On repeated parameter sampling in Monte Carlo simulations

In a realistic model of a biological system there is usually uncertainty in some of the model parameters. A conventional Monte Carlo simulation handles this situation by randomly choosing parameters at the start of the simulation (from specified probability distributions) and then keeping them fixed for the duration of the simulation. This is certainly appropriate in situations where the parameters are thought to be constant through time but the precise values are not known with certainty. If any of the parameters vary through time in the real system, however, it is intuitively appealing to allow the model parameters to vary by resampling at intervals during the simulation. Previous work on a simple model of algal competition had suggested that the second of these two approaches gave qualitatively different (and biologically more reasonable) results than the first. By analyzing the behavior of the model more thoroughly we explain the reasons for these results, and show that in fact when the procedure is carried out correctly, there is little or no difference in model output between the two types of simulation.