The Complexity-Stability Debate, Chemical Organization Theory, and the Identi cation of Non-Classical Structures in Ecology

TL;DR

This paper introduces Chemical Organization Theory as a novel framework to analyze ecological systems, revealing stable species groups and connecting ecological stability with reaction network properties, including non-boolean lattice structures.

Contribution

It applies COT to ecology, identifying stable species organizations and uncovering non-classical algebraic structures in ecological stability analysis.

Findings

COT identifies all stable species groups in ecological systems.

The organizational structure can form non-boolean lattices.

Provides new mathematical tools for the complexity-stability debate.

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.