  We use the first systematic data sets of CO molecular line emission in z~1-3
normal star forming galaxies for a comparison of the dependence of
galaxy-averaged star formation rates on molecular gas masses at low and high
redshifts, and in different galactic environments. Although the current high-z
samples are still small and biased toward the luminous and massive tail of the
actively star-forming 'main-sequence', a fairly clear picture is emerging.
Independent of whether galaxy integrated quantities or surface densities are
considered, low- and high-z SFG galaxy populations appear to follow similar
molecular gas-star formation relations with slopes 1.1 to 1.2. The
gas-depletion time scale in these SFGs grows from 0.5 Gyrs at z~2 to 1.5 Gyrs
at z~0. Because star formation depletion times are significantly smaller than
the Hubble time at all redshifts sampled, star formation rates and gas
fractions are set by the balance between gas accretion from the halo and
stellar feedback. In contrast, very luminous gas rich major mergers at both
low-z and high-z produce on average 4 to10 times more far-infrared luminosity
per unit gas mass. Only some fraction of this difference can be explained by
uncertainties in gas-mass or luminosity estimators; much of it must be
intrinsic. The most likely interpretation is that the star formation relation
is driven by global dynamical effects. For a given mass, the more compact
merger systems produce stars more rapidly because their gas clouds are more
compressed with shorter dynamical times, so that they churn more quickly
through the available gas reservoir than the typical normal disk galaxies. When
the dependence on galactic dynamical time scale is explicitly included, disk
galaxies and mergers appear to follow similar gas to star-formation relations.
The mergers may be forming stars at slightly higher efficiencies than the
disks.
