the universe is then $13.6
\times 10^{9}$ yr. The positions and velocities of all particles were stored at 63 epochs spaced approximately logarithmically in expansion factor at early times and at approximately 300 Myr intervals after $z=2$. For each such snapshot a friends-of-friends group-finder was used to locate all virialised structures, and their self-bound substructures (subhalos) were identified using [SUBFIND]{} [@swtk01]. Halos and subhalos in neighbouring outputs were then linked in order to build formation history trees for all the subhalos present at each time. These data are publicly available at the Millennium release site[^3]. A “Milky Way” halo at $z=0$ typically contains a few thousand particles and several resolved subhalos.

Galaxy formation was simulated within these merging history trees by using semi-analytic models to follow the evolution of the baryonic components associated with each halo/subhalo. Processes included are radiative cooling of diffuse gas, star formation, the growth of supermassive black holes, feedback of energy and heavy elements from supernovae and AGN, stellar population evolution, galaxy merging and effects due to a reionising UV background. The $z=0$ galaxy catalogue we analyse here corresponds to the specific model of @croton06 and details of its assumptions and parameters can be found in 