Spatial pattern and power function deviation in a cellular automata model of an ant population

A spatially explicit model previously developed to apply to a population of arboreal nesting ants in southern Mexico is explored in detail, including notions of criticality and robust criticality and expected power law adjustment. Introduction Spatial pattern has long been a preoccupation of ecologists, from the observational work of early botanists (e.g. Clements, 1916; Shelford, 1913) to the theoretical explorations of modern theoreticians (Tilman and Karieva, 1997; Levin, 1992; Dieckmann et al., 2000). In this note we elaborate on the details of a stochastic cellular automata model previously developed (Vandermeer et al., 2008) and thought to adequately represent the spatial dynamics of a population of a tropical ant species. Non-random spatial patterns are ubiquitous in nature. Some are evidently a consequence of exogenous forcing from environmental variables such as moisture, temperature, substrate, and so forth. Others seem to emerge as a consequence of the dynamic interaction of the organisms of concern, of special interest when interactions occur at a local level and pattern emerges at a larger scale, frequently referred to as selforganization. Self-organization in spatial ecology has been reported for both spatial models (e.g., Pascual et al. 2002; Kefi et al., 2011; Rietkerk et al., 2004; Roy et al., 2003) and field data (Vandermeer et al., 2008; Wooten, 2001). One framework that seems to correspond qualitatively with many natural circumstances is an arrangement that mimics the so-called Turing mechanism in which foci expand locally (metaphorically acting like Turing’s activators) but are restricted as the clusters formed from those foci become subject to some controlling force (metaphorically acting like Turing’s repressor). An example from classical ecological thought is the Janzen/Connell effect, in which plants produce seeds that, when falling near the parent, produce a locally abundant seedling population which in turn is attacked by a predator or disease of the seedling (or seed) (Martin and Canham, 2010; Peterman et al., 2008). Plant dispersal thus is the activating process and seed or seedling