Network perspectives on ecological indicators and actuators: Enfolding, observability, and controllability

The subject of ecological indicators is both complex and technical. Indicators are low signal/noise read-outs from systems reflecting deeply embedded processes. Informal, single factor indicators reflect superficial properties. Complex systems require formal, multifactorial measures. Conceptual basis, importance and bandwidth of variables, reliability and statistical properties, data and skill requirements, data quality and archiving, robustness under technology change, and cost/benefit issues are factors in indicator design. Network models enable formalism to be brought to the indicator problem. Networks are oriented in time-forward and reverse directions, giving rise to environs. Output environs span network flows derived from inputs, and input environs encompass flows leading to outputs. Both have mathematical descriptions. Variable embedding is a key difficulty in defining and interpreting indicators. Formally, all system energy and matter flows are enfolded within each empirical stock and flow. Embedding in output flows is the source of low signal/noise ratios of indicators. Network enfolding is a powerful expression of systemic holism and the source of what is termed the "indicator problem". Observability and controllability are formal system properties related, respectively, to indication and its reciprocal, actuation. These are defined and illustrated for simple cases. Composite systems have mixed controllable (c), observable (o), uncontrollable (c'), or unobservable (o') elements, in four possible combinations-(c, o), (c, o'), (c', o), and (c', o'). To exert control based on indicators, what available indicators indicate must be matched to what available actuators actuate. That is, (c, o) sectors must jointly be in output environs of manipulated inputs and input environs of indicator outputs-the relevant environs must intersect. If S-a is a linear system to be controlled and S-b a linear controller, theory gives that if S-a and S-b are individually controllable (c) or observable (o), then any uncontrollable (c') or unobservable (o') elements of the control system SaSbSa... will always be in S-b, never in S-a. This means the system to be controlled can be ignored as a source of c' or o', and improved control can be sought exclusively within the management system, S-b. Though this is limited to linear systems, it illustrates how formal theory can help structure the indicator problem and its relationship to management. A wildlife management (deer) example is discussed both without and with modeling incorporated into S-b. Application of ecological indicators to monitor and manage complex systems is a difficult technical problem. Guidance from formal theory can help clarify its technical dimensions. (C) 2005 Elsevier Ltd. All rights reserved.