Comparisons between H I fraction, Ω_H I(z), from different simulations (solid lines) and observational data (open circles) from Lah et al. (2007), Guimarães et al. (2009), Prochaska & Wolfe (2009), Noterdaeme et al. (2012), Delhaize et al. (2013), Rhee et al. (2013), Zafar et al. (2013), Crighton et al. (2015), Hoppmann et al. (2015), Sánchez-Ramírez et al. (2016), Rao et al. (2017), Bera et al. (2019). For further details, see Table 2 of Walter et al. (2020). The top panel shows all the H I in the galaxies and the IGM with no selection. We refer to Fig. 4 of Guo et al. (2023) for more details about the observations. The bottom panel shows Ω_H I of different theoretical models with a mass threshold of M_* > 10^8.5 M_⊙ (dashed lines). The labels are the same as in Figure 1.