stellar particles. HOP uses a two-step procedure to identify individual galaxies. First, the algorithm assigns a density to each star particle based on the distribution of the surrounding particles and then hops from a particle to its densest nearby neighbor until a maximum is reached. All particles (with densities above a minimum threshold, $\delta_{outer}$) that reach the same maximum are identified as one coherent group. In the second step, groups are combined if the density at the saddle point which connects them is greater than $\delta_{saddle}$). We use HOP because of its physical basis, although we expect similar results would be found using a friends-of-friends halo finder. This has been tested and is robust using reasonable ranges of values (e.g. Tonnesen, Bryan, & van Gorkom 2007).

After we identify galaxies using stellar particles, we create our sample using only well-resolved galaxies within our refinement region. First, we restrict our sample to galaxies that have resided in the refined region since the beginning of the simulation. To do this, we require that all of the dark matter particles within the virial radius (in detail, we use r$_{200}$, the radius within which the average density is 200 times the critical density, which 