Cellular automata have been used in ecology since the publication of Wolfram’s 1986 book. In this talk I will summarize the history of CA models used in ecological systems and highlight examples of CA models that provide different insights than traditional differential equation models.
One early use of CA modeled the dynamics of single species populations using a one-dimensional totalistic nearest-neighbor CA model (Molofsky 1994). In this simplistic model in which a cell can either be occupied or empty, one can explore the complete universe of possible outcomes and determine how often such dynamics are expected to occur. Moreover, one can determine how small differences in the structure of the rule can affect the system’s dynamics. The simplicity of this approach limits its applicability to many problems in ecology.
A slightly more complex approach used probabilistic CA models (Molofsky and Bever 2004). Molofsky and Bever 2002 used a probabilistic CA model to determine the diversity of a plant community following application of a local probabilistic transition rule in which the dynamics develop based on the local abundance of each species in a neighborhood. The diversity of the community depended on the degree of positive or negative association between the different species, the scale of the interactions, and the amount of area inhabited by the species within the grid.
In a recent example, we used a probabilistic CA model to examine the conditions under which a new species is likely to successfully invade a new landscape and establish a series of criteria under which an invasion is expected to take place (Eppstein et al. 2006, Molofsky and Eppstein in preparation).