@Manera12, it is well known that these approximations break down at small scales (e.g. @CWP09).

Alternatively, mock catalogs can be created using simulations which capture non-linear structure growth to smaller scales, and inherently include redshift-space distortions (velocity information of the dark matter particles is known). Ideally we would like large-volume cosmological simulations with both N-body and hydrodynamics, however, such simulations are computationally expensive. Hence, the large number of mocks necessary for obtaining robust error measurements renders this approach impractical. Fortunately, since pure N-body simulations are relatively inexpensive, the literature has been rife with methods for populating the dark matter halos found in these simulations with galaxies. One of the most popular methods for doing this is using halo occupation distributions (HODs) which is an analytic model for determining the number of galaxies ($N_{gal}$) that should form in a halo given its properties (e.g. @Zea09). More recently, subhalo abundance matching (SHAM) has become very prevalent (e.g. @CWK07 [@Vea10]). This method relies on being able to correctly identify the subhalos within a halo, a very difficult problem in its own right due to resolution limitations (see e.g. @Bea11). It then assumes that each subhalo contains a single galaxy with a stellar mass 