Self-generating autocatalytic networks: structural results, algorithms, and their relevance to evolutionary processes

The concept of an autocatalytic network of reactions that can form and persist, starting from just an available food source, has been formalised by the notion of a Reflexively-Autocatalytic and Food generated (RAF) set. The theory and algorithmic results concerning RAFs have been applied to a range of settings, from metabolic questions arising at the origin of life, to ecological networks, and cognitive models in cultural evolution. In this paper, we present new structural and algorithmic results concerning RAF sets, the identification of irreducible RAFs, and determining when certain reactions must occur before other reactions in a RAF (or, more generally, any F-generated set). We also describe how RAF theory extends to allow certain reactions to not require catalysis, and/or to require only catalysts that are not present in the food set, as well as to find minimal sets that are both a RAF and produce a given subset of elements. In all cases, the theory leads to efficient (polynomial-time) algorithms. We also briefly illustrate applications of RAF theory to two evolutionary processes in biology, namely, early metabolism and modelling the evolution of holobionts. ### Competing Interest Statement The authors have declared no competing interest.