  We utilize detailed time-varying models of the coupled evolution of stars and
the HI, H_2, and CO-bright H_2 gas phases in galaxy-sized numerical simulations
to explore the evolution of gas-rich and/or metal-poor systems, expected to be
numerous in the Early Universe. The inclusion of the CO-bright H_2 gas phase,
and the realistic rendering of star formation as an H_2-regulated process (and
the new feedback processes that this entails) allows the most realistic
tracking of strongly evolving galaxies, and much better comparison with
observations. We find that while galaxies eventually settle into states
conforming to Schmidt-Kennicutt (S-K) relations, significant and systematic
deviations of their star formation rates (SFRs) from the latter occur,
especially pronounced and prolonged for ...
  ...This indicates potentially serious limitations of (S-K)-type relations as
reliable sub-grid elements of star formation physics in simulations of
structure formation in the Early Universe. We anticipate that galaxies with
marked deviations from the S-K relations will be found at high redshifts as
unbiased inventories of total gas mass become possible with ALMA and the EVLA.
