Schuster, Peter

The single-step autocatalytic reaction A + X ↔ 2X in different environments—batch reactor, flow reactor, logistic equation—is studied by means of conventional deterministic kinetics and as a stochastic process. Self-enhancement requires an initial concentration of the autocatalyst X—at least in seeding amounts—for starting the reaction. Deterministic solution curves have sigmoid shapes. At small concentrations, three stochastic phenomena are observed: (1) thermal fluctuations, (2) stochastic delay, and (3) stochastic bifurcations and anomalous fluctuations in case of multiple final states. The introduction of heterogeneous populations containing subspecies with different fitness values gives rise to natural selection in all three environments investigated here. In large populations, survival of the fittest is observed, whereas random fluctuations may result in selection of each of the subspecies. Then, the fitness values determine only probabilities of selection. The fittest subspecies, of course, has the largest probability of selection. There is a smooth transition to neutral evolution where the probabilities of selection are the same for all subspecies.