Dynamic Complexity in Exploited Marine Ecosystems

Marine ecosystems are increasingly recognized as exhibiting the principal hallmarks of complex systems, including the possibility of sudden shifts in state among alternative basins of attraction and both periodic and aperiodic dynamical behavior. Over the last several decades a well-defined theory of complexity has emerged, integrating earlier (and inter-related) concepts based on bifurcation theory, catastrophe theory, and chaos theory. In this review, we trace aspects of the historical development of these ideas and their application to marine systems. The manifestations of nonlinear dynamics in marine ecosystems include regime shifts; mirage correlations in which causally-connected system components can appear to be in-phase, asynchronous, or anti-correlated over different stanzas of time; and related state-dependent behavior in which the response of a focal variable to a driver differs depending on the present state of the system. We describe the analytical underpinnings of each of these dynamical behaviors. Although nonlinear dynamical systems are often portrayed in a deterministic setting, we emphasize the phenomenon of stochastic resonance in which an underlying nonlinear system acts as a noise amplifier in the presence of random perturbations. We next review the tools available for analyzing nonlinear dynamical systems based on the concept of state-space reconstruction and the application of techniques in nonlinear time series analysis. Finally, we address the management implications of nonlinear dynamics in exploited marine species and argue that considerations of predictability and forecast skill can serve as effective criteria for model selection and inference.