91-00-002

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Dynamics of Small Autocatalytic Reaction Network IV:

Inhomogeneous Replicator Equations

## Peter F. Stadler

The *inhomogeneous replicator equation* is derived as the
continuous time model for parallel first and second order
autocatalytic replication of macromolecules in a flow reactor based on
mass action kinetics. It is shown that the total concentration of
replicating material determines the relative importance of the first
order and the second order mechanism. A complete description of the
dynamics of the first order model and some special features of the
inhomogeneous replicator equation are presented. A minimal prebiotic
scenario with the potentiality to develop cooperation is derived from
the inhomogeneous replicator equation. In this model cooperation can
emerge when the total concentration of replication material exceeds a
certain threshold. Below this value, a single species is selected;
which one is determined by the rate constants of the first order
reaction alone. Above this threshold the second order process becomes
important and may lead to cooperative behaviour such as hypercycles.

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