  Using a cosmological N-Body simulation and a sample of re-simulated
cluster-like haloes, we study the mass loss rates of dark matter subhaloes, and
interpret the mass function of subhaloes at redshift zero in terms of the
evolution of the mass function of systems accreted by the main halo progenitor.
When expressed in terms of the ratio between the mass of the subhalo at the
time of accretion and the present day host mass the unevolved subhalo mass
function is found to be universal. However, the subhalo mass function at
redshift zero clearly depends on $M_0$, in that more massive host haloes host
more subhaloes. To relate the unevolved and evolved subhalo mass functions, we
measure the subhalo mass loss rate as a function of host mass and redshift. We
find that the average, specific mass loss rate of dark matter subhaloes depends
mainly on redshift. These results suggest a pleasingly simple picture for the
evolution and mass dependence of the evolved subhalo mass function. Less
massive host haloes accrete their subhaloes earlier, which are thus subjected
to mass loss for a longer time. In addition, their subhaloes are typically
accreted by denser hosts, which causes an additional boost of the mass loss
rate. To test the self-consistency of this picture, we use a merger trees
constructed using the extended Press-Schechter formalism, and evolve the
subhalo populations using the average mass loss rates obtained from our
simulations, finding the subhalo mass functions to be in good agreement with
the simulations. [abridged]
