The CO SLEDs of local galaxies and high-redshift SMGs normalised by L_IR⁴. Grey symbols indicate the Gaussian mean and deviation of the ratio for local galaxies mostly with  10⁹ L_⊙ ≤ L_IR ≤ 10¹² L_⊙ (Liu et al. 2015). We also include a typical local ULIRG, Arp 220 (purple dashed line and open triangles, Rangwala et al. 2011), an AGN-dominated source, Mrk 231 (red dashed line and open diamond, van der Werf et al. 2010), and a LIRG, NGC 7771 (green dashed line and open square, Liu et al. 2015). Red symbols show high-redshift SMGs from both Carilli & Walter (2013) and from this work. The dots without error bars (J_up = 10, 11) indicate that the volume of the values is insufficient for a normal-distribution fitting. We thus only indicate their mean value here. It is clear that the ratio of decreases with increasing J_up for local galaxies while it remains flat for high-redshift SMGs and a typical starburst-dominated ULIRG, Arp 220.