Fisher Information and dynamic regime changes in ecological systems

• Published in: Ecological modelling 2006-05, Vol.195 (1), p.72-82
• Main Authors: Mayer, Audrey L., Pawlowski, Christopher W., Cabezas, Heriberto
• Format: Article
• Language: English
• Subjects: Animal and plant ecology; Animal, plant and microbial ecology; Biological and medical sciences; Dynamic regimes; Ecosystem flips; Ecosystems; Fisher Information; Fundamental and applied biological sciences. Psychology; General aspects; General aspects. Techniques; Information theory; Methods and techniques (sampling, tagging, trapping, modelling...); Synecology
• ISSN: 0304-3800; 1872-7026
• DOI: 10.1016/j.ecolmodel.2005.11.011

Ecosystems often exhibit transitions between multiple dynamic regimes (or steady states), such as the conversion of oligotrophic to eutrophic conditions and associated aquatic ecological communities, due to natural (or increasingly) anthropogenic disturbances. 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. An increasingly integral aspect of many ecological, economic, and social decisions is their impact on the sustainability of particular dynamic regimes of ecosystems. Sustainability entails a human preference for one particular regime versus another, and the persistence of that regime with regard to the human and natural perturbations exacted on the system. Information theory has significantly advanced our ability to quantify the organizational complexity inherent in systems despite imperfect observations or ‘signals’ from the source system. Fisher Information is one of several measures developed under the theme of estimation theory. Fisher Information 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; as a measure of the disorder or chaos of a system. Fisher Information may be a useful measure to identify the degree to which a system is at risk of “flipping” into a different dynamic regime. We developed a Fisher Information index for dynamic systems in a periodic steady state and applied it to a simple, two species Lotka–Volterra predator–prey model. Changes in the carrying capacity (size) of the system resulted in different stable steady states establishing themselves, each with a characteristic Fisher Information. By repeatedly calculating Fisher Information over time, transitions or “flips” between steady states were identified with changes in Fisher Information. We then examined data collected from four ecological systems (of increasingly large spatial and temporal scale) that have demonstrated regime transitions: the Bering Strait/Pacific Ocean food web; the western Africa savanna; the Florida (USA) pine–oak system; the global climate system. These datasets are noisy and reflect several to many cycles that are out of phase, which complicates the identification of both dynamic regimes and transitions