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.
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