{
  "abstract": "We propose and analyse a mathematical model of evolutionary adaptation for non-degenerate (permanent) replicator systems, in which the fitness landscape matrix evolves on a slow timescale -- the evolutionary time -- while the species dynamics unfold on a fast timescale. Under a two-timescale separation justified by Tikhonov's theorem, the adaptation problem reduces to maximising the mean fitness at steady state over a convex admissible set of fitness landscape matrices. We derive a fitness variation formula and establish necessary and sufficient conditions for a fitness maximum, showing that the optimisation reduces at each step to a linear programming problem. The algorithm is applied to four canonical replicator systems: the hypercycle, the bi-hypercycle, the anthill system, and the RNA molecule network. In all cases the evolutionary process follows a universal three-phase pattern: an initial phase of fitness growth without equilibrium shift, during which purely altruistic replication gives way to mixed altruistic-selfish behaviour; a second phase of dominant species emergence; and a stabilisation phase analogous to the error catastrophe threshold in quasispecies models. A key consequence is that all evolved systems acquire resistance to parasitic species. We further prove that without non-degeneracy constraints the process leads to sequential species annihilation, with a provable spectral lower bound on fitness increase by dimension reduction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.04456",
  "author_total": 3,
  "authors": [
    {
      "name": "Alexander S. Bratus"
    },
    {
      "name": "Sergey Drozhzhin"
    },
    {
      "name": "Tatiana Yakushkina"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56wastw27ntd6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.04456",
  "fulltext_url": null,
  "id": "56wastw27ntd6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.04456",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "openalex",
      "1311|Evolution and Genetic Dynamics"
    ]
  ],
  "openalex": "W7167608552",
  "pdf_url": "https://arxiv.org/pdf/2607.04456",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56wastw27ntd6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2607.04456",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.04456"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Mathematical Model of Evolution of Non-Degenerate Replicator Systems",
  "title_text": "Mathematical Model of Evolution of Non-Degenerate Replicator Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:02Z",
  "url": "https://research.draconitic.com/paper/56wastw27ntd6",
  "venue": "arXiv",
  "versions": []
}