follows: in section \[s:simulation\] we describe the $N$-body simulation, the halo finding algorithm that was used to obtain a halo catalogue and the treatment of ‘orphaned’ galaxies. Section \[s:galaxies\] specifies our model: we motivate the form of the stellar-to-halo mass (SHM) relation and constrain it by requiring that the observed SMF is reproduced. The clustering properties of galaxies are then inferred from those of the halo population. We discuss the meaning of the parameters of the SHM relation and demonstrate that clustering puts only weak constraints on them. In section \[s:cmf\] we introduce the CMF, which describes how halos are occupied by galaxies, and compute the occupation numbers. Section \[s:comparison\] gives a comparison between our results and several other models and observations. In section \[s:redshift\] we apply our method to higher redshifts and determine the redshift dependence of the SHM relation. We make predictions of the stellar mass dependent galaxy CF at higher redshift which we use to compute the galaxy bias. Finally, we summarize our methods and conclusions in section \[s:conclusions\].

Throughout this paper we assume a $\Lambda$CDM cosmology with ($\Omega_m$,$\Omega_{\Lambda}$,$h$,$\sigma_8$,$n$) = ($0.26$,$0.74$,$0.72$,$0.77$,$0.95$). We employ a @kroupa01 initial mass function (IMF) and convert all stellar masses to this IMF. 