  We study the dependence of the galaxy content of dark matter halos on
large-scale environment and halo formation time using semi-analytic galaxy
models applied to the Millennium simulation. We analyze subsamples of halos at
the extremes of these distributions and measure the occupation functions for
the galaxies they host. We find distinct differences in these occupation
functions. The main effect with environment is that central galaxies (and in
one model also the satellites) in denser regions start populating lower-mass
halos. A similar, but significantly stronger, trend exists with halo age, where
early-forming halos are more likely to host central galaxies at lower halo
mass. We discuss the origin of these trends and the connection to the stellar
mass -- halo mass relation. We find that, at fixed halo mass, older halos and
to some extent also halos in dense environments tend to host more massive
galaxies. Additionally, we see a reverse trend for the satellite galaxies
occupation where early-forming halos have fewer satellites, likely due to
having more time for them to merge with the central galaxy. We describe these
occupancy variations also in terms of the changes in the occupation function
parameters, which can aid in constructing realistic mock galaxy catalogs.
Finally, we study the corresponding galaxy auto- and cross-correlation
functions of the different samples and elucidate the impact of assembly bias on
galaxy clustering. Our results can inform theoretical models of assembly bias
and attempts to detect it in the real universe.
