  Recent derivations of the galaxy star formation rate density (SFRD) obtained
from sub-millimetre (sub-mm) surveys (e.g., SCUBA-2) show a tension with
previous works based on Herschel and multi-wavelength data. Some of these works
claim that the SFRD derived by pushing the Herschel surveys beyond z~2 are
incorrect. However, the current sub-mm surveys obtained from SCUBA-2 data and
the methods used to construct the total infrared (IR) luminosity function (LF)
and the SFRD could be affected by some limitations. Here we show how these
limitations (i.e., selection bias and incompleteness effects) might affect the
total IR LF, making the resulting dusty galaxy evolution of difficult
interpretation. In particular, we find that the assumed spectral energy
distribution (SED) plays a crucial role in the total IR LF derivation,
moreover, we confirm that the long-wavelength (e.g., 850-micron) surveys can be
incomplete against "warm" SED galaxies, and that the use of a wide spectral
coverage of IR wavelengths is crucial to limit the uncertainties and biases.
