Modelling using stochastic, finite state cellular automata: rule inference from continuum models

A methodology is presented, that allows the simulation time step to be included in the transition rules of stochastic, finite-state cellular automata (CA) models. It is shown that the transition probability should incorporate an exponentially decreasing function of the simulation time step. It is also possible to deduce the transition rules from the parameters of classical, ordinary differential equations. The method is demonstrated by applications to first-order linear kinetics and to the Lotka–Volterra (LV) equations that describe prey–predator interactions. The simulation results from the CA models are shown to be in close agreement with those of the continuum-based models, provided the number of individuals in the CA model is sufficient. Such a `sufficient number' may be highly dependent on the nature of the phenomena to be modelled, with at least 5×104 individuals needed to approximate correctly the LV equations