{
  "abstract": "We give a probabilistic proof of a multivariate Bernstein duality for a multivariate Wright--Fisher frequency process with selection encoded by a finite tournament. The construction includes nontransitive interactions, such as rock--paper--scissors selection. Its dual is a pure-jump process of coefficient functions in the multinomial Bernstein basis. Selection increases the Bernstein degree through a winner--loser averaging operator, whereas neutral resampling decreases it through a duplication operator. For the proof, we construct a continuous forward process independently of duality, use duality to establish uniqueness, and obtain a weak stochastic differential equation representation and invariance of the simplex faces. This provides a sampling-based treatment of the tournament specialization of multitype Bernstein duality, extending an open problem in the binary Kingman setting of Cordero, Hummel, and Schertzer (2022).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.13731",
  "author_total": 1,
  "authors": [
    {
      "name": "Osvaldo Angtuncio Hernández"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18saev7sqqjbn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.13731",
  "fulltext_url": null,
  "id": "18saev7sqqjbn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.13731",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.13731",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18saev7sqqjbn.ris",
  "sources": [
    {
      "first_seen": "2026-11-11T06:21:55Z",
      "native_id": "2611.13731",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.13731"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Multivariate Bernstein duality for tournament Wright--Fisher diffusions",
  "title_text": "Multivariate Bernstein duality for tournament Wright--Fisher diffusions",
  "type": "preprint",
  "updated_at": "2026-11-13T06:20:14Z",
  "url": "https://research.draconitic.com/paper/18saev7sqqjbn",
  "venue": "arXiv",
  "versions": []
}