Are Ecosystems Dynamical Systems?

The paradigm of dynamical systems as frame of description has been extremely successful for a variety of controlled systems. The ingredients of such an approach are an (assumed or known) fixed number of degrees of freedom, a phase space, state variables, and a (usually differential) equation of motion governing the temporal evolution of the system, or its movement in phase space along certain trajectories. Our focus of investigation are forest ecosystems. We will argue that they constitute a kind of system which does not belong to this class. The presence of memory effects and evolutionary processes demonstrate that the local history of these systems, embedded in an environment which is also partially created by them, is of utmost importance. There is no phase space for these systems. We therefore conjecture to characterize the system by its input-output mapping, considering it as a filter. Properties of this filter are quantified by time series analysis tools, identifying relevant time scales, correlations, periodicities, recurrences and other temporal structures. We show examples from hydrology and solution chemistry.