Velocity widths versus metallicity relation. Shaded area: the simulated data from Revaz & Jablonka (2018) and Roca-Fàbrega et al. (2021) at six redshifts from z = 4.12 to 0.33 (numbers in gray), with vertical lines marking different models. Symbols show the data obtained from observations: total metallicities [M/H]_tot corrected for dust depletion by Velichko et al. (2024) and Δv₉₀ found in the literature in the redshift ranges z ≤ 2.1 (violet diamonds) and z > 2 (green diamonds). Gray lines show the best fit of data on 70 DLAs at redshifts of 1.7 < z < 2.43 (dashed line) and 2.43 < z < 4.3 (dash-dotted line) from Ledoux et al. (2006), biased in metallicity by +0.2 and +0.35 dex for the high- and low-z subsamples, respectively, to roughly take into account the dust depletion.