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FISHER INFORMATION AND DYNAMIC REGIME CHANGES IN ECOLOGICAL SYSTEMS
Citation:
Mayer**, A, C. W. Pawlowski**, AND H C. Cabezas*. FISHER INFORMATION AND DYNAMIC REGIME CHANGES IN ECOLOGICAL SYSTEMS. Presented at 3rd Conference of International Society for Ecological Imforatics, Rome, ITALY, August 26 - 30, 2002.
Impact/Purpose:
To inform the public.
Description:
Fisher Information and Dynamic Regime Changes in Ecological Systems
Abstract for the 3rd Conference of the International Society for Ecological Informatics
Audrey L. Mayer, Christopher W. Pawlowski, and Heriberto Cabezas
The sustainable nature of particular dynamic regimes of ecosystems is an increasingly integral aspect of many ecological, economic, and social decisions. Sustainability usually refers to a human preference for one particular regime versus another, and whether that regime is relatively stable with regard to the human and natural perturbations exacted on the system. As ecosystems experience perturbations of varying regularity and intensity, they may either remain within the state space neighborhood of the current regime, or "flip" into the neighborhood of a regime with different characteristics. Previous research has identified the presence of stable states and transitions between them in several time series. We used this data to test the ability of an Information Theory-based index to differentiate between dynamic regimes and transitions between them.
Information theory has significantly advanced our ability to quantify the organizational complexity inherent in systems in spite of imperfect observations or 'signals' from the source system. Fisher Information (FI) is one of several metrics developed under the rubric of estimation theory. FI can be described in three ways: as a measure of the degree to which a parameter (or state of a system) can be estimated; as a measure of the relative amount of information that exists between different states of a system; and as a measure of the disorder or chaos of a system. Highly disordered, chaotic systems have a low probability of being observed in any one particular state, and therefore have low information. Conversely, systems that are more ordered and follow a regular or repeating trajectory have higher information. FI may be a very useful measure to apply to the state of the system in order to identify the degree to which a system is at risk of "flipping" into a different steady state.
We have developed an FI index for dynamic systems and applied it to a simple, two species Lotka-Volterra predator-prey model. As we increased the carrying capacity (size) of the system, FI decreased when the system entered a transient phase between stable equilibria. This result indicated that the index was sensitive to transitions or "flips" from one state to another. We also examined data collected from three ecological systems (of increasingly large spatial and temporal scale) that have demonstrated regime changes. In the Bering Strait/Pacific Ocean food web, regime flips in 1977 and 1989 occurred in many of the environmental and biological variables collected over a thirty-year time period. Two flips in western Africa, from an arid system to a humid system and back again, have been recorded in western Africa (in ocean sediment cores) in the past 25,000 years. Similar flips have occurred in Florida ecosystems (in pollen records) across the Atlantic. Both systems are influenced by climate conditions modulated by the oceanic thermohaline conveyor of the Northern Atlantic. Finally, over the past 160,000 years, the Earth's climate has fluctuated between warm and cold (interglacial and glacial) periods (as recorded in ice cores), which have demonstrated differing stability and persistence. All of these datasets are noisy, and reflect several to many cycles that are out of phase and operate over a range of timescales.
Our paper will investigate the degree to which FI is useful in not only distinguishing a system's transitions between regimes in past data, but whether it also can indicate when systems currently in a stable dynamic regime are entering a transition phase. Humans may be able to reverse behavior or inputs into the system to prevent the system's flip into a less-desirable steady state (or continue the behavior if the resultant steady state is desirable, such as in ecosystem restoration efforts), if systems entering these transition phases could be detected early enough.