  Observations of globular clusters (GCs) and field stars in the halos of the
giant elliptical galaxy Cen A and the spiral galaxy M31 show a large range of
cluster-to-star number ratios ('specific frequencies'). The cluster-to-star
ratio decreases with increasing metallicity by a factor of 100-1000, at all
galactocentric radii and with a slope that does not seem to depend on radius.
In dwarf galaxies, the GCs are also more metal-poor than the field stars on
average. These observations indicate a strong dependence of either the cluster
formation efficiency or the cluster destruction rate on metallicity and
environment. We aim to explain these trends by considering various effects that
may influence the observed cluster-to-star ratio as a function of metallicity,
environment and cosmological history. We show that both the cluster formation
efficiency and the maximum cluster mass increase with metallicity, so they
cannot explain the observed trend. Destruction of GCs by tidal stripping and
dynamical friction destroy clusters over too small a range of galactocentric
radii. We show that cluster destruction by tidal shocks from giant molecular
clouds in the high-density formation environments of GCs becomes increasingly
efficient towards high galaxy masses and, hence, towards high metallicities.
The predicted cluster-to-star ratio decreases by a factor 100-1000 towards high
metallicities and should only weakly depend on galactocentric radius due to
orbital mixing during hierarchical galaxy merging, consistent with the
observations. The observed, strong dependence of the cluster-to-star ratio on
metallicity and the independence of its slope on galactocentric radius can be
explained by cluster destruction and hierarchical galaxy growth. As a result,
we find that the metallicity-dependence of the cluster-to-star ratio does not
reflect a GC formation efficiency, but a survival fraction. (Abridged)
