Scaling relations of the ALPINE targets. Top panels: M_dust vs. age (panel a) and M_gas vs. age (b). Middle panels: SFR vs. age (c) and M_dust vs. M_⋆ (d). Bottom panels: M_dust vs. SFR (e) and M_dust vs. M_gas (f). M_dust is computed by means of a MBB fit and assuming T = 25 K and β = 1.8. The blue and red points show detections at 4 < z < 5 and 5 < z < 6, respectively. In panel a the triangles around the points indicate galaxies classified as mergers or dispersion-dominated objects (Le Fèvre et al. 2020), whereas the black vertical dashed lines indicate the age of the Universe at redshift 4.5 and z = 5.5 (corresponding to an age of the Universe of 1.35 Gyr and 1.05 Gyr, respectively). The empty squares in panel c represent the ALPINE galaxies non-detected in continuum. The curves represent the chemical evolution models described in Sect. 4.1. The yellow, orange, and red solid lines represent proto-spheroid models of baryonic mass 3 × 10¹⁰, 10¹¹, and 10¹² M_⊙, respectively, computed with a standard Salpeter IMF (Salpeter 1955). The light green, green, and dark green dot-dashed lines are for three PSPHs with the same baryonic masses as above, but characterised by a top-heavy IMF (Larson 1998). The light cyan, cyan, and blue solid lines represent models for a dwarf spiral, an intermediate-mass spiral, and an M101-like spiral, respectively (Calura et al. 2017). The stars and squares plotted along each curve and in the same colour indicate the evolutionary times of 0.1 and 0.5 Gyr, respectively.