  A very simple physical model of galaxies, in which the formation of stars is
instantaneously regulated by the mass of gas in a reservoir, links together
three different aspects of the evolving galaxy population:(a) the cosmic time
evolution of the specific star-formation rate sSFR relative to the growth of
haloes, (b) the gas-phase metallicities across the galaxy population and over
cosmic time, and (c) the ratio of the stellar to dark matter mass of haloes. If
the SFR efficiency and wind mass loading are constant, the sSFR is set to the
specific accretion rate of the galaxy: more realistic situations lead to an
sSFR which is perturbed from this identity. The metallicity is set by the
instantaneous operation of the regulator system rather than by the past history
of the system. The regulator system naturally produces a Z(mstar, SFR)
relation, with SFR as a second parameter in the mass-metallicity relation. This
will be the same at all epochs unless the efficiency and mass-loading change
with time, naturally producing a so-called "fundamental metallicity relation".
The observed Z(mstar) relation of SDSS galaxies implies a strong dependence of
stellar mass on halo mass that reconciles the different faint end slopes of the
stellar and halo mass-functions in standard {\Lambda}CDM. It also boosts the
sSFR relative to the specific accretion rate and produces a different
dependence on mass, both of which are observed. The derived Z(mstar, SFR)
relation for the regulator system is fit to published Z(mstar, SFR) data. The
fitted efficiency is consistent with observed molecular gas-depletion
timescales in galaxies while the fitted mass-loading is also plausible. The
model also successfully reproduces the mass-metallicity relation of
star-forming galaxies at z ~ 2.
