  The cumulative comoving number-density of galaxies as a function of stellar
mass or central velocity dispersion is commonly used to link galaxy populations
across different epochs. By assuming that galaxies preserve their
number-density in time, one can infer the evolution of their properties, such
as masses, sizes, and morphologies. However, this assumption does not hold in
the presence of galaxy mergers or when rank ordering is broken owing to
variable stellar growth rates. We present an analysis of the evolving comoving
number density of galaxy populations found in the Illustris cosmological
hydrodynamical simulation focused on the redshift range $0\leq z \leq 3$. Our
primary results are as follows: 1) The inferred average stellar mass evolution
obtained via a constant comoving number density assumption is systematically
biased compared to the merger tree results at the factor of $\sim$2(4) level
when tracking galaxies from redshift $z=0$ out to redshift $z=2(3)$; 2) The
median number density evolution for galaxy populations tracked forward in time
is shallower than for galaxy populations tracked backward in time; 3) A similar
evolution in the median number density of tracked galaxy populations is found
regardless of whether number density is assigned via stellar mass, stellar
velocity dispersion, or dark matter halo mass; 4) Explicit tracking reveals a
large diversity in galaxies' assembly histories that cannot be captured by
constant number-density analyses; 5) The significant scatter in galaxy linking
methods is only marginally reduced by considering a number of additional
physical and observable galaxy properties as realized in our simulation. We
provide fits for the forward and backward median evolution in stellar mass and
number density and discuss implications of our analysis for interpreting
multi-epoch galaxy property observations.
