for a decline in L(850 (rest)) at $z>4$, so in common with other parts of the simulation we assume a decline of the form $(1+z)^{-7.9}$ at $z>4.8$. We note, however, that Rawlings et al. (2004) found any explicit redshift dependence to be small or absent. Although Willott et al. (2002) found tentative evidence for an anti-correlation between radio-source size and sub-mm luminosity for quasars, no such trend was found for the radio galaxy sample of Reuland et al. (2004) and we have chosen not to incorporate one.

Finally, we remark that our treatment of the infrared SED is confined to reprocessed dust emission due to star formation and AGN heating. As a result, we have not endeavoured to incorporate an infrared synchrotron emission component in the beamed radio-loud AGN. If required, such a component could be added as an extrapolation of the radio SED given in the $S^{3}$ database, following the beaming treatment described by W08. It would only have a significant effect on the predicted source counts at the brightest flux densities.

COMPARISON WITH EXISTING OBSERVATIONS
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The prescriptions outlined in section 2 constitute our ‘baseline model’. Here we compare its source counts and other derived quantities against observations. 