Thermodynamics of Darwinian selection in molecular replicators

Abstract

We consider the relationship between thermodynamics, fitness, and Darwinian selection in autocatalytic molecular replicators. We uncover a thermodynamic bound that relates fitness, replication rate, and thermodynamic affinity of replication. This bound applies to a broad range of systems, including elementary and non-elementary autocatalytic reactions, polymer-based replicators, and certain kinds of autocatalytic sets. In addition, we show that the critical selection coefficient (the minimal fitness difference visible to selection) is bounded by a simple function of the affinity. Our results imply fundamental thermodynamic bounds on selection strength in molecular evolution, complementary to other bounds that arise from finite population sizes and error thresholds. These bounds may be relevant for understanding thermodynamic constraints faced by early replicators at the origin of life. We illustrate our approach on several examples, including a classic model of replicators in a chemostat.