Notes. ⁽¹⁾ All the models are based on two SF mode formalism. Stellar mass function (SMF) is described by a double Schechter function: , where M^* is the characteristic mass of the Schechter break. The M^* is the redshift invariant in the Béthermin et al. (2012) model, and evolves with redshift in the other two presented models. For redshifts z > 4, the model of Béthermin et al. (2017) assumes a single Schechter function fixing at zero, while the model of Schreiber et al. (2016) adopts double Schechter fitting to results of Grazian et al. (2015) for 4.5 < z < 7. ⁽²⁾ The specific star-formation rate, definedas sSFR = SFR/M_*. In Béthermin et al. (2012) the sSFR increases with redshift up to z = 2.5 and than flattens. This trend is independent of the chosen range of stellar masses. In the latter two models the evolution is different, see Eq. (6) in Béthermin et al. (2017). ⁽³⁾Modelled width of themain sequence (as log-normal scatter).