M_min versus M₁ for the HODs produced when one non-mass parameter is varied and M₁ and M_min are optimized to achieve the target bias and density. The ends of each curve are marked with an open square for the lowest value of that parameter and a filled square for the highest (see Table 1 for the parameter ranges). All HOD curves intersect at the location of the baseline model. Top panel: HODs that vary the parameters α_hod, σ_{log M}, and f_cen. Middle panel: HODs that vary the assembly bias parameters A_cent, A_sat, B_cent, and B_sat (inset: closeup of the curves for A_cent and A_sat). Bottom panel: HODs that vary the target values of bias and density while keeping the non-mass parameters fixed at baseline. Gray dashed curves in each panel correspond to the curves from the other two panels for reference.