The ecology and evolution of sub-exponential replicators

Systems of oligonucleotide chemical replicator molecules provide some of the finest, empirically realizable models of prebiotic evolution. Yet, a full understanding of their eco-evolutionary implications is hampered by conflicting assumptions, modeling strategies, and therefore predictions in the literature. Here we construct a model of these systems that accounts for the reversible association of templates and copies, ultimately leading to self-inhibition and sub-exponential growth. We show that, contrary to predictions from simplified model descriptions, there are well-defined limits on the attainable diversity of different replicator species. We also demonstrate that increasing the overall concentration of the system increases diversity, but counterintuitively, an analogous increase in the available resource concentration has the opposite effect. Most notably, if an exponentially-growing replicator is also present in the system, it absorbs any increase in the total replicator concentration, while the concentrations of the sub-exponential replicators remain unchanged. In the context of prebiotic evolution, this means that in high-concentration local environments, an exponential replicator can reach disproportionately high concentrations even if its copying rate is lower than that of the sub-exponential replicators. In a variable environment, this can lead to the eventual stochastic extinction of its competitors, with the exponentially growing species taking over the community.