  Globular cluster (GC) systems around galaxies of a vast mass range show
remarkably simple scaling relations. The combined mass of all GCs is a constant
fraction of the total galaxy mass and the mean metallicity and metallicity
dispersion of the GC system scale up weakly with galaxy mass. The metallicity
of massive, metal-poor ("blue") clusters increases with cluster mass, while
that of metal-rich ("red") clusters does not. A significant age-metallicity
relation emerges from analysis of resolved stellar populations in Galactic GCs
and unresolved populations in nearby galaxies. Remarkably, all these trends can
be explained by a simple merger-based model developed in previous work and
updated here using recent observations of galaxy scaling relations at high
redshift. We show that the increasing dispersion of GC metallicity
distributions with galaxy mass is a robust prediction of the model. It arises
from more massive galaxies having more mergers that combine satellite GC
systems. The average metallicity also increases by 0.6~dex over 3~dex in halo
mass. The models show a non-linear trend between the GC system mass and host
galaxy mass which is consistent with the data. The model does not consider GC
self-enrichment, yet predicts a correlation between cluster mass and
metallicity for massive blue clusters. The age-metallicity relation is another
robust prediction of the model. Half of all clusters are predicted to form
within the redshift range $5<z<2.3$, corresponding to ages of $10.8-12.5$~Gyr,
in halos of masses $10^{11}-10^{12.5} M_{\odot}$.
