| Summary: | © 2017 The Authors. Galaxy cumulative 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 (1) the non-conservative nature of total galaxy number density driven by galaxies combining in mergers (which we tabulate as a galaxy 'coagulation' rate) and (2) galaxy 'mass rank scatter' driven by stochasticity in stellar-mass growth rates from in situ star formation and mergers. We quantify the relative contribution of these two effects to the total mass rank order evolution using the Illustris simulation. 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, coagulation has been the dominant effect since z = 2.2, but a galaxy population at 10 11 M was dominated by mass rank scatter until z = 0.6. We show that although the forward and backward median cumulative number density evolution tracks are asymmetric, the backward median cumulative number density evolution can be obtained by convolving the descendant distribution function with progenitor relative abundances. We tabulate fits for the median cumulative number density evolution and scatter that can be applied to improve the way galaxy populations are linked in multi-epoch observational data sets.
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