Retrospective Approach to Complex Systems Analysis

Complex systems theory evolved within the framework of general systems theory, mathematics, and philosophy in the 1960s and 1970s by integrating concepts from catastrophe theory, chaos theory, hierarchy theory, non-equilibrium thermodynamics, and self-organization theory. It aims at describing the behavior of coupled human and ecological systems characterized by a large number of components that interact in a nonlinear way and exhibit intrinsic uncertainties and adaptive properties through time. Such systems are referred to as social-ecological systems (SESs) and are examples of a broader class of systems defined as complex adaptive systems (CASs). An SES differs from a CAS as it explicitly recognizes the primary role of humans as driving force in shaping and modifying intentionally systems' compositions and processes.

A fundamental shift in ecological theory mediated by CAS or SES analysis centers on the change in perception of systems from static entities in equilibrium to complex systems that are dynamic and unpredictable across time and space. In the past 30 or so years, many concepts ranging from succession or island biogeography to carrying capacity or ecological disturbance, that were considered central to ecology in previous decades and were all dominated by equilibrium assumptions, have since been thoroughly revised. Complex systems are deemed to exhibit alternative stable organizations, so possessing multiple stable states. Transitions between different stable states are due to changes in the interactions of structuring variables and processes. For example, gradual adjustment in a slow variable alters the interactions among fast variables pushing a system beyond a threshold (Figure 1); or by explicitly recognizing the adaptive nature of a complex system (modeled by Holling's adaptive cycle), disturbance and disturbance regimes are no more judged as a rare, external event, but intrinsic and inherent feature ofsystem dynamics.

Frequent disturbances make ecosystems subject to sudden, unanticipated changes, which may cause systems to flip into entirely new states. Large infrequent disturbance can have a long-lasting legacy effect on system dynamics that may persist long after the disturbance regime has been restored. As such, uncertainty is normal, and predictable endpoints to system evolution are not always apparent. Equilibria are temporary artifacts resulting from the scale of the observational framework (i.e., sampling intensity, data resolution, study area extent, time span of the research or monitoring activities), not intrinsic system properties.

The centrality of disturbance and the contingency of the consequent course ofsystem evolution brings history to the fore, thus urging a retrospective approach to system analysis. System history emphasizes the contingency of current conditions so that the unique nature of a specific system is based on a particular history of events, including the composition and pattern of those events. Historical contingency reflects the cumulative pattern of the impact of a diversity of processes at various scales within the systems hierarchy. All processes act in the context of and are constrained by other processes, and their temporal sequence may be critical. As a consequence, the endpoint of many successional processes is not a predictably uniform outcome; rather, several states are possible depending on the contingent circumstances. These multiple states may be resilient for long periods of time, depending on the

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Figure 1 Example of a state space where the same set of fast and slow variables describe two different stability domains (left) and corresponding evolutionary trajectory in terms of system's properties (right) for a particular SES. A threshold for the fast variable marks the limits of the two domains and a solid line collects all possible combination of system's variables for different states of the SES within a domain. System's properties are modified whenever the SES changes from one state to another. For example, the system's vulnerability/fragility is modified when the system moves from S1 to S2, or it is highly increased shifting to S3. System's resilience is changed accordingly and it is lower in S3. Here because of an external shock or disturbance the SES exceeds its resilience and can flip from domain A to B, where it reorganizes along different values of system's describing variables. In domain B, resilience is higher than domain A, but the SES still can evolve with the domain moving among states. A retrospective approach aims to rebuild and describe the evolutionary trajectory based on empirical evidence gathered by the analysis of the history of the system.

particular circumstances of the disturbance regimes experienced and the nature of the biophysical bounds that precede and follow it. As a consequence a retrospective approach is needed to understand the present system conditions in the context of a trajectory of change that encompasses system past, disturbance regimes, and cross-scale interactions and constraints in a hierarchy of systems, in addition to endogenous self-organizational processes.

Studying and modeling a complex system, as SESs, through a retrospective analysis focuses research efforts to quantify and evaluate systems' properties as responses to change processes and disturbance regimes, both of natural and human components, instead of the arbitrary information of system properties at any random occasion in time. By using time as a vertical process, an inherent chronology is attached to system patterns and processes and an effort is made to consider what might be the driving forces and human actions behind changes and the main consequences of these processes in relation to the present-day situation. Retrospective analysis is useful, as it links the present-day system status with its past dynamics and enables the identification of possible evolutionary trajectories to reveal continuity, turnover, directions, or degree of changes. By providing a means for analyzing short- and long-term system dynamics and for assessing the complex structure of the multiscale relationships in SESs and CASs, retrospective observational studies are valuable as they can address the role and nature of feedback mechanisms and scale-dependent interactions in systems.

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