  A central challenge in observational studies of galaxy formation is how to
associate progenitor galaxies with their descendants at lower redshifts. One
promising approach is to link galaxies at fixed number density, rather than
fixed luminosity or mass. This method is effective if stellar mass rank order
is broadly conserved through cosmic time. In this paper, we use the Guo et al.
(2011) semi-analytical model to analyze under what circumstances this
assumption is valid in the context of a cosmological simulation. Specifically,
we select progenitor galaxies at a constant number density and compare the
stellar mass evolution of their descendants to the evolution at a constant
number density. The median stellar mass of the descendants increases by a
factor of four (0.6 dex) from z = 3 to z = 0. Constant number density selection
reproduces this to within 40% (0.15 dex) over a wide range of number densities.
We show that the discrepancy primarily results from scatter in the stellar mass
growth rates and merging. After applying simple, observationally-based
corrections for these processes, the discrepancy is reduced to 12% (0.05 dex).
We conclude that number density selection can be used to predict the median
descendant mass of high-redshift progenitor galaxies. The main uncertainty in
this study is that semi-analytical models do not reproduce the observed mass
evolution of galaxies, which makes the quantitative aggregate effects of star
formation, merging, and quenching on the rank order of galaxies somewhat
uncertain.
