{
  "abstract": "Phylogenetic networks provide a natural framework for representing reticulate evolutionary events such as horizontal gene transfer and hybridization. In the present manuscript, we investigate the identifiability of phylogenetic networks under (hardwired) parsimony, a natural extension of Maximum Parsimony from trees to networks. More precisely, we ask which structural features of a network can be uniquely inferred from so-called $A_k$-alignments under this criterion. While identifiability has been studied extensively for phylogenetic trees under parsimony, little is known about the identifiability of networks under hardwired parsimony. We take a first step towards addressing this gap by developing a general framework for studying identifiability under hardwired parsimony. We then use this framework to show that the tree of blobs of a phylogenetic network can be reconstructed from its $A_1$-alignment. This result can be viewed as a natural extension of Buneman's well-known splits equivalence theorem. Finally, we show that, under hardwired parsimony, cycles of length at least $5$ cannot in general be uniquely identified from character data, establishing a fundamental limitation of hardwired parsimony.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41725",
  "author_total": 2,
  "authors": [
    {
      "name": "Mirko Wilde"
    },
    {
      "name": "Mareike Fischer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4j74ryprqwk90.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41725",
  "fulltext_url": null,
  "id": "4j74ryprqwk90",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41725",
  "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.CO"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41725",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4j74ryprqwk90.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41725",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41725"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An extension of the classic Buneman theorem from phylogenetic trees to networks",
  "title_text": "An extension of the classic Buneman theorem from phylogenetic trees to networks",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/4j74ryprqwk90",
  "venue": "arXiv",
  "versions": []
}