Evolution of HMF (cyan line) vs. SMF (magenta) from z = 0.2 to 5.5. In each panel halo mass is multiplied by a factor 0.018, that is, the SHMR at z = 0 and (according to Behroozi et al. 2013). Shaded cyan regions show the uncertainties in the HMF shift by taking the 1σ error of the SHMR parametrisation. At z> 2.5, the solid magenta line is our fiducial fit of the SMF, while the dashed magenta line is the Schechter function with log (ℳ_⋆/ ℳ_⊙) fixed to 10.6 (see Fig. 8). The shaded magenta regions combine the 1σ CL of the two fits, to give a conservative estimate of the uncertainties. A grey shaded area highlights the “forbidden region” where, according to the Ω_b/ Ω_m ratio, no galaxies are expected. Black dotted lines at z> 3 are the SMFs predicted from the semi-analytical model of Garel et al. (2016), converted to the IMF of Chabrier (2003).