plays a role. This foundation of the HOD method has its origins in the Press-Schechter formalism and the uncorrelated nature of the random walks used to describe halo assembly in excursion set theory. This leads to the prediction that the halo environment is correlated with halo mass but not with how the halo is assembled [@Bond:1991; @Lemson:1999; @White:1999]. This is, however, not the case for haloes in $N$-body simulations where halo populations of the same mass but with a different ‘secondary property’ display different clustering, an effect that is now generally termed [*(halo) assembly bias*]{}. This was convincingly demonstrated in the Millennium N-body simulation of [@Springel:2005] by [@Gao:2005] who showed the age-dependence of the clustering of haloes of the same mass (see also @Sheth:2004); this dependence of halo clustering on secondary properties besides mass was later extended to, e.g., concentration, spin, substructure (e.g., @Wechsler:2006 [@Gao:2007; @Jing:2007; @Lacerna:2012; @Xu:2017; @Villarreal:2017; @Mao:2018]).

[@Croton:2007] used a SAM applied to the Millennium Simulation to show that halo assembly bias also impacts the clustering of galaxies, an effect that is now commonly referred to as [*galaxy assembly bias*]{}, namely halo assembly bias as reflected in the galaxy distribution (see also @Zhu:2006 [@Zu:2008; @Lacerna:2011; @Chaves-Montero:2016]). This 