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Sustainable network dynamics

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  • Dragicevic, Arnaud Z.
  • Sinclair-Desgagné, Bernard

Abstract

We propose a dynamic graph-theoretic model for ecosystem management as a control over networked system composed of target nodes and unmarked nodes. The network is represented by a complete graph, in which all vertices are connected by a unique edge. Target nodes are attracted by the objective function issued from the ecosystem-based management. They pull the network toward the objective position. The management policy is considered successful if the graph remains connected in time, that is, target nodes attain their objectives and unmarked nodes stay in the convex hull. At the time of the ecosystem network transfer, the model yields a separation theorem as well as a sustainability criterion to maintain full connectivity of the ecosystem. Our definition of sustainability can be easily linked to the general definition of sustainability as ecosystem integrity preservation. At last, we identify three management rules, dependent on the nature of connections, to ensure the maintenance of connectivity in time. The necessary and sufficient conditions for connectivity are (1) synchronous time-delays; (2) coequal magnitudes of increasing objective functions; and (3) nonnegativity of the objective function.

Suggested Citation

  • Dragicevic, Arnaud Z. & Sinclair-Desgagné, Bernard, 2013. "Sustainable network dynamics," Ecological Modelling, Elsevier, vol. 270(C), pages 43-53.
    • Handle: RePEc:eee:ecomod:v:270:y:2013:i:c:p:43-53
    DOI: 10.1016/j.ecolmodel.2013.09.003
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    References listed on IDEAS

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    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    2. Smith, Martin D. & Sanchirico, James N. & Wilen, James E., 2009. "The economics of spatial-dynamic processes: Applications to renewable resources," Journal of Environmental Economics and Management, Elsevier, vol. 57(1), pages 104-121, January.
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    Cited by:

    1. Arnaud Z. Dragicevic, 2019. "Market Coordination Under Non-Equilibrium Dynamics," Networks and Spatial Economics, Springer, vol. 19(3), pages 697-715, September.
    2. repec:wsi:acsxxx:v:21:y:2018:i:08:n:s0219525918500182 is not listed on IDEAS
    3. Dragicevic, Arnaud Z., 2020. "The economics of the Sylvo-Cynegetic equilibrium," Forest Policy and Economics, Elsevier, vol. 120(C).
    4. Dragicevic, Arnaud Z. & Shogren, Jason F., 2021. "Preservation Value in Socio-Ecological Systems," Ecological Modelling, Elsevier, vol. 443(C).

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    More about this item

    Keywords

    Bioeconomics; Ecosystem-based management; Forests; Graph theory; Connectedness;
    All these keywords.

    JEL classification:

    • Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation
    • Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics

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