Line ratios between dense-gas tracers and CO as a function of the intrinsic L_IR. Comparison samples are shown with the same symbols as in Fig. 6. In particular, the line ratios of local LIRGs and ULIRGs are taken from Baan et al. (2008, J = 1–0 transitions, blue triangles). The additional filled squares show HCN(3–2) in the Cosmic Eyelash and other upper flux density limits presented in Danielson et al. (2011). The CO(4–3) fluxes of the local star-forming galaxies and ULIRGs of Zhang et al. (2014, yellow squares) are taken from Rosenberg et al. (2015).