MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Molecular Replicator Dynamics

Bärbel M. R. Stadler and Peter F. Stadler


Template-dependent replication at the molecular level is the basis of reproduction in nature. A detailed understanding of the peculiarities of the chemical reaction kinetics associated with replication processes is therefore an indispensible prerequisite for any understanding of evolution at the molecular level. Networks of interacting self-replicating species can give rise to a wealth of different dynamical phenomena, from competitive exclusion to permanent coexistence, from global stability to multi-stability and chaotic dynamics. Nevertheless, there are some general principles that govern their overall behavior.

We focus on the question to what extent the dynamics of replication can explain the accumulation of genetic information that eventually leads to the emergence of the first cell and hence the origin of life as we know it. A large class of ligation based replication systems, which includes the experimentally available model systems for template directed self-replication, is of particular interest because its dynamics bridges the gap between the survival of a single fittest species to the global coexistence of everthing. In this intermediate regime the selection is weak enough to allow the coexistence of genetically unrelated replicators and strong enough to limit the accumulation of disfunctional mutants.

self-replication, ligation, autocatalytic network, quasispecies, hypercyle, replicator equation,, chemical kinetics, emergence

Related publications

2003 Repository Open Access
Peter F. Stadler and Bärbel M. R. Stadler

Molecular replicator dynamics

In: Advances in complex systems, 6 (2003) 1, pp. 47-77