Self-Replication as the Precondition of Evolution: The Error Threshold, the Eigen Paradox and Open Problems

Why must life copy itself, and how long can a copied message be before errors destroy it? This paper is part of the BILM programme (Bioelectric Integrity of Living Matter); it is a review that serves as the reference point for self-replication in the other papers of the programme. It rests on the literature; our own reasoning is marked in the text. Three concepts that everyday speech runs together are separated: autocatalysis, template-directed replication and reproduction. Von Neumann's requirements for a self-reproducing system are presented, together with Eigen's error threshold in its full form: without an accurate copying enzyme, the length of a sequence that can be maintained is no greater than ln σ / μ (μ — the error rate per site; σ — how much faster the error-free copy multiplies than erroneous ones). For copying without enzymes this is from about ten to two hundred monomers, whereas coding for an accurate enzyme usually requires a longer sequence. This mismatch — Eigen's paradox — remains one of the main unresolved gaps; recent small polymerase ribozymes narrow it but do not close it. The ways in which living things reproduce are listed, from DNA copying and cell division to sexual reproduction. Sex appears to have been present already in the common ancestor of eukaryotes, before multicellularity in eukaryotes; bacterial multicellularity appears to be older and manages without sex. Where the literature admits two readings (for example, whether the common ancestor of animals was a hermaphrodite), both are named together with what would decide between them. Lewontin's conditions for selection, the major evolutionary transitions, the germline and ageing are set out. Status: a review; Eigen's paradox is open; it is stated explicitly that neither the diversity of species nor the directedness of evolution follows from self-replication alone. Relation to the BILM programme and disclosure. The programme proposes one formulation of life: the self-replication of systems, each of which maintains its own biological voltage — a paid ion difference on its closed boundary (lineages copy themselves; units hold the voltage). This paper covers the first half of that formulation — self-replication of lineages. Companion papers: What Is the Self? A Bioelectric Definition from Bacteria to Humans (10.5281/zenodo.21779503); Can Life Experience Change the Mutations of Offspring? (10.5281/zenodo.24056523); The Evolution of Multicellularity (10.5281/zenodo.21772046); Origin of Life: Five Steps from Chemistry to the First Cell (10.5281/zenodo.21761285); the main paper of the programme — What Is Life? A Testable Definition (10.5281/zenodo.21779018). The cosmological counterpart is the author's paper Self-Replication as a Universal Principle (10.5281/zenodo.21762123). A non-peer-reviewed preprint by the author. Literature searches, source checks and critical review were carried out with the AI assistant Claude (Anthropic) under the author's direction; AI tools also helped to draft the text and to translate it into English (the author checked it and is responsible for the content). The working correspondence is available on request. The work was carried out without external funding, at the author's own expense; there are no competing interests.