We continue a study in which we statistically analyze the dynamics of vibrational energy flow in a model system of anharmonic oscillators which are nonlinearly coupled, with a local topology. Average spectra are obtained from individual spectra of many basis states of similar energy, for different values of the magnitude of the coupling between states. The survival probabilities of the density are then determined from the average spectra. When the average fluctuation in spectral intensities is small then the density survival probability closely follows the average survival probability presented in our earlier paper for short times. For longer times, when the average survival probability shows a power law decay, this decay does not appear in the density survival probability. In addition, when spectral fluctuations are large, the two survival probabilities differ strongly.