Comparison of HCN(1–0) and FIR luminosity in our sample (blue) with low-redshift galaxies (Gao & Solomon 2004b; Krips et al. 2008; García-Burillo et al. 2012) and high-redshift DSFGs and QSOs. For the lensed sources, we show the source-plane (de-lensed) values. The upper limit from the stacked spectrum (Fig. 4) is shown in orange. The purple line indicates the mean HCN/FIR ratio from Jiménez-Donaire et al. (2019) ±1σ scatter (Eq. (1)). The bulk of our sample falls below the linear HCN-FIR trend, in agreement with the expectations of a sub-linear correlation in highly star-forming galaxies (Krumholz & Thompson 2007; Narayanan et al. 2008).