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Dynamic environ analysis of compartmental systems: A computational approach

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  • Shevtsov, Jane
  • Kazanci, Caner
  • Patten, Bernard C.

Abstract

Ecosystems are often modeled as stocks of matter or energy connected by flows. Network environ analysis (NEA) is a set of mathematical methods for using powers of matrices to trace energy and material flows through such models. NEA has revealed several interesting properties of flow–storage networks, including dominance of indirect effects and the tendency for networks to create mutually positive interactions between species. However, the applicability of NEA is greatly limited by the fact that it can only be applied to models at constant steady states. In this paper, we present a new, computationally oriented approach to environ analysis called dynamic environ approximation (DEA). As a test of DEA, we use it to compute compartment throughflow in two implementations of a model of energy flow through an oyster reef ecosystem. We use a newly derived equation to compute model throughflow and compare its output to that of DEA. We find that DEA approximates the exact results given by this equation quite closely – in this particular case, with a mean Euclidean error ranging between 0.0008 and 0.21 – which gives a sense of how closely it reproduces other NEA-related quantities that cannot be exactly computed and discuss how to reduce this error. An application to calculating indirect flows in ecosystems is also discussed and dominance of indirect effects in a nonlinear model is demonstrated.

Suggested Citation

  • Shevtsov, Jane & Kazanci, Caner & Patten, Bernard C., 2009. "Dynamic environ analysis of compartmental systems: A computational approach," Ecological Modelling, Elsevier, vol. 220(22), pages 3219-3224.
    • Handle: RePEc:eee:ecomod:v:220:y:2009:i:22:p:3219-3224
    DOI: 10.1016/j.ecolmodel.2009.07.022
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    References listed on IDEAS

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    1. David Kendrick, 1972. "On the Leontief Dynamic Inverse," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 86(4), pages 693-696.
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    Cited by:

    1. Zell, Chris & Hubbart, Jason A., 2013. "Interdisciplinary linkages of biophysical processes and resilience theory: Pursuing predictability," Ecological Modelling, Elsevier, vol. 248(C), pages 1-10.
    2. Rodríguez, Ricardo A. & Herrera, Ada Ma. & Riera, Rodrigo & Delgado, Juan D. & Quirós, Ángel & Perdomo, María E. & Santander, Jacobo & Miranda, Jezahel V. & Fernández-Rodríguez, María J. & Jiménez-Rod, 2015. "Thermostatistical distribution of a trophic energy proxy with analytical consequences for evolutionary ecology, species coexistence and the maximum entropy formalism," Ecological Modelling, Elsevier, vol. 296(C), pages 24-35.
    3. Coskun, Huseyin, 2018. "Dynamic Ecological System Analysis," OSF Preprints 35xkb, Center for Open Science.
    4. Borrett, S.R. & Freeze, M.A., 2011. "Reconnecting environs to their environment," Ecological Modelling, Elsevier, vol. 222(14), pages 2393-2403.
    5. Varga, M. & Csukas, B., 2017. "Generation of extensible ecosystem models from a network structure and from locally executable programs," Ecological Modelling, Elsevier, vol. 364(C), pages 25-41.
    6. Schaubroeck, Thomas & Staelens, Jeroen & Verheyen, Kris & Muys, Bart & Dewulf, Jo, 2012. "Improved ecological network analysis for environmental sustainability assessment; a case study on a forest ecosystem," Ecological Modelling, Elsevier, vol. 247(C), pages 144-156.
    7. Kazanci, C. & Ma, Q., 2012. "Extending ecological network analysis measures to dynamic ecosystem models," Ecological Modelling, Elsevier, vol. 242(C), pages 180-188.
    8. Liu, G.Y. & Yang, Z.F. & Chen, B. & Zhang, Y., 2011. "Ecological network determination of sectoral linkages, utility relations and structural characteristics on urban ecological economic system," Ecological Modelling, Elsevier, vol. 222(15), pages 2825-2834.
    9. Tuominen, Lindsey K. & Whipple, Stuart J. & Patten, Bernard C. & Karatas, Zekeriya Y. & Kazanci, Caner, 2014. "Contribution of throughflows to the ecological interpretation of integral network utility," Ecological Modelling, Elsevier, vol. 293(C), pages 187-201.
    10. Borrett, S.R. & Salas, A.K., 2010. "Evidence for resource homogenization in 50 trophic ecosystem networks," Ecological Modelling, Elsevier, vol. 221(13), pages 1710-1716.
    11. Patten, Bernard C., 2016. "The cardinal hypotheses of Holoecology," Ecological Modelling, Elsevier, vol. 319(C), pages 63-111.

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