  Globular clusters (GC) are important objects for tracing the early evolution
of a galaxy. We study the relation between the properties of globular cluster
systems - as quantified by the GC specific frequency (SN) - and the properties
of their host galaxies. In order to understand the origin of the relation
between the GC specific frequency (SN) and galaxy mass, we devise a theoretical
model for the specific frequency (SN,th). GC erosion is considered to be an
important aspect for shaping this relation, since observations show that
galaxies with low densities have a higher SN, while high density galaxies have
a small SN. We construct a model based on the hypothesis that star-formation is
clustered and depends on the minimum embedded star cluster mass (Mecl,min), the
slope of the power-law embedded cluster mass function (beta) and the relation
between the star formation rate (SFR) and the maximum star cluster mass
(Mecl,max). We find an agreement between the primordial value of the specific
frequency (SNi) and our model for beta between 1.5 and 2.5 with Mecl,min <10^4
Msun.
