Molecular gas depletion timescales plotted for the ALPINE nonmerger galaxies distributed in two redshift bins of 4.4 <  z <  4.6 and 5.1 <  z <  5.9 (red circles; encircled red circles mark the ALPINE galaxies detected in FIR dust continuum; crossed red circles mark the ALPINE galaxies with dynamical mass measurements; and light-red arrows correspond to 3σ upper limits) and for our compilation of CO-detected MS SFGs from the literature color-coded in six redshift bins of z = 0 (pink crosses), 0 <  z <  0.1 (yellow pluses), 0.1 <  z <  1 (orange stars), 1 <  z <  1.5 (violet open pentagons), 1.5 <  z <  2.5 (green squares), and 2.5 <  z <  3.7 (blue triangles, plus the Pavesi et al. 2019 object at z = 5.65). Left panel: molecular gas depletion timescales shown as a function of redshift. The respective means, errors on the means, and standard deviations per redshift bin are indicated by the large black/gray crosses. The light-gray shaded area corresponds to the depletion timescales obtained by Béthermin et al. (2015) from FIR SED stacks. The t_depl means per redshift bin follow a decrease out to z ∼ 6, but much shallower than the (1 + z)^−1.5 decline predicted in the framework of the bathtub model (dotted line). Middle panel: molecular depletion timescales shown as a function of specific star formation rate. A strong anti-correlation between t_depl and sSFR is observed at z = 0 (yellow solid line from Saintonge et al. 2011) and at high redshift. The displacement along the sSFR-axis for galaxies at higher redshift is compatible with the sSFR evolution with redshift (violet dashed line at z = 1, green dashed-dotted line at z = 2, and red dotted line at z = 5, as computed using the sSFR(z) parametrization from Speagle et al. 2014, Eq. (28)). Right panel: molecular depletion timescales restricted to z = 1 − 5.9 SFGs and shown as a function of stellar mass. No correlation between t_depl and M_stars is observed.