Molecular gas fractions, f_gas = M_gas/ (M_gas + M_∗), as a function of redshift plotted for our low-L_IR-selected SFGs (squares) and our comparison sample of SFGs and local spirals with CO measurements from the literature (see Sect. 2.2). The molecular gas fractions are computed assuming a “Galactic” CO–H₂ conversion factor for all galaxies, but for z< 0.4 and z> 1 SFGs (pentagons, triangles, and squares) the dotted lines, in addition, show the interval of possible f_gas values as determined with two extreme CO–H₂ conversion factors α = 4.36 (“Galactic” value) and 1.1 (local ULIRG value). Four redshift bins are considered, ⟨ z_0.2 ⟩ = [ 0.055,0.4 ], ⟨ z_1.2 ⟩ = [ 1,1.6 ], ⟨ z_2.2 ⟩ = [ 2,2.5 ], and ⟨ z_3.0 ⟩ = [ 2.7,3.2 ], for f_gas means shown with large black crosses with their 1σ dispersion. A net rise of f_gas is observed from ⟨ z_0.2 ⟩ to ⟨ z_1.2 ⟩, followed by a very mild increase toward higher redshifts. The color-coding refers to four stellar mass intervals: log (M_∗/M_⊙) < 10 (black), 10.2 < log (M_∗/M_⊙) < 10.7 (red), 10.7 < log (M_∗/M_⊙) < 11 (green), and log (M_∗/M_⊙) > 11 (blue), as defined in Sect. 6.2.