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Connecting galaxies with their descendants (or progenitors) at differentredshifts can yield strong constraints on galaxy evolution. Observationalstudies have historically selected samples of galaxies using a physicalquantity, such as stellar mass, either above a constant limit or at a constantcumulative number density. Investigation into the efficacy of these selectionmethods has not been fully explored. Using a set of four semi-analytical modelsbased on the output of the Millennium Simulation, we find that selectinggalaxies at a constant number density (in the range $-4.3 < \log\ n\[\mathrm{Mpc}^{-3}\ h^{3}] < -3.0$) is superior to a constant stellar massselected sample, although it still has significant limitations. Recovery of theaverage stellar mass, stellar mass density and average star-formation rate ishighly dependent on the choice of number density but can all be recovered towithin $<50\%$ at the commonly employed choice of $\log\ n\ [\mathrm{Mpc}^{-3}\h^{3}] = -4.0$, corresponding to $\log M_\odot / h \sim 11.2$ at $z=0$, butthis increases at lower mass limits. We show that there is a large scatterbetween the location of a given galaxy in a rank ordering based on stellar massbetween different redshifts. We find that the inferred velocity dispersion maybe a better tracer of galaxy properties, although further investigation iswarranted into simulating this property. Finally, we find that over largeredshift ranges selection at a constant number density is more effective intracing the progenitors of modern galaxies than vice-versa.

Tracing galaxy populations through cosmic time: A critical test of methods for connecting the same galaxies between different redshifts at $z < 3$