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Abstract
Minimizing subtle variations in network environ analysis (NEA), the two mathematical building blocks of NEA, the law of conservation and the definition of throughflow, are separately developed and then carefully combined to construct a consistent NEA derivation. The conservation equations are derived using the Reynolds transport theorem with an Eulerian control volume to differentiate the concepts of flow and storage. Terms and concepts related to NEA, such as self-flow, turnover rate, storage, accumulation, and the necessary inclusion of a discrete time step in environ storage analysis, are clarified. A comparative NEA methodology is then derived to holistically explore controlling relationships in ecosystems where the term distributed control is adopted to describe a diffuse and decentralized concept of control residing in the complexity of network organization. Starting with open-loop control theory, three ecological control metrics (control ratio, CR; control difference, CD; and system control, scj) are defined in an environ-theoretic framework by considering pair-wise and system-wide distributed control relationships. These control relationships are then explored using a sixteen-season seven compartment steady-state model of nitrogen flow in the Neuse River estuary, North Carolina, USA (Christian, R.R, Thomas, C.R., 2003. Network analysis of nitrogen inputs and cycling in the Neuse River Estuary, N.C., USA. Estuaries 26 (3):815-828). Model compartments of particulate nitrogen in sediment (Sediment) and Nitrates-Nitrites (NOx) are shown to participate in opposing roles. If a greater nitrogen-exchange magnitude denotes proportional dominance and therefore control, the control metrics reveal Sediment is overwhelmingly controlled by all components, whereas NOx controls all components. However, if a limiting factor perspective is used (e.g., Sediment sequestering N with a controlled release to NOx), the conclusions are opposite; Sediment controls all other components and all other components control NOx. The meaning of control in connection with resource stocks and flows in ecosystems still needs resolution. Low ratios of component throughflow and their respective boundary flows are shown to be possible indicators of a components control dominance.