The spontaneous emission spectra of a 1.28?m InAs/GaAs QD (Quantum Dot) Fabry-Pérot laser device has been measured under continuous wave operation at a fixed junction temperature of 300K. At low carrier densities, empirically observed static peak wavelength position and a fixed spectral shape of the spontaneous emission spectra are indicative of the random-like population distribution rather than a global Fermi level in the system. A theoretical model based on the Monte-Carlo method has been shown to have good agreement with the empirical results. In addition the evolutions of spontaneous emission spectral shapes are also explained in terms of many body effects.