Average SHMFs (upper) and SHVFs (lower) obtained by averaging over 10 000 merger trees each. Left-hand panel: the unevolved (dashed) and evolved (solid) subhalo mass and velocity functions of different host halo masses. Middle: the evolved mass and velocity functions of subhaloes of different orders, for host halo mass M₀ = 10¹³ h^{− 1}M_⊙. Right-hand panel: the unevolved (dashed) and evolved (solid) subhalo mass and velocity functions for halo mass M₀ = 10¹³ h^{− 1}M_⊙ at different redshifts as indicated.