a)–f) Differential extragalactic number counts used for the fit. h) Monochromatic LFs at different wavelengths and redshifts. a)–h) The fitted points are thicker. Black solid line: our best-fit model. Black dashed line: 1-σ range of the model. a)–c) Red diamonds: Béthermin et al. (2010a)Spitzer legacy number counts. c) Green triangles: Berta et al. (2010)Herschel/PEP number counts. d)–f) Red diamonds: Oliver et al. (2010)Herschel/Hermes number counts. Green triangles: Glenn et al. (2010)Herschel/Hermes P(D) analysis. Clements et al. (2010)Herschel/ATLAS number counts. Purple cross: Béthermin et al. (2010b) BLAST number counts. g) Green triangles: Scott et al. (2010) AzTEC number counts in the CDFS field. Green triangles: Austermann et al. (2010) AzTEC number counts in the SHADES field. h) Red plus: Rodighiero et al. (2010) local 24 μm LF (not fitted points in grey). Green diamonds: Saunders et al. (1990) local 60 μm LF (shifted by a factor 10 on the y-axis; not fitted points in grey); blue triangles: Rodighiero et al. (2010) 15 μm LF at z = 0.6 (shifted by a factor 100 on the y-axis; not fitted points in grey). Purple squares: Rodighiero et al. (2010) 12 μm LF at z = 1 (shifted by a factor 1000 on the y-axis; not fitted points in grey). Cyan crosses: Caputi et al. (2007) 8 μm LF at z = 2 (shifted by a factor 10 000 on the y-axis).