Redshift evolution of various model quantities, shown as following from top to bottom. Panel (a): Statistical prediction of the Mg II comoving line density dN/dX for three cuts in W_r²⁷⁹⁶ chosen to match published data (colored lines). Data points with the same color codes are from Sebastian et al. (2024) and Chen (2017). Panel (b): Observed L > 0.01L^⋆ luminosity-weighted space density of UV-bright galaxies (Bouwens et al. 2021) shown for both fixed and evolving β. Panel (c): Statistical prediction of the Mg II halo radius. Panel (d): Same as panel (c) but for the volume filling factor. Since W_r is binned, both R and f_V are averages. The magenta line in panels (a), (c), and (d) represents a constant-velocity wind starting at the Big Bang. Model uncertainties are propagated from those of f and ϕ. A non-evolving β would shift ⟨n⟩_L upward by a factor of ≈3, and shift R and f_V downward by ≈1.7 and ≈5, respectively.