  We present the redshift distribution of the SHADES galaxy population based on
the rest-frame radio-mm-FIR colours of 120 robustly detected 850um sources in
the Lockman Hole East (LH) and Subaru XMM-Newton Deep Field (SXDF). The
redshift distribution derived from the full SED information is shown to be
narrower than that determined from the radio-submm spectral index, as more
photometric bands contribute to a higher redshift accuracy. The redshift
distribution of sources derived from at least two photometric bands peaks at z
~ 2.4 and has a near-Gaussian distribution, with 50 per cent (interquartile
range) of sources at z=1.8-3.1. We find a statistically-significant difference
between the measured redshift distributions in the two fields; the SXDF peaking
at a slightly lower redshift (median z ~ 2.2) than the LH (median z ~ 2.7),
which we attribute to the noise-properties of the radio observations. We
demonstrate however that there could also be field-to-field variations that are
consistent with the measured differences in the redshift distributions, and
hence, that the incomplete area observed by SHADES with SCUBA, despite being
the largest sub-mm survey to date, may still be too small to fully characterize
the bright sub-mm galaxy population. Finally we present a brief comparison with
the predicted, or assumed, redshift distributions of sub-mm galaxy formation
and evolution models, and we derive the contribution of these SHADES sources
and the general sub-mm galaxy population to the star formation-rate density at
different epochs.
