  Many results in modern astrophysics rest on the notion that the Initial Mass
Function (IMF) is universal. Our observations of HI selected galaxies in the
light of H-alpha and the far-ultraviolet (FUV) challenge this notion. The flux
ratio H-alpha/FUV from these two star formation tracers shows strong
correlations with the surface-brightness in H-alpha and the R band: Low Surface
Brightness (LSB) galaxies have lower ratios compared to High Surface Brightness
galaxies and to expectations from equilibrium star formation models using
commonly favored IMF parameters. Weaker but significant correlations of
H-alpha/FUV with luminosity, rotational velocity and dynamical mass are found
as well as a systematic trend with morphology. The correlated variations of
H-alpha/FUV with other global parameters are thus part of the larger family of
galaxy scaling relations. The H-alpha/FUV correlations can not be due to dust
correction errors, while systematic variations in the star formation history
can not explain the trends with both H-alpha and R surface brightness. LSB
galaxies are unlikely to have a higher escape fraction of ionizing photons
considering their high gas fraction, and color-magnitude diagrams. The most
plausible explanation for the correlations are systematic variations of the
upper mass limit and/or slope of the IMF at the upper end. We outline a
scenario of pressure driving the correlations by setting the efficiency of the
formation of the dense star clusters where the highest mass stars form. Our
results imply that the star formation rate measured in a galaxy is highly
sensitive to the tracer used in the measurement. A non-universal IMF also calls
into question the interpretation of metal abundance patterns in dwarf galaxies
and star formation histories derived from color magnitude diagrams. Abridged.
