Evolution of the dust to stellar mass ratio and of the gas fraction of QGs. The filled blue circles mark the M_dust/M_* of the stacked QGs in the 0.3 < z < 2.0 range, including the results from G18. The grey shaded region depicts the trend for MS galaxies from Kokorev et al. (2021). The orange shaded region captures the range of M_dust/M_* for local QGs, as drawn from the literature (see text). The dotted blue line (blue shaded region) corresponds to the best fit (scatter) to the 0.0 < z < 1.0 M_dust/M_* data of QGs, with a functional form of M_dust/M_* ∝ (1 + z)^5.0. The bold, dashed purple line (shaded region) depicts the evolution (scatter) of M_dust/M_* (and of f_gas) as derived from the progenitor bias analysis of Gobat et al. (2020), which is discussed in Sects. 5.2 and 6. The conversion of M_dust/M_* to f_gas assumes solar metallicity and GDR = 92.