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Equivalence of throughflow- and storage-based environs

Author

Listed:
  • Bata, Seth A.
  • Borrett, Stuart R.
  • Patten, Bernard C.
  • Whipple, Stuart J.
  • Schramski, John R.
  • Gattie, David K.

Abstract

An environ is a within-system partition of the environment associated with each ecosystem component. The methodologies for calculating throughflow-based and storage-based environs have heretofore been considered quantitatively and qualitatively different. Below, we show, from the fundamental environ equations, that these two approaches are mathematically equivalent by proving the throughflow-storage-equivalence relationship, TE=SE. This implies that ecosystem flows of energy or matter to storage and throughflow are one and the same, differing only in storage delays (flow impedances) along the way in the storage case.

Suggested Citation

  • Bata, Seth A. & Borrett, Stuart R. & Patten, Bernard C. & Whipple, Stuart J. & Schramski, John R. & Gattie, David K., 2007. "Equivalence of throughflow- and storage-based environs," Ecological Modelling, Elsevier, vol. 206(3), pages 400-406.
    • Handle: RePEc:eee:ecomod:v:206:y:2007:i:3:p:400-406
    DOI: 10.1016/j.ecolmodel.2007.04.005
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    References listed on IDEAS

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    1. Schramski, J.R. & Gattie, D.K. & Patten, B.C. & Borrett, S.R. & Fath, B.D. & Whipple, S.J., 2007. "Indirect effects and distributed control in ecosystems: Distributed control in the environ networks of a seven-compartment model of nitrogen flow in the Neuse River Estuary, USA—Time series analysis," Ecological Modelling, Elsevier, vol. 206(1), pages 18-30.
    2. Whipple, Stuart J. & Borrett, Stuart R. & Patten, Bernard C. & Gattie, David K. & Schramski, John R. & Bata, Seth A., 2007. "Indirect effects and distributed control in ecosystems: Comparative network environ analysis of a seven-compartment model of nitrogen flow in the Neuse River estuary, USA—Time series analysis," Ecological Modelling, Elsevier, vol. 206(1), pages 1-17.
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    Cited by:

    1. Fath, Brian D., 2014. "Sustainable systems promote wholeness-extending transformations: The contributions of systems thinking," Ecological Modelling, Elsevier, vol. 293(C), pages 42-48.
    2. Borrett, S.R. & Freeze, M.A. & Salas, A.K., 2011. "Equivalence of the realized input and output oriented indirect effects metrics in Ecological Network Analysis," Ecological Modelling, Elsevier, vol. 222(13), pages 2142-2148.
    3. Whipple, Stuart J. & Patten, Bernard C. & Borrett, Stuart R., 2014. "Indirect effects and distributed control in ecosystems," Ecological Modelling, Elsevier, vol. 293(C), pages 161-186.
    4. Zhang, Yan & Yang, Zhifeng & Yu, Xiangyi, 2009. "Ecological network and emergy analysis of urban metabolic systems: Model development, and a case study of four Chinese cities," Ecological Modelling, Elsevier, vol. 220(11), pages 1431-1442.

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