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The Complexity–Stability Debate, Chemical Organization Theory, and the Identification of Non-classical Structures in Ecology

  • Tomas VelozEmail author
Article
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Abstract

We present a novel approach to represent ecological systems using reaction networks, and show how a particular framework called chemical organization theory (COT) sheds new light on the longstanding complexity–stability debate. Namely, COT provides a novel conceptual landscape plenty of analytic tools to explore the interplay between structure and stability of ecological systems. Given a large set of species and their interactions, COT identifies, in a computationally feasible way, each and every sub-collection of species that is closed and self-maintaining. These sub-collections, called organizations, correspond to the groups of species that can survive together (co-exist) in the long-term. Thus, the set of organizations contains all the stable regimes that can possibly happen in the dynamics of the ecological system. From here, we propose to conceive the notion of stability from the properties of the organizations, and thus apply the vast knowledge on the stability of reaction networks to the complexity–stability debate. As an example of the potential of COT to introduce new mathematical tools, we show that the set of organizations can be equipped with suitable joint and meet operators, and that for certain ecological systems the organizational structure is a non-boolean lattice, providing in this way an unexpected connection between logico-algebraic structures, popular in the foundations of quantum theory, and ecology.

Keywords

Ecological modeling Complexity stability debate Reaction networks Chemical organization theory Non-boolean lattice 

Notes

Acknowledgements

This work was supported by the postdoctoral Project Fondecyt 3170122.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Center Leo Apostel for Interdisciplinary StudiesVrije Universiteit BrusselBrusselsBelgium
  2. 2.Instituto de Filosofía y Ciencias de la Complejidad and Fundación DICTASantiagoChile
  3. 3.Departamento Ciencias Biológicas Facultad Ciencias de la VidaUniversidad Andres BelloSantiagoChile

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