Among the variety of properties characterizing a complex system, both in a natural or a social-ecological context, some are of major interest as descriptors and organizing concepts for the study of systems' dynamics. They are ecological resilience, vulnerability/fragility, system adaptability, and cross-scale interactions.
Such system-level properties differ in three important ways from traditional ecological indicators. First, they need to be addressed by holistic measures describing, as far as possible, the entire system, not just specific subsystems or components. Second, as any important aspects of SESs may not be directly observable, they must be inferred only indirectly using surrogates, whose relationship between systems' properties may be dynamic, complex, and multidimensional. As a system evolves and adapts in time, the components and functions sustaining particular system properties change so that a surrogate is useful only in a particular context or time frame. Third, some features of a complex system (e.g., system resilience) focus on properties that underlie the capacity of the SES
to provide ecosystem goods and services, whereas other indicators often address only the current state of the system component or service.
When evaluated retrospectively such properties are described in terms of the ability of an SES to evolve as a consequence of past exposure to pressures, disturbances, and shocks. History of the SES is assessed to classify more-or-less distinct dynamic regimes, and analyze events during the transitions. During a certain time span an SES can visit different stability domains and change its sensitivity to disturbance events and regimes. Then it becomes crucial to specify (1) what system state is being considered, (2) what perturbations, changes, or disturbance regimes (i.e., disturbance timing, frequency, predictability, and severity) are of interest, and (3) within what particular range of spatial and temporal scales (i.e., resolution and extent of the study system) such an assessment is made. Conclusions and patterns derived for one state, one type of disturbance, and one scale are highly context sensitive and they may be inappropriate or wrong when transferred or compared to a different situation where one or more of the three elements is modified.
Furthermore, despite complex systems theory acknowledging that inferences about SES phenomena are scale and system dependent, retrospective studies are complicated and somehow restricted to be primarily descriptive, because of the impossibility of applying a traditional scientific experimental design with system-controlled manipulation and statistical hypothesis-testing procedures. History is deemed as a kind of experimental manipulation of the system, though generally unplanned but otherwise unachievable. Little attention can be paid to determine appropriate scales of measurement (e.g., plot or grain size) as they are generally fixed by the availability and quality of historical data that different organizations may collect for their own special needs. No control could be exercised by researcher on system-driving forces or variables' levels, and the experiment cannot be replicated or compared to an untreated control case. Thus we rely on the assumption that the historical system trajectory reconstruction could be detailed enough to let the inherent system properties emerge and patterns described. We assign meaning to these patterns and properties, but as it may turn out, this meaning could be completely inappropriate for describing the underlying processes, or understanding the system, because artifacts of the scales sampled by the data or imposed by how the system definition adopted.
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