Dependence of strong-line diagnostics on the ionization parameter. Upper panels: Strong-line diagnostics colour-coded according to the [S III]λλ9069, 9531/[S II]λλ6717, 6731 line ratio. Lower panels: Strong-line diagnostics colour-coded according to the [O III]λ5007/[O II]λλ3726, 3729 line ratio. We have labelled as ‘local’ the data from CHAOS, Curti’s, Guseva’s and Nakajima’s catalogues and as ‘high-z’ data from Sanders et al. (2023) and Laseter et al. (2024). The plotted curves are our diagnostic calibrations plus the high-redshift calibration from Sanders et al. (2023) for R₃.