  Galaxy populations at different cosmic epochs are often linked together by
comoving cumulative number density in observational studies. Many theoretical
works, however, have shown that the number densities of tracked galaxy
populations evolve in bulk and spread out over time. We present a number
density method for linking progenitor and descendant galaxy populations which
takes both of these effects into account. We define probability distribution
functions that capture the evolution and dispersion of galaxy populations in
comoving number density space, and use these functions to assign galaxies at
one redshift $z_f$ probabilities of being progenitors or descendants of a
galaxy population at another redshift $z_0$. These probabilities are then used
as weights for calculating distributions of physical properties such as stellar
mass, star formation rate, or velocity dispersion within the
progenitor/descendant population. We demonstrate that this probabilistic method
provides more accurate predictions for the evolution of physical properties
then either the assumption of a constant number density or the assumption of an
evolving number density in a bin of fixed width by comparing the predictions
against galaxy populations directly tracked through a cosmological simulation.
We find that the constant number density method performs most poorly at
recovering galaxy properties, the evolving number method density slightly
better, and the probabilistic number density method best of all. The
improvement is present for predictions of both stellar mass as well as inferred
quantities such as star formation rate and velocity dispersion which were not
included in the number density fits. We demonstrate that this method can also
be applied robustly and easily to observational data, and provide a code
package for doing so.
