Regime changes in ecological systems: an information theory approach

We present our efforts at developing an ecological system index using information theory. Specifically, we derive an expression for Fisher Information based on sampling of the system trajectory as it evolves in the space defined by the state variables of the system, i.e. its state space. The Fisher Information index, as we have derived it, is a measure of system order, and captures the characteristic variation in speed and acceleration along the system's periodic steady-state trajectories. When calculated repeatedly over the system period, this index tracks steady states and transient behavior. We believe that such an index could be useful in detecting system 'flips' associated with a regime change, i.e. determining when systems are in a transient between one steady state and another. We illustrate the concepts using model ecosystems.