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tokens: Acknowledgements The authors thank the anonymous referee for very helpful comments that improved this paper. The authors further thank A. Ferrara, R. Bouwens and N. Reddy for very helpful discussions related to this work. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00151.S, ADS/JAO.ALMA#2013.1.00034.S and ADS/JAO.ALMA#2012.1.00523.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under ESO programme ID 179.A-2005 and on data products produced by TERAPIX and the Cambridge Astronomy Survey Unit on behalf of the UltraVISTA consortium. This work was supported by the Swiss National Science Foundation through the SNSF Professorship grant 157567 ‘Galaxy Build-up at Cosmic Dawn’. ES acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 694343). BG gratefully acknowledges the support of the Australian Research Council as the recipient of a Future Fellowship (FT140101202). MTS acknowledges support from a Royal Society Leverhulme Trust Senior Research Fellowship (LT150041). VS acknowledges support from the European Union's Seventh Frame-work programme under grant agreement 337595 (ERC Starting Grant, ‘CoSMass’). OLF acknowledges support from the European Research Council Advanced Grant ERC-2010-AdG-268107-EARLY.