  In Dou et al. (2021), we introduced the Fundamental Formation Relation (FFR),
a tight relation between specific SFR (sSFR), H$_2$ star formation efficiency
(SFE$_{\rm H_2}$), and the ratio of H$_2$ to stellar mass. Here we show that
atomic gas HI does not follow a similar FFR as H$_2$. The relation between
SFE$_{\rm HI}$ and sSFR shows significant scatter and strong systematic
dependence on all of the key galaxy properties that we have explored. The
dramatic difference between HI and H$_2$ indicates that different processes
(e.g., quenching by different mechanisms) may have very different effects on
the HI in different galaxies and hence produce different SFE$_{\rm HI}$-sSFR
relations, while the SFE$_{\rm H_2}$-sSFR relation remains unaffected. The
facts that SFE$_{\rm H_2}$-sSFR relation is independent of other key galaxy
properties, and that sSFR is directly related to the cosmic time and acts as
the cosmic clock, make it natural and very simple to study how different galaxy
populations (with different properties and undergoing different processes)
evolve on the same SFE$_{\rm H_2}$-sSFR $\sim t$ relation. In the gas regulator
model (GRM), the evolution of a galaxy on the SFE$_{\rm H_2}$-sSFR($t$)
relation is uniquely set by a single mass-loading parameter $\lambda_{\rm
net,H_2}$. This simplicity allows us to accurately derive the H$_2$ supply and
removal rates of the local galaxy populations with different stellar masses,
from star-forming galaxies to the galaxies in the process of being quenched.
This combination of FFR and GRM, together with the stellar metallicity
requirement, provide a new powerful tool to study galaxy formation and
evolution.
