  We explore the inter-relationships between mass, star-formation rate and
environment in the SDSS, zCOSMOS and other surveys. The differential effects of
mass and environment are completely separable to z ~ 1, indicating that two
distinct processes are operating, "mass-quenching" and "environment-quenching".
Environment-quenching, at fixed over-density, evidently does not change with
epoch to z ~ 1, suggesting that it occurs as large-scale structure develops in
the Universe. The observed constancy of the mass-function shape for
star-forming galaxies, demands that the mass-quenching of galaxies around and
above M*, must be proportional to their star-formation rates at all z < 2. We
postulate that this simple mass-quenching law also holds over a much broader
range of stellar mass and epoch. These two simple quenching processes, plus
some additional quenching due to merging, then naturally produce (a) a
quasi-static Schechter mass function for star-forming galaxies with a value of
M* that is set by the proportionality between the star-formation and
mass-quenching rates, (b) a double Schechter function for passive galaxies with
two components: the dominant one is produced by mass-quenching and has exactly
the same M* as the star-forming galaxies but an alpha shallower by +1, while
the other is produced by environment effects and has the same M* and alpha as
the star-forming galaxies, and is larger in high density environments.
Subsequent merging of quenched galaxies modifies these predictions somewhat in
the denser environments, slightly increasing M* and making alpha more negative.
All of these detailed quantitative relationships between the Schechter
parameters are indeed seen in the SDSS, lending strong support to our simple
empirically-based model. The model naturally produces for passive galaxies the
"anti-hierarchical" run of mean ages and alpha-element abundances with mass.
