  This paper examines several methods of tracing galaxies in N-body simulations
and their effects on the derived galaxy statistics, especially measurements of
velocity bias. Using two simulations with identical initial conditions, one
following dark matter only and the other following dark matter and baryons,
both collisionless and collisional methods of tracing galaxies are compared to
one another and against a set of idealized criteria. None of the collisionless
methods proves satisfactory, including an elaborate scheme developed here to
circumvent previously known problems. The main problem is that galactic
overdensities are both secularly and impulsively disrupted while orbiting in
cluster potentials. With dissipation, the baryonic tracers have much higher
density contrasts and much smaller cross sections, allowing them to remain
distinct within the cluster potential. The question remains whether the
incomplete physical model introduces systematic biases. Statistical measures
determined from simulations can vary significantly based solely on the galaxy
tracing method utilized. The two point correlation function differs most on
sub-cluster scales with generally good agreement on larger scales. Pairwise
velocity dispersions show less uniformity on all scales addressed here. All
tracing methods show a velocity bias to varying degrees, but the predictions
are not firm: either the tracing method is not robust or the statistical
significance has not been demonstrated. Though theoretical arguments suggest
that a mild velocity bias should exist, simulation results are not yet
conclusive.
