Fig. 6: Redshift evolution of galaxy scaling relations.

The star-forming sequence (SFS, a, b), neutral gas sequence (NGS, c, d), and molecular gas sequence (MGS, e, f) and their redshift evolutions as predicted by two simple analytic models that link star formation rates (SFRs) and gas masses (M_gas) of galaxies via \({\rm{SFR}}={M}_{{\rm{gas}}}{f}_{{\rm{H}}2}/{t}_{{\rm{dep}},{{\rm{H}}}_{2}}\) and \({t}_{{\rm{dep}},{{\rm{H}}}_{2}}\propto {M}_{{\rm{star}}}^{0.28}\ {{\rm{SFR}}}^{-0.24}\). In both models, the stellar mass (M_star) is the integral of the SFR, i.e., stellar mass loss and mergers are ignored. Furthermore, the molecular-to-total gas mass ratio (f_H2) is assumed to depend only on stellar mass with f_H2(M_star) given by the scalings of the molecular and neutral gas sequences. In each panel, solid lines connect galaxy populations at a fixed redshift (z = 6–0 from top to bottom), while dashed lines show the time evolution of individual galaxies. Linear slopes are indicated by dotted lines. a, c, e Predictions of an equilibrium model in which M_gas does not change with time. The SFS has a slope of 1, while the slope of the MGS (NGS) is slightly steeper (less steep) than linear. b, d, f Predictions of a model with a time-dependent M_gas such that M_gas peaks at earlier times in more massive galaxies ('downsizing'). This second model is successful in reproducing the sub-linear slopes of the SFS, MGS, and NGS (thick straight lines). Furthermore, it predicts that the slope of the SFS becomes steeper and more linear at higher redshift in qualitative agreement with observations^38,48,49.