  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. (2004) 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
proto-spheroidal galaxies. For the latter objects we predict the counts and
redshift distributions of strongly lensed sources at 250, 350, 500, and 850
micron, the angular correlation function of sources detected in the surveys
considered, 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 proto-spheroidal 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 1-halo and 2-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
sub-millimeter 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.

Astrophysics