Upper panel: cosmic evolution of molecular gas fraction (f_gas) in our DSFGs, estimated from the functional form of Liu et al. (2019a) and illustrated with shaded areas. The model predictions for MS and SB DSFGs are overplotted with dashed and dotted lines, respectively. Purple, blue, and grey lines correspond to P19, SIMBA, and B17 respectively. For P19 and SIMBA, the f_gas is derived self-consistently, while for B17, we test the same scaling relation we apply in our observations. Lower panel: δ_DGR as a function of f_gas for the full sample of observed and modelled galaxies. Observed mean ratios with corresponding 1σ uncertainty are presented with black circles. The significance of colours that correspond to modelled values is the same as in the upper panel.