{
  "abstract": "Sequences in a protein family do not explore the sequence space freely: folding, packing, and binding couple residues, so the set of viable sequences is irreducibly correlated, a phenomenon referred to as epistasis. We show that such correlations lower the \\emph{intrinsic dimension} $d_{\\rm IN}$ of sequence space, counteracting the concentration of measure and broadening the distribution of pairwise distances. Consequentially, they make it likely that independently evolving lineages \\emph{recur}, approaching one another by chance long after they last shared an ancestor. Using Kac's lemma we show that the logarithmic mean recurrence time grows linearly with the intrinsic dimension, $\\log τ_{\\rm rec} \\propto {d_{\\rm IN}}$ for typical sequences, so strongly constrained (low-dimensional) families recur often and generate sequence similarity that carries no genealogical signal. We establish this first in a solvable Ising-like model with tunable correlation, then in a real protein family using Potts models and Markov chain Monte Carlo, where $d_{\\rm IN}$ remains predictive of recurrence even in multi-basins landscapes. Because recurrence is a property of the evolutionary process rather than of any estimator, it bounds the recoverability of deep history for distance-based and likelihood methods alike.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00360",
  "author_total": 4,
  "authors": [
    {
      "name": "Pietro Chiarantoni"
    },
    {
      "name": "Mina Mahboubi"
    },
    {
      "name": "Jason Lamanna"
    },
    {
      "name": "Vincenzo Carnevale"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5z2zwgexk7c8a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00360",
  "fulltext_url": null,
  "id": "5z2zwgexk7c8a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00360",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "q-bio.QM"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00360",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5z2zwgexk7c8a.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.00360",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00360"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.QM",
      "subfield": "bioinformatics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Recurrence in Sequence Space: How Epistasis Mimics Shared Ancestry",
  "title_text": "Recurrence in Sequence Space: How Epistasis Mimics Shared Ancestry",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:13Z",
  "url": "https://research.draconitic.com/paper/5z2zwgexk7c8a",
  "venue": "arXiv",
  "versions": []
}