The relation between subhalo mass fraction, f_s, and the host halo's ‘dynamical age’, N_τ, defined as the number of dynamical time-scales elapsed since the formation of the (average) host halo (see equation 17). The left- and right-hand panels correspond to first- and second-order subhaloes, respectively. Symbols of different size and shades indicate different cosmologies. For each cosmology, there are five points, corresponding to the five halo masses, log (M₀/ h^{− 1}M_⊙) = 11, 12, …, 15. The red lines are the best-fitting relations given by equations (19) and (20).