A Case Study for Self-Organized Criticality in Forest Ecology

Janine Bolliger
Swiss Federal Research Institute (WSL/FNP), CH-8903 Birmensdorf, Switzerland
and
Julien C. Sprott
Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
(Submission Date: May 2, 2002)

ABSTRACT

In ecology, the phenomenon of self-organized criticality may provide a powerful approach to complete current theoretical frameworks (e.g., metapopulation theory) with a profound understanding of how ecological feedback, interaction, and historical coincidence act together so that biotic units co-occur at their present locations.

The goal of this study is to investigate the self-organized critical state and the complexity of the historical landscape of southern Wisconsin (60,000 km²).

The landscape was classified into 27 discrete forest types using statistical cluster analysis. The data for classification was derived from the United States General Land Office Surveys that were conducted during the 19^th century prior to Euro-American settlement.

We applied a two-dimensional cellular automaton model with a single adjustable parameter. The model evolves by replacing a cell that dies out at random times by a cell chosen randomly within a circular radius r (neighborhood), where r takes values between 1 (local) and 10 units (regional). Clusters measure the degree of organization.

Good agreement is found when comparing the simulated to the observed landscape using fractal dimension (spatial), cluster probability (temporal), and algorithmic complexity (interaction characteristics). All results are robust towards a variety of perturbations.

In our example, the self-organized state, in both time and space, is strongly dependent on the neighborhood size chosen for the model runs.

Ref: J. Bolliger, InterJournal Complex Systems, 558

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