subhalo merger tree. The semi-analytical code uses these merger trees as the starting point to build its galaxy catalogue. Here, the mass of a dark matter halo, $\rm M_{h}$, is defined as the mass within the radius where the halo overdensity is 200 times the critical density of the simulation (referred to as “m\_crit200” in the public database).

The galaxy and halo samples {#Sec:Samples}
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### Classifying samples by galaxy properties

For the main part of our analysis we use samples defined by galaxy number density. To do this we rank the model galaxies either by stellar mass or SFR and include all galaxies above a particular value of the stellar mass or SFR threshold that provides the desired number density. We construct galaxy samples for three different number densities, $n = 0.01, 0.00316$ and $ 0.001 
\,h^{3}\, {\rm Mpc}^{-3}$, and for a wide range of redshifts: $z=0, 0.5, 1, 1.5,
2, 2.5$ and $ 3$. The samples are chosen to be evenly spaced in logarithmic number density with differences of half a decade in log abundance.

The cumulative comoving number density of galaxies ranked by stellar mass is often used to link galaxy populations across cosmic time (e.g., @Padilla:2010 