{
  "abstract": "Population fragmentation is a common feature of many biological systems. Understanding mutant fixation in such systems is challenging because the underlying stochastic dynamics are high-dimensional. In this work, we develop a general mathematical framework for analyzing stochastic evolution in fragmented populations connected by rare migration. The framework is sufficiently general to accommodate heterogeneous deme sizes, deme-dependent birth and death processes, and migration on arbitrary strongly connected directed networks with asymmetric migration rates. We show that, in the limit where migration occurs on a much slower timescale than within-deme dynamics, the full stochastic process can be reduced to a lower-dimensional Markov chain whose states correspond to configurations of fully mutant and fully wild-type demes. The reduction theorem establishes that fixation probabilities and absorption times of the original process are asymptotically determined by the corresponding quantities of a reduced chain. As an application, we derive explicit formulas for mutant fixation probabilities and fixation times in fragmented populations initiated by the introduction of a single mutant. The results provide a general and tractable approach for studying evolutionary dynamics in complex fragmented populations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.23946",
  "author_total": 2,
  "authors": [
    {
      "name": "Yi Fu"
    },
    {
      "name": "Natalia L. Komarova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0k5z9nx6qers4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.23946",
  "fulltext_url": null,
  "id": "0k5z9nx6qers4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.23946",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "openalex",
      "1311|Evolution and Genetic Dynamics"
    ]
  ],
  "openalex": "W7165762258",
  "pdf_url": "https://arxiv.org/pdf/2606.23946",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0k5z9nx6qers4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:56Z",
      "native_id": "2606.23946",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.23946"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    }
  ],
  "title": "Mutant Fixation for a Stochastic Evolutionary Model in Fragmented Populations",
  "title_text": "Mutant Fixation for a Stochastic Evolutionary Model in Fragmented Populations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:56Z",
  "url": "https://research.draconitic.com/paper/0k5z9nx6qers4",
  "venue": "arXiv",
  "versions": []
}