Comparison of the S₈₅₀ flux densities of the EAGLE galaxies calculated using the RT or the parametric relation given in Equation (1) with the parameter values listed in Table 2. Here, the solid blue color shows the RT results, dotted orange shows the results for the Hayward et al. (2013) relation (H13), dashed green the Lovell et al. (2021) relation (L21), and dash-dotted pink the Cochrane et al. (2023) relation (C23). The shaded regions represent 1σ uncertainties. Panels (a) and (b) show the evolution of the co-moving number density for, respectively submillimeter-bright galaxies (S₈₅₀ > 1 mJy), and submillimeter-faint star-forming galaxies (S₈₅₀ < 1 mJy, SFR > 80 M_⊙/yr). The L21 and C23 relations exhibit very similar results and are consistent with the RT calculations. However, the H13 relation overestimates the submillimeter flux densities compared to RT.