Studying self-organisation across the biosphere with process-enablement graphs (2411.17012v2)

Abstract: At the heart of many contemporary theories of life is the concept of biological self-organisation: organisms have to continuously produce and maintain the conditions of their own existence in order to stay alive. The way in which these accounts articulate this concept, however, differs quite significantly. As a result, it can be difficult to identify self-organising features within biological systems, and to compare different descriptions of such features. In this paper, we develop a graph theoretic formalism -- process-enablement graphs -- to study the organisational structure of living systems. Cycles within these graphs capture self-organising components of a system in a general and abstract way. We build the mathematical tools needed to compare biological models as process-enablement graphs, facilitating a comparison of their corresponding descriptions of self-organisation in a consistent and precise manner. We apply our formalism to a range of classical theories of life and demonstrate exactly how these models are similar, and where they differ, with respect to their organisational structure. While our current framework does not demarcate living systems from non-living ones, it does allow us to better study systems that lie in the grey area between life and non-life.