Compilation of HCN(4–3) vs. far-IR luminosity (upper) and HCO⁺(4–3) vs. far-IR luminosity (lower) observations. Individual datapoints show z = 0 galaxy-averaged (grey filled points Greve et al. 2009; Papadopoulos et al. 2014; Zhang et al. 2014) and resolved observations (grey open points Tan et al. 2018), and high-z detections in individual galaxies (Riechers et al. 2011a; Cañameras et al. 2021, black, solid) and Rybak et al. (in prep., black, open points) and spectral stacks (Spilker et al. 2014; Hagimoto et al. 2023). Where appropriate, luminosities are corrected for the lensing magnification. Dashed lines indicate the empirical trends from Zhang et al. (2014). The error bars for the HCO⁺(4–3) flux in SDP.81 are smaller than the data point (S/N ≈ 4). SDP.81 is ≈1σ above the mean Zhang et al. (2014) HCO⁺(4–3)-FIR trend.