Inferred hierarchical parameters with depletion effects, for the five models listed in Table 1. Top: hierarchical merger rates and cluster parameters for hierarchical mergers with depletion effects considered. Note that the fiducial model, based on globular clusters, vastly underestimates the inferred cluster scales. Bottom: merger cross-section indices for ﹩{\rm{\Gamma }}\propto {M}^{a}\,{\eta }^{b}﹩, for different models both with and without depletion. Note that the only significant difference comes from using the Fryer natal population.