The ubiquity of scaling relations--indicative of power law distributions in natural and artificial systems (from earthquakes to fossil extinction record to Internet traffic)--has for some time been a puzzle for scientists.

The existence of power laws has long been noted in physics, where they are associated with phase transitions and critical phenomena, and characterized by the global state of a system undergoing a drastic change when one or more parameters of the system are increased beyond a critical value. The critical point is usually very sensitive to perturbations, however, and has to be tuned very carefully. Outside the carefully controlled laboratory, it is unusual to expect that such careful tuning is responsible for the observed scaling relations in nature. Further, the presence of environmental fluctuations makes it unlikely that the critical state can be maintained for any length of time, to enable the observation of these power laws.

One suggested explanation, known as self-organized criticality, states that natural systems somehow self-tune themselves to the critical state. The authors of this paper present an alternative explanation, which looks at the detailed spatial relations among the components making up the entire system. They consider a three-state cellular automata, with nearest neighbor interactions and probabilistic updating rules, to model a spatial ecological system consisting of a predator and a prey. They observe power law relations existing over a broad range of parameters, which they associate not with drastic changes in the global variables of the system (namely, the predator and prey densities), but rather with a more subtle change in the connectedness of the prey units across the system.

The formation of a connected cluster across the entire system, known as percolation transition in physics, is found to be responsible for the emergence of scaling. Although the immediate relevance of the authors’ results to ecology is unclear, their findings support the growing realization that long-range spatial correlations among the components of a system underlie many scaling relations in nature.