  We have investigated the Cosmic Infrared Background (CIB) anisotropies in the
framework of the physical evolutionary model for proto-spheroidal galaxies by
Granato et al. (2004). After having re-calibrated the cumulative flux function
$dS/dz$ at $\lambda \ge 850\,\mu$m using the available determinations of the
shot noise amplitude (the original model already correctly reproduces it at
shorter wavelengths) the CIB power spectra at wavelengths from $250\,\mu$m to
$2\,$mm measured by {\it Planck}, {\it Herschel}, SPT and ACT experiments have
been fitted using the halo model with only 2 free parameters, the minimum halo
mass and the power-law index of the mean occupation function of satellite
galaxies. The best-fit {\it minimum} halo mass is $\log(M_{\rm min}/M_\odot) =
12.24 \pm 0.06$, higher than, but consistent within the errors, with the
estimate by Amblard et al. (2011) and close to the estimate by Planck
Collaboration (2011). The redshift evolution of the volume emissivity of
galaxies yielded by the model is found to be consistent with that inferred from
the data. The derived {\it effective} halo mass, $M_{\rm eff} \simeq 5\times
10^{12}\,M_\odot$, of $z\simeq 2$ sub-millimeter galaxies is close to that
estimated for the most efficient star-formers at the same redshift. The
effective bias factor and the comoving clustering radius at $z\simeq 2$ yielded
by the model are substantially lower than those found for a model whereby the
star formation is fueled by steady gas accretion, but substantially higher than
those found for a merging-driven galaxy evolution with a top-heavy initial mass
function.
