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

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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.

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Notes

  1. We omit the mathematical formulation of this property for simplicity.

  2. This is known in reaction network modeling as a flux vector. A flux vector is an specification of the relative rates of occurrence of reactions in the network.

  3. The ecological model we present in Fig. 2 might be a little unrealistic for an ecologist. However, it is important to note that this example aims at obtaining a non-distributive organizational structure for the smallest possible system. It is possible to find non-distributive organizational structures following only the interactions depicted in Table 2, but using a larger number of species and interactions.

  4. Non-reactive organizations such as \(\{s_1\}\) and \(\{s_2\}\) are omitted for simplicity

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Acknowledgements

This work was supported by the postdoctoral Project Fondecyt 3170122.

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  1. Center Leo Apostel for Interdisciplinary Studies, Vrije Universiteit Brussel, Brussels, Belgium

    Tomas Veloz

  2. Instituto de Filosofía y Ciencias de la Complejidad and Fundación DICTA, Santiago, Chile

    Tomas Veloz

  3. Departamento Ciencias Biológicas Facultad Ciencias de la Vida, Universidad Andres Bello, 8370146, Santiago, Chile

    Tomas Veloz

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Veloz, T. The Complexity–Stability Debate, Chemical Organization Theory, and the Identification of Non-classical Structures in Ecology. Found Sci 25, 259–273 (2020). https://doi.org/10.1007/s10699-019-09639-y

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