PAS P2a, Time Series Analysis evaluates the behavior of models by simulation. The user has to specify the length of the simulation run (default = 20, maximum = 100), the initial population densities (default = first data points), and whether a deterministic or stochastic simulation is desired. If a stochastic simulation is requested, P2a asks for standard deviations for each species (default = standard deviations estimated from the regression). Simulations are performed by recursively solving the step-ahead forecasting equation
where N(t) is the density of the species in question at time t, R is its per-capita rate of change calculated from the regression equation or, in the case of no interaction, from the P1a model, and V is a random deviate chosen from a normal distribution with mean zero and standard deviation selected by the user. Simulated trajectories are displayed first as a time-series (see figure), then superimposed in phase-space on the data (see figure). Comparison of the simulated trajectory with the data can be used to choose an appropriate standard deviation or to make decisions about the structure of the model; i.e., which of several alternative structures provides the best description of the data.