Evolution of the mean molecular gas fraction in massive galaxies (>3 × 10¹⁰M_⊙). The starbursts are represented by red squares and the main-sequence galaxies by blue triangles or light blue diamonds depending on wether the gas fraction is estimated using a broken or an universal FMR, respectively. These results are compared with previous estimate using dust masses of Magdis et al. (2012a, black plus) and Santini et al. (2014, gray area), using CO for two z> 3 galaxies (Magdis et al. 2012b, black crosses), and the compilation of CO measurements of Saintonge et al. (2013, black asterisks). The predictions of the models of Lagos et al. (2012) and Lacey et al. (in prep.) for the same mass cut are overplotted with a three-dot-dash line and a long-dash line, respectively.