Ecosystems as evolutionary complex systems: Network analysis of fitness models

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 through-flow (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, indirect-to-direct effects ratio, and synergism. Here we modify the NK model slightly 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. Furthermore, we calculate several ecosystem level goal functions and compare their progression during increasing fitness and determine that at least at this stage there is not a good correspondence between the reductionistic and holistic drivers for the system. 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. (c) 2006 Elsevier Ltd. All rights reserved.