  We use the Millennium Simulation, a 10 billion particle simulation of the
growth of cosmic structure, to construct a new model of galaxy clustering. We
adopt a methodology that falls midway between the traditional semi-analytic
approach and the halo occupation distribution(HOD) approach. In our model, we
adopt the positions and velocities of the galaxies that are predicted by
following the orbits and merging histories of the substructures in the
simulation. Rather than using star formation and feedback `recipes' to specify
the physical properties of the galaxies, we adopt parametrized functions to
relate these properties to the quantity M_{infall}, defined as the mass of the
halo at the epoch when the galaxy was last the central dominant object in its
own halo. We test whether these parametrized relations allow us to recover the
basic statistical properties of galaxies in the semi-analytic catalogues,
including the luminosity function, the stellar mass function and the shape and
amplitude of the two-point correlation function evaluated in different stellar
mass and luminosity ranges. We then use our model to interpret recent
measurements of these quantities from Sloan Digital Sky Survey data. We derive
relations between the luminosities and the stellar masses of galaxies in the
local Universe and their host halo masses. Our results are in excellent
agreement with recent determinations of these relations by Mandelbaum et al
using galaxy-galaxy weak lensing measurements from the SDSS.
