Detection of substructures at a rest-frame wavelength of 1 μm for the entire sample (black) and for three substructure types: clumps (blue), moderately large ones (orange), and extended ones (pink). See Sect. 4.2 for more details. Left: fraction of galaxies with at least one substructure detected with the optimal approach (see Sect. 3.2) as a function of redshift. We show the rest-frame NIR detections carried out by Kalita et al. (2024) (red dashed line) and those in the rest-frame UV by Sattari et al. (2023) (green line and crosses). Middle: same but for the intrinsic detection approach (see Sect. 3.3). We show as a light red line a comparable 2σ detection (k_p = 2, see reference) carried out in the rest-frame UV from Ribeiro et al. (2017) and, as a light green line, estimated fractions from the simulations studied in Mandelker et al. (2017, see Appendix D). In both figures on the left-hand side and in the middle, for each sample, we show uncertainties (16th and 84th percentiles) as shaded areas with similar colors. Right: median fraction of flux in substructures as a function of redshift for galaxies with at least one substructure. The uncertainties are shown with a blue shaded area for clumps, a double-dashed orange area for moderately large substructures, a single-dashed pink area for extended substructures, and a black shaded area for the entire sample.