Preprint 01-09-052

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Evolution in Systems of Ligation-Based Replicators

Bärbel M. R. Stadler, Peter F. Stadler, Peter R. Wills

The population dynamics of macromolecules that reproduce by means of template-directed ligation of two fragments are shown to be represented by a replicator equation with a special non-linear response function. This result is obtained through detailed consideration of the mechanism of ligation autocatalysis. In contrast to treatments which involve simplification to a parabolic growth law and the expectation of global coexistence of all species, we find that strong selection can take place in such systems, even when there is slow uncatalysed synthesis of replicators. Also, systems of this type are subject to invasion by new species that have a selective advantage. An expression is derived for the survival threshold in terms of species parameters and it is shown that this threshold depends on the total concentration of all species in the system. For a plausible distribution of species parameters, the number of surviving species coexisting above the threshold increases monotonically with increasing concentration. Illustrative numerical simulations are presented.

Autocatalytic Reaction Networks, Parabolic Growth, Extinction Threshold, Metadynamics

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