Forward and backward galaxy evolution in comoving number density space
  Galaxy comoving number density is commonly used to forge
progenitor/descendant links between observed galaxy populations at different
epochs. However, this method breaks down in the presence of galaxy mergers, or
when galaxies experience stochastic growth rates. We present a simple analytic
framework to treat the physical processes that drive the evolution and
diffusion of galaxies within comoving number density space. The evolution in
mass rank order of a galaxy population with time is influenced by the galaxy
coagulation rate and galaxy "mass rank scatter" rate. We quantify the relative
contribution of these two effects to the mass rank order evolution. We show
that galaxy coagulation is dominant at lower redshifts and stellar masses,
while scattered growth rates dominate the mass rank evolution at higher
redshifts and stellar masses. For a galaxy population at $10^{10} M_\odot$,
coagulation has been the dominant effect since $z=2.2$, but a galaxy population
at $10^{11} M_\odot$ was dominated by mass rank scatter until $z=0.6$. We show
that although the forward and backward median number density evolution tracks
are asymmetric, the backward median number density evolution can be obtained by
convolving the descendant distribution function with progenitor relative
abundances. We tabulate fits for the median number density evolution and
scatter which can be applied to improve the way galaxy populations are linked
in multi-epoch observational datasets.
