[@Leja:2013; @Mundy:2015; @Torrey:2015; @C17]). This type of selection is preferred over using a constant stellar mass cut to select galaxies at different epochs since it mitigates the need to assume a specific evolution model for the stellar mass, is insensitive to systematic shifts in the calculation of stellar masses and can be readily applied to observations. It also facilitates the comparison with galaxy samples selected using different properties (here, e.g., with galaxies selected by their SFR). [@C13] also showed that the HOD predictions for samples defined in this way are robust among different SAMs at a fixed redshift.

Fig. \[Fig:AMF\] shows the cumulative stellar mass function (top panel) and SFR function (bottom panel) for all redshifts studied here. The horizontal dashed lines show the different number density cuts we consider. The galaxies selected in each case are those to the right of the intersection with their associated dashed line. The top panel exhibits the expected growth of the galaxy stellar mass with time, while the bottom panel shows that there are fewer star forming galaxies at low redshifts than at high redshift.

![The cumulative stellar mass function (top panel) and the cumulative SFR function (bottom panel) predicted by the G13 