Gas fraction as a function of stellar mass and sSFR. The red symbols show the AMAZE+LSD galaxies at z ~ 3–5 (same symbol-coding as Fig. 2). The solid lines show the incompleteness limit in the AMAZE unlensed (black) and lensed (red) galaxies. In the left panel the orange dots show the average gas fractions of local massive galaxies in bins of stellar mass, while green asterisks and triangles show the averages of the galaxies at 1 < z < 2 and 2 < z < 2.73, respectively, whose gas content has been measured through CO observations (Daddi et al. 2010; Saintonge et al. 2011, 2013; Tacconi et al. 2013). The upper-right error bars show the median error on the gas fraction and on the stellar mass in our sample. Right panel: gas fraction as a function of the sSFR, with the same symbol code as in the left panel.