Ecosystems as Evolutionary Complex Systems: A Synthesis of Two System-Theoretic Approaches Based on Boolean Networks

Understanding and managing ecosystems as biocomplex wholes is the compelling scientific challenge of our times. Several different system-theoretic approaches have been proposed to study biocomplexity and two in particular, Kauffman’s NK networks and Patten’s ecological network analysis, have shown promising results. This research investigates the similarities between these two approaches, which to date have developed separately and independently. Kauffman (1993) has demonstrated that networks of non-equilibrium, open thermodynamic systems can exhibit profound order (subcritical complexity) or profound chaos (fundamental complexity). He uses Boolean NK networks to describe system behavior, where N is the number of nodes in the network and K the number of connections at each node. Ecological network analysis uses a different Boolean network approach in that the pair-wise node interactions in an ecosystem food web are scaled by the throughflow (or storage) to determine the probability of flow along each pathway in the web. These flow probabilities are used to determine system-wide properties of ecosystems such as cycling index (Finn 1976), indirect-to-direct effects ratio, and synergism. Here we use a modified version of the NK model to develop a fitness landscape of interacting species and calculate how the network analysis properties change as the model’s species coevolve. We find that, of the parameters considered, network synergism increases modestly during the simulation whereas the other properties generally decrease. This research is largely a proof of concept test and will lay the foundation for future integration and model scenario analysis between two important network techniques.