We present predictions for the clustering of galaxies selected by their emission at far infra-red (FIR) and sub-millimetre wavelengths. This includes the first predictions for the effect of clustering biases induced by the coarse angular resolution o
f single-dish telescopes at these wavelengths. We combine a new version of the GALFORM model of galaxy formation with a self-consistent model for calculating the absorption and re-emission of radiation by interstellar dust. Model galaxies selected at $850$ $mu$m reside in dark matter halos of mass $M_{rm halo}sim10^{11.5}-10^{12}$ $h^{-1}$ M$_{odot}$, independent of redshift (for $0.2lesssim zlesssim4$) or flux (for $0.25lesssim S_{850murm m}lesssim4$ mJy). At $zsim2.5$, the brightest galaxies ($S_{850murm m}>4$ mJy) exhibit a correlation length of $r_{0}=5.5_{-0.5}^{+0.3}$ $h^{-1}$ Mpc, consistent with observations. We show that these galaxies have descendants with stellar masses $M_{star}sim10^{11}$ $h^{-1}$ M$_{odot}$ occupying halos spanning a broad range in mass $M_{rm halo}sim10^{12}-10^{14}$ $h^{-1}$ M$_{odot}$. The FIR emissivity at shorter wavelengths ($250$, $350$ and $500$ $mu$m) is also dominated by galaxies in the halo mass range $M_{rm halo}sim10^{11.5}-10^{12}$ $h^{-1}$ M$_{odot}$, again independent of redshift (for $0.5lesssim zlesssim5$). We compare our predictions for the angular power spectrum of cosmic infra-red background anisotropies at these wavelengths with observations, finding agreement to within a factor of $sim2$ over all scales and wavelengths, an improvement over earli
Recent observational evidence suggests that the coarse angular resolution ($sim20$ FWHM) of single-dish telescopes at sub-mm wavelengths has biased the observed galaxy number counts by blending together the sub-mm emission from multiple sub-mm galaxi
es (SMGs). We use lightcones computed from an updated implementation of the galform semi-analytic model to generate $50$ mock sub-mm surveys of $0.5$ deg$^2$ at $850$ $mu$m, taking into account the effects of the finite single-dish beam in a more accurate way than has been done previously. We find that blending of SMGs does lead to an enhancement of source extracted number counts at bright fluxes ($S_{mathrm{850}mumathrm{m}}gtrsim1$ mJy). Typically, $sim3{-}6$ galaxies contribute $90%$ of the flux of an $S_{850mumathrm{m}}=5$ mJy source and these blended galaxies are physically unassociated. We find that field-to-field variations are comparable to Poisson fluctuations for our $S_{850mumathrm{m}}>5$ mJy SMG population, which has a median redshift $z_{50}=2.0$, but are greater than Poisson for the $S_{850mumathrm{m}}>1$ mJy population ($z_{50}=2.8$). In a detailed comparison to a recent interferometric survey targeted at single-dish detected sources, we reproduce the difference between single-dish and interferometer number counts and find a median redshift ($z_{50}=2.5$) in excellent agreement with the observed value ($z_{50}=2.5pm 0.2$). We also present predictions for single-dish survey number counts at $450$ and $1100$ $mu$m, which show good agreement with observational data.
