Information bounds production in replicator systems

Abstract: We investigate minimal replicator systems that are able to use information in a functional manner. We consider a population of autocatalytic replicators in a flow reactor that are subject to fluctuating environments. We derive expressions of replicator production in terms of information-theoretic quantities, reflecting separate contributions from environmental uncertainty, side information, and distribution mismatch. We also derive the optimal strategy for preparing replicator concentrations, as well as a universal information-theoretic bound on the increase of productivity. We compare and contrast our findings with existing results, including 'Kelly gambling' in information theory and 'substitutional load' in evolutionary biology. The results are illustrated on a model of real-world self-assembled molecular replicators. In this real-world system, we demonstrate the benefit of internal memory when subjected to environments with temporal correlations, and we propose a plausible experimental setup for detecting the signature of functional information. We briefly discuss the role that information-processing may play in guiding the evolution of prebiotic replicator networks.