Abstract
Several model systems of self-reproducing molecular species subject to the constraint of constant organization are investigated to see under what conditions more than one species may coexist over extended periods of time. It is found that while coexistence is not possible for systems of simple autocatalytic competitors, it can indeed occur if the nature of the reproductive process gives rise to “catalytic niches”. For systems catalyzed by
n Michaelis-Menten type enzymes, it is shown that no more than n species may coexist. A precise characterization is provided of “how different” two such enzymes must be in order to allow coexistence of two species. Under certain conditions, one observes a transition from one dominant species to another which may occur either via a coexistent state or directly, but with hysteresis.