Growth of a hypercycle and comparison with conventional autocatalysis

The hypercycle is a chemical model for reproduction which has been advocated for early stages of biological evolution. Its advantage is thought to lie in the high rate of growth conferred by hyperbolic kinetics. Earlier work has also indicated a saturation phase at large constituent concentrations. The present paper shows that both the saturation phase and the phase of hyperbolic growth have been introduced into the kinetics by making some of the reactions reversible. Reversibility is not essential to the operation of the hypercycle and the system with irreversible reactions grows faster. However, even the fastest hypercycle does not grow as fast as the simple autocatalyst obtained by removing that reaction which is characteristic of the hypercycle. Also, both because the hypercycle is not a coherent system and because its growth requires reactions among separated constituents in the medium, it is more subject to decay than a simple autocatalytic particle. With greater complexity, slower growth, and more severe decay, the hypercycle is not a satisfactory alternative to conventional models of reproduction.