Autocatalytic Sets and Models of Early Life
summary
Proves that self‑sustaining autocatalytic sets (RAFs) appear when the average number of reactions catalyzed per molecule μ grows about linearly with polymer length N — slower than linear gives vanishing probability, faster than linear gives near certainty — while the stronger constructively autocatalytic (CAF) notion needs exponential growth. Gives a polynomial‑time algorithm to find the maximal RAF, shows finding the smallest RAF is NP‑hard and that irreducible RAFs can be exponentially many, and uses Gillespie simulations to match lab data for a 16‑reaction, 18‑molecule RNA network with ~264 catalysis pairs.
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