Predicting dynamics of spatial automata models using Hamiltonian equations

Grid-based models such as cellular automata are useful tools for investigating spatial dynamics in ecological systems. Quantitative measures have been proposed for characterizing static spatial patterns, but techniques for examining the dynamics of spatial pattern are less developed. I present an adaptation of Hamiltonian free energy equations to predict numbers of state changes resulting from different ecological mechanisms in spatial automata models. The three terms in the Hamiltonian estimate the number of grid cells changing state due to spontaneous state changes, to interactions among cells, and to heterogeneity in the behavior of different cells in the grid. PComp is a simple competition model in which each cell in the grid can be occupied by a single individual plant. The simulation calculates the Hamiltonian at each time step to indicate how many of the observed changes in cell occupancy are due to basic colonization and death rates, crowding effects, dispersal from adjacent cell, and differences in substrate suitability.