Computing the adaptive cycle

The importance of resilience in ecosystem development has been pointed out by Holling in 1986 introducing the metaphor of the adaptive cycle. The metaphor describes a circle of four phases of ecosystem development, being characterized by the dynamic interplay of three variables: potential, connectedness and resilience. The adaptive cycle became a central part of panarchy theory, as been established by the Resilience Network in 2002 (Gunderson & Holling 2002). Pushing the metaphor towards empirical validation, the abstract notions of potential, connectedness and resilience have to be underpinned with measurable quantities.
We present an approach of quantifying potential, connectedness and resilience using concepts of information theory. The notions are based on a mathematical model of a system as directed graph of information transfer. Such a network can be inferred from time series of abundance data using Schreiber’s concept of transfer entropy (Schreiber 2000). Our abstract approach has the advantage of being applicable to any set of appropriate time series, as long as one can expect the data to directly or indirectly reflect interaction strength among agents of a system.
To provide realistic examples, we applied our method to ecological plant data as well as economic data of European countries. In both cases, we could identify phases of the adaptive cycle of the respective systems.