We exploit the continuity equation approach and “main-sequence” star formation timescales to show that the observed high abundance of galaxies with stellar masses ≳ a few 1010 M ⊙ at redshift z ≳ 4 implies the existence of a galaxy population featuring large star formation rates (SFRs) ψ ≳ 102 M ⊙ yr‐1 in heavily dust-obscured conditions. These galaxies constitute the high-redshift counterparts of the dusty star-forming population already surveyed for z ≲ 3 in the far-IR band by the Herschel Space Observatory. We work out specific predictions for the evolution of the corresponding stellar mass and SFR functions out to z ∼ 10, determining that the number density at z ≲ 8 for SFRs ψ ≳ 30 M ⊙ yr‐1 cannot be estimated relying on the UV luminosity function alone, even when standard corrections for dust extinction based on the UV slope are applied. We compute the number counts and redshift distributions (including galaxy-scale gravitational lensing) of this galaxy population, and show that current data from the AzTEC-LABOCA, SCUBA-2, and ALMA-SPT surveys are already addressing it. We demonstrate how an observational strategy based on color preselection in the far-IR or (sub-)millimeter band with Herschel and SCUBA-2, supplemented by photometric data from on-source observations with ALMA, can allow us to reconstruct the bright end of the SFR functions out to z ≲ 8. In parallel, such a challenging task can be managed by exploiting current UV surveys in combination with (sub-)millimeter observations by ALMA and NIKA2 and/or radio observations by SKA and its precursors.
