  In a previous paper, we described a new method for including detailed
information about substructure in semi-analytic models of halo formation based
on merger trees. In this paper, we compare the predictions of our model with
results from self-consistent numerical simulations. We find that in general the
two methods agree extremely well, particularly once numerical effects and
selection effects in the choice of haloes are taken into account. As expected
from the original analyses of the simulations, we see some evidence for
artificial overmerging in the innermost regions of the simulated haloes, either
because substructure is being disrupted artificially or because the
group-finding algorithms used to identify substructure are not detecting all
the bound clumps in the highest-density regions. Our analytic results suggest
that greater mass and force resolution may be required before numerical
overmerging becomes negligible in all current applications. We discuss the
implications of this result for observational and experimental tests of halo
substructure, such as the analysis of discrepant magnification ratios in
strongly lensed systems, terrestrial experiments to detect dark matter
particles directly, or indirect detection experiments searching for positrons,
gamma-rays, neutrinos or other dark matter decay products.
