  The aim of this paper is to quantify the amplitude of the predicted plateau
in [alpha/Fe] ratios associated with the most metal-poor stars of a galaxy. We
assume that the initial mass function in galaxies is steeper if the star
formation rate (SFR) is low -- as per the integrated galactic initial mass
function (IGIMF) theory. A variant of the theory, in which the IGIMF depends
upon the metallicity of the parent galaxy, is also considered. The IGIMF theory
predicts low [alpha/Fe] plateaus in dwarf galaxies, characterised by small
SFRs. The [alpha/Fe] plateau is up to 0.7dex lower than the corresponding
plateau of the Milky Way. For a universal IMF one should expect instead that
the [alpha/Fe] plateau is the same for all the galaxies, irrespective of their
masses or SFRs. Assuming a strong dependence of the IMF on the metallicity of
the parent galaxy, dwarf galaxies can show values of the [alpha/Fe] plateau
similar to those of the Milky Way, and almost independent on the SFR. The
[Mg/Fe] ratios of the most metal-poor stars in dwarf galaxies satellites of the
Milky Way can be reproduced either if we consider metallicity-dependent IMFs or
if the early SFRs of these galaxies were larger than we presently think.
Present and future observations of dwarf galaxies can help disentangle between
these different IGIMF formulations.
