simulation using a friends-of-friends (FoF) halo finder. Substructures inside the FoF groups are then identified using the [SUBFIND]{} code described in [@springel01]. For the most massive subgroup in a FoF group the virial radius and mass are determined with a spherical overdensity criterion: the density inside a sphere centered on the most bound particle is required to be greater than or equal to the value predicted by the spherical collapse model for a tophat perturbation in a $\Lambda$CDM cosmology [@bryan98]. As discussed above, for subhalos we use the maximum mass over its past history, which is typically the mass when the halo was last a distinct halo and did not yet overlap with its later host. Merger trees were constructed out of the halo catalogs at 94 time-steps, equally spaced in expansion factor ($\Delta a=0.01$), based on the particle overlap of halos at different time-steps.

Due to the finite mass resolution of the simulation ($M_{\rm min,halo}\simeq 10^{10} {\!\,{\rm M}_\odot}$), subhalos can no longer be identified when their mass has dropped below this limit due to tidal stripping. Since mass loss can be substantial (&gt;90%) this is important even for fairly massive subhalos. A special treatment of these so-called “orphans” is 