function and roughly a power-law for the satellites. For samples defined by SFR or color, the shape of the halo occupation function is more complex to account for the paucity of blue/star forming centrals in massive haloes (e.g., @Zehavi:2005 [@Geach:2012; @C13; @Gonzalez:2018]). We emphasize that the HODs presented in this work are all calculated directly from the SAMs, rather than inferred from the clustering, as is commonly done with observational data.

The correlation function (CF) is the most fundamental measure of the spatial distribution of haloes and galaxies. It is defined as the excess probability of finding a pair of objects at a given separation compared to a random distribution. Following [@Gao:2007] and Z18, whenever we measure the CF for the full galaxy sample we calculate the auto CF (the correlation of a given sample of objects with respect to the same sample). In contrast, when we measure the CF of a subsample of galaxies (e.g., the ones associated with the 20 per cent earliest-formed haloes) we measure the cross CF between this sample and the full galaxy sample. As explained in Z18 (see specifically their Appendix B) using the cross CF increases the signal-to-noise of the measurements and facilitates 