Time evolution of the neutral hydrogen fraction (1 − Q_HII) for models with different slope indexes n_B. The reference simulation (full box) is indicated by the gray curve. The model predictions are compared to observational constraints of the neutral hydrogen fraction from Ly-α absorption of quasars (Fan et al. 2006b) as brown downward triangles; (McGreer et al. 2015) pink pentagons; (Schroeder et al. 2013) purple, (Davies et al. 2018a,b) red, (Greig et al. 2017, 2019) green, (Bañados et al. 2018) orange, and (Durovčíková et al. 2020) blue circles; or gamma-ray bursts (Totani et al. 2006) as a green cross; and by Ly-α emitting galaxies (Ouchi et al. 2010) as an orange star, and (Ono et al. 2012) cyan, (Schenker et al. 2014) gray, and (Tilvi et al. 2014) yellow triangles.