Illustration of our method. Panels (a) is a sketch of the richness-mass (N–M) relation measured at two different redshifts, at e.g., z = 1 (green) and z = 0.3 (black); the line and shaded regions represent relations and the associated uncertainties. Panel (b) is an example merger tree; the size and the color of the circles represent the mass and specific star formation rate of the halos. For our method, merger trees from a dark matter-only simulation are sufficient. We shall use panels (b), (c) and (d) to demonstrate our approach. Briefly speaking, one starts from a real cluster at high-z (step 1 in panel (c)); using the measured N–M relation at that redshift (e.g., green line in panel (a)), one infers a corresponding halo mass (step 2 in panel (c)), and try to find the closest halo in terms of mass at that redshift (step 2 in panel (b)). For a real cluster at low-z (step 3 in panel (d)), we use the low-z N–M relation to find the most appropriate mass (step 4 in panel (d)), then search for the best matched halo at that redshift (step 4 in panel (b)). This way, one can “connect” two observed clusters at the two cosmic epochs and study how the galaxy populations evolve (step 5). Panel (b) is generated courtesy of the IllustrisTNG collaboration (D. Nelson et al. 2019).