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Michael M Fuller

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Bio-Physics: My Work on Self-Organizing Systems

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During the 1990s, a small group of physicists (Bak, Tang, and Wiesenfeld) developed a new theory for complex systems, which they called self-organized criticality (SOC). Their theory was intended to explain a broad range of phenomena that show "punctuated equilibria": long periods of low activitiy, interspersed with sudden large events. Large earthquakes, for example, appear abruptly, although low-level seismic activity goes on all the time. Sand piles display SOC dynamics and were often used by the group to describe SOC. Therefore, SOC quickly became known as the "sand pile model".

A key member of the group was the Danish physicist, Per Bak (1948-2002), who worked hard to promote SOC as an explanation for a broad class of pheneomena, including the stock market, freeway traffic, and extinction events in the fossil record. He summed up his arguments, and the evidence for SOC, in his ambitiously titled book, How Nature Works".

graph of species trajectories
Changes in density of
dominant species groups in
a small pond over time.
Click image to enlarge.
graph of species trajectories
Times to extirpation of
dominant species in
two small ponds over time.
Click image to enlarge.

For my MS Thesis at the University of Oklahoma, I collaborated with Dr. Bak and his wife and colleague, Maya Paczuski. My academic advisor at OU was the aquatic ecologist, Dr. Caryn Vaughn. I was also extremely fortunate to connect with Caren Marzban, in the OU Physics department, who encouraged me to expand my science boundaries, and who gave essential guidance and moral support as I ventured into academic terra incognita.

Our goal was to test the theory of SOC as an explanation for ecological patterns. The theory of SOC applies to systems of tightly integrated, interacting parts. Ecosystems are perhaps the canonical example of such systems. We wondered whether SOC might help to explain the temporal changes observed in the composition and structure of ecological systems? We hypothesized that ecological relationships among organisms in a closed system could evolve the system to a critical state, as described by SOC. If so, the populations of individual species would show abrupt, correlated changes in abundance. Such cascading effects would arise because of the dependence of each species on other species in the system. In addition, the magnitude of these population adjustments should follow a power-law distribution if the system behaves according to SOC. To look for evidence for SOC in an ecological system, I recorded temporal changes in the populations of 72 species of aquatic organisms found in small temporary ponds.

My MS work revealed that the aquatic systems I investigated did indeed show rapid shifts in the abundances of different species. Often, these shifts in abundance occurred as correlated events, as predicted by SOC. In addition, the distribution of "event sizes", which here represented the magnitude of population changes, and species lifetimes (time to local extinction, or extirpation; see figure at left) appeared to follow power laws. These observations lend support to the idea that ecological systems could self-organize to a critical state, as predicted by SOC. However, the observed population variation could also be explained by rapid changes in the environmental conditions of the ponds, which I also observed.

To account for the influence of such environmental forcing, I recorded data on the pond's water chemistry and physical properties at the same time that I recorded population changes. I discovered that many of the population fluctuations were correlated to periods of rapid environmental change related to seasonal changes in temperature and humidity. In addition, the pond community appeared to show successional dynamics, wherein early colonizing species were replaced by later species over the course of 8-10 weeks. Succession is a well known property of ecological systems, and it is indeed thought to arise due to species interactions, and the influence of species on their environment. In a sense, one could say that succession represents the observed correlated changes predicted by SOC. Yet, environmental effects are not included in the theory of SOC, which states that cascading events arise purely from direct interactions. As an indirect effect, species-mediated environmental change lies outside the theory.

The data I collected pointed to two very different explanations for the observed pond dynamics:

  1. the community had achieved a self-organized critical state (SOC)
  2. the community dynamics were driven by rapid changes in environmental conditions.
Of course, it is also possible that both SOC and environmental forcing influenced the system. In the end, although I could not state unequivocally whether the pond system showed SOC, my project revelaed the importance of environmental effects for community dynamics, and underscored the difficulty of testing theories such as SOC in naturally varying systems.

More important for me, on a personal level, was the thrill of collaborating with brilliant people outside my field. My work with Per Bak, Maya Paczuski, and Caren Marzban transformed my view, not only of natural systems, but of myself as a scientist. At the same time, Caryn Vaughn helped keep my project grounded in ecology, and imparted an appreciation for the beauty and complexity of aquatic ecosystems. The impact of our collaboration on my world view, and on how I approach science, continues to influence my work today.