  We use the Millennium Simulation database to compare how different versions
of the Durham and Munich semi-analytical galaxy formation models populate dark
matter haloes with galaxies. The models follow the same physical processes but
differ in how these are implemented. All of the models we consider use the
Millennium N-body Simulation; however, the Durham and Munich groups use
independent algorithms to construct halo merger histories. We compare the
predicted halo occupation distributions (HODs) and correlation functions for
galaxy samples defined by stellar mass, cold gas mass and star formation rate.
The predictions for the HOD are remarkably similar for samples ranked by
stellar mass. The predicted bias averaged over 5-25 Mpc/h is consistent between
models to within 10%. At small pair separations there is a difference in the
predicted clustering. This arises because the Durham models allow some
satellite galaxies to merge with the central galaxy in a halo when they are
still associated with resolved subhaloes. The agreement between the models is
less good for samples defined by cold gas mass or star formation rate, with the
small scale clustering differing by an order of magnitude, reflecting the
uncertainty in the modelling of star formation. The model predictions in these
cases are qualitatively similar, with a markedly shallower slope for the
correlation function than is found for stellar mass selected samples and with
the HOD displaying an asymmetric peak for central galaxies. We provide
illustrative parametric fits to the HODs predicted by the models. Our results
reveal the current limitations on how well we can predict galaxy bias in a
fixed cosmology, which has implications for the interpretation of constraints
on the physics of galaxy formation from galaxy clustering measurements and the
ability of future galaxy surveys to measure dark energy.
