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.