  We describe an equilibrium model that links the metallicity of low-redshift
galaxies to stellar evolution models. It enables the testing of different
stellar initial mass functions and metal yields against observed galaxy
metallicities. We show that the metallicities of more than 80,000 Sloan Digital
Sky Survey (SDSS) galaxies in the low-redshift range $0.07\leq z\leq 0.3$
considerably constrain stellar evolution models that simultaneously relate
galaxy stellar mass, metallicity, and star formation rates (SFRs) to the infall
rate of low-metallicity extragalactic gas and outflow of enriched matter. A
feature of our model is that it encompasses both the active star forming phases
of a galaxy and epochs during which the same galaxy may lie fallow. We show
that the galaxy-mass-metallicity-star-formation relation can be traced to
infall of extragalactic gas mixing with native gas from host galaxies to form
stars of observed metallicities, the most massive of which eject oxygen into
extragalactic space. Most consequential among our findings is that, on average,
extragalactic infall accounts for one half of the gas required for star
formation, a ratio that is remarkably constant across galaxies with stellar
masses ranging at least from $M* = 2 \times 10^9$ to $6\times 10^{10}
M_{\odot}$. This leads us to propose that star formation is initiated when
extragalactic infall roughly doubles the mass of marginally stable interstellar
clouds. The processes described may also account quantitatively for the
metallicity of extragalactic space, though to check this the fraction of
extragalactic baryons will need to be more firmly established.
