion. We
conclude that tidal erosion is an important contributor to the u-shaped
relation between GC specific frequency and host galaxy luminosity. It must be
taken into account when inferring primordial star cluster formation
efficiencies from observations of GC systems in the nearby universe.
