The analytic equations used to solve predator-prey relationships can give surprizingly accurate information regarding the population dynamics. One drawback to this approach, however, is that result of the Volterra-Lotka equation is based on the average behavior of the population and uniform spatial distributions. The behavior of many populations is not constant over time, there are diurnal and seasonal effects, there are density dependent effects, there are migrational effects, etc. The location of a animal groups may change periodically and are, in general, concentrated. Thus, analytic equations cannot reflect trends dependent on behavioral variability.
It is worth pointing out at this point that stochastic simulations are based on random walks rather than determinism. In each simulation, the computer will generate a set of numbers that determine random behavior. Therefore, to get accurate results from a stochastic simulation, we need run the simulation a statistically significant nubmer of times. From these runs, we can determine the mean and standard deviations of the variables we are measuring. We cannot simply assume that a single run of a stochastic simulation is inherently significant.