{
  "abstract": "Like pairwise distances, quartets can be highly redundant and correlated on a phylogenetic tree, and their number grows on the order of n^4 rather than n^2. I explore BME-like weights for reweighting quartet scores before summing them to score a full tree. Three weights are considered on an unrooted binary tree: w_ext(q)=2^(-I_ext(q)), w_int(q)=2^(-I_int(q)), and w_tot(q)=2^(-I_tot(q))=w_ext(q)w_int(q), where the exponents count specified internal nodes in the minimal connecting subtree of a quartet. Exact tree-shape counts, total quartet-weight sums, and internal-edge crossing sums are calculated for all unlabeled unrooted binary tree shapes on 6-10 taxa. For w_ext, the total quartet weight is tree-shape-invariant and the edge-crossing sum depends only on split size. For any n-leaf tree, we prove sum_q w_ext(q)=(n-2)(n-3)/8, and the sum over quartets crossing an internal edge with split a|b equals (a-1)(b-1)/4. Exact tree-shape-specific normalizers are also derived for w_int and w_tot. A degree-corrected hard-polytomy extension is given for multifurcating trees, and a conditional consistency result shows that these positive weights preserve consistency when the underlying quartet estimates are themselves consistent for the true induced quartet states. These results provide a mathematical foundation for evaluating and applying BME-like quartet weights to reduce redundancy with the particular aim of improving statistical efficiency with finite data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00614",
  "author_total": 1,
  "authors": [
    {
      "name": "Peter J. Waddell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cq1dq7mvy0k8g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00614",
  "fulltext_url": null,
  "id": "cq1dq7mvy0k8g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00614",
  "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",
      "q-bio.PE"
    ],
    [
      "openalex",
      "1312|Genomics and Phylogenetic Studies"
    ]
  ],
  "openalex": "W7206214590",
  "pdf_url": "https://arxiv.org/pdf/2609.00614",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cq1dq7mvy0k8g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:05Z",
      "native_id": "2609.00614",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00614"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    }
  ],
  "title": "BME-like Quartet Weights for Phylogenetic Trees",
  "title_text": "BME-like Quartet Weights for Phylogenetic Trees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:05Z",
  "url": "https://research.draconitic.com/paper/cq1dq7mvy0k8g",
  "venue": "arXiv",
  "versions": []
}