Error Threshold

The error threshold is the mathematical limit on the fidelity of replication in evolving systems, first derived by Manfred Eigen in the 1970s. It states that a self-replicating information carrier can only maintain its identity if the copying error rate per symbol is lower than the reciprocal of its sequence length. A replicator of length L with an error rate ε per symbol can only be stably transmitted if ε < 1/L. Above this threshold, errors accumulate faster than selection can eliminate them, and the information content of the replicator collapses.

The error threshold is a fundamental constraint on the evolution of complexity. It explains why early life, presumably based on RNA replication without proofreading, was limited to simple molecular sequences. It also explains why the transition to DNA — with its dedicated polymerases and repair mechanisms — was a prerequisite for the evolution of complex cells. The error threshold is not merely a biological phenomenon. It applies to any system that transmits information through replication: memes, software, institutional knowledge, and cultural traditions all face analogous thresholds.

The error threshold has a dual. Below the threshold, replication is stable and information can accumulate. Above the threshold, replication is unstable and information degrades. The boundary between the two regimes is sharp, and crossing it is typically irreversible. In complex systems, the error threshold interacts with selection pressure to produce a dynamics in which complexity can only increase when error-correction mechanisms co-evolve with the replicators they protect. The evolution of complexity is, in this sense, the evolution of error-correction.