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 $0leq z leq 3$. 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.
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