We present a quantitative analysis of the astrophysical and cosmological information that can be extracted from the many important wide-area, shallow surveys that will be carried out in the next few years. Our calculations combine the predictions of the physical model by Granato et al. for the formation and evolution of spheroidal galaxies with up-to-date phenomenological models for the evolution of starburst and normal late-type galaxies and of radio sources. We compute the expected number counts and the redshift distributions of these source populations separately and then focus on protospheroidal galaxies. For the latter objects, we predict the counts and redshift distributions of strongly lensed sources at 250, 350, 500 and 850μm, the angular correlation function of sources detected in the surveys considered, and the angular power spectra due to clustering of sources below the detection limit in Herschel and Planck surveys. An optimal survey for selecting strongly lensed protospheroidal galaxies is described, and it is shown how they can be easily distinguished from the other source populations. We also discuss the detectability of the imprints of the one-halo and two-halo regimes on angular correlation functions and clustering power spectra, as well as the constraints on cosmological parameters that can be obtained from the determinations of these quantities. The novel data relevant to derive the first submillimetre estimates of the local luminosity functions of starburst and late-type galaxies, and the constraints on the properties of rare source populations, such as blazars, are also briefly described.
