  Some ultra-compact dwarf galaxies have large dynamical mass to light (M/L)
ratios and also appear to contain an overabundance of LMXB sources, and some
Milky Way globular clusters have a low concentration and appear to have a
deficit of low-mass stars. These observations can be explained if the stellar
IMF becomes increasingly top-heavy with decreasing metallicity and increasing
gas density of the forming object. The thus constrained stellar IMF then
accounts for the observed trend of metallicity and M/L ratio found amongst M31
globular star clusters. It also accounts for the overall shift of the
observationally deduced galaxy-wide IMF from top-light to top-heavy with
increasing star formation rate amongst galaxies. If the IMF varies similarly to
deduced here, then extremely young very massive star-burst clusters observed at
a high redshift would appear quasar-like (Jerabkova et al. 2017) .
