  We investigate the variations in galaxy occupancy of the dark matter haloes
with the large-scale environment and halo formation time, using two
state-of-the-art hydrodynamical cosmological simulations, EAGLE and Illustris.
For both simulations, we use three galaxy samples with a fixed number density
ranked by stellar mass. For these samples we find that low-mass haloes in the
most dense environments are more likely to host a central galaxy than those in
the least dense environments. When splitting the halo population by formation
time, these relations are stronger. Hence, at a fixed low halo mass,
early-formed haloes are more likely to host a central galaxy than late-formed
haloes since they have had more time to assemble. The satellite occupation
shows a reverse trend where early-formed haloes host fewer satellites due to
having more time to merge with the central galaxy. We also analyse the stellar
mass -- halo mass relation for central galaxies in terms of the large-scale
environment and formation time of the haloes. We find that low mass haloes in
the most dense environment host relatively more massive central galaxies. This
trend is also found when splitting the halo population by age, with
early-formed haloes hosting more massive galaxies. Our results are in agreement
with previous findings from semi-analytical models, providing robust
predictions for the occupancy variation signature in the halo occupation
distribution of galaxy formation models.
