We investigate anisotropies in the cosmic infrared background (CIB) using a combination of the physical evolutionary model for proto-spheroid galaxies of Granato et al. and an independent halo occupation distribution analysis. After having re-calibrated the cumulative flux function dS/dz at m using the available determinations of the shot-noise amplitude (the original model already correctly reproduced it at shorter wavelengths), the CIB power spectra at wavelengths from m to 2 mm measured by Planck, Herschel, South Pole Telescope and Atacama Cosmology Telescope experiments have been fitted using the halo model with only two free parameters, the minimum halo mass and the power-law index of the mean occupation function of satellite galaxies. The best-fitting minimum halo mass is log (Mmin/M⊙) = 12.24 ± 0.06, higher than, but consistent within the errors, the estimate by Amblard et al. and close to the estimate by Planck Collaboration. 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 effective halo mass, Meff≃ 5 × 1012 M⊙, of z≃ 2 submillimetre 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≃ 2 yielded by the model are substantially lower than those found for a model whereby the star formation is fuelled by steady gas accretion, but substantially higher than those found for a merger-driven galaxy evolution with a top-heavy initial mass function.