{
  "abstract": "Approximate solutions are found for Feller-like neutral multi-type branching diffusions $\\big{(}\\mathbf{X}(t)\\big{)}_{t \\in \\mathbb{R}_{\\ge 0}}$ in the limit of small mutation rates. The method employed involves solving approximations to the Laplace transformed forward Kolmogorov equation by integrating along characteristics. To leading order in the scale $θ$ of the overall mutation rate the super-critical diffusion is found to collapse onto a line density aligned with the stationary left eigenvector of the rate matrix following a rapid change of behaviour at a critical time $t_{\\rm c}$, which has a weak logarithmic dependence on $θ$. First order in $θ$ approximations to the density and moments of $\\mathbf{X}(t)$ are also determined. The first-order approximation corresponds to allowing at most one mutation in the coalescent tree of a sample and is valid for $t < t_{\\rm c}$ in the supercritical case, and more generally for the critical and sub-critical cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05804",
  "author_total": 1,
  "authors": [
    {
      "name": "Conrad J. Burden"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eqdqdymhxsrr0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05804",
  "fulltext_url": null,
  "id": "eqdqdymhxsrr0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05804",
  "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.PR"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7220741131",
  "pdf_url": "https://arxiv.org/pdf/2610.05804",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eqdqdymhxsrr0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05804",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05804"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Multi-type branching diffusions with small mutation rates",
  "title_text": "Multi-type branching diffusions with small mutation rates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:11Z",
  "url": "https://research.draconitic.com/paper/eqdqdymhxsrr0",
  "venue": "arXiv",
  "versions": []
}