Evidence map›Paper›PMID 40332676›Full record

ArticleBulletin of mathematical biology2025

Asymptotic Enumeration of Normal and Hybridization Networks via Tree Decoration.

Michael Fuchs, Mike Steel, Qiang Zhang

Abstract read
PubMed Full text at PMC Publisher
In one paragraph

Article in Bulletin of mathematical biology, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.

0numbers the graph read from it
0cells of the map it votes in
3citing papers in PubMed
–field-weighted citation impact
1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

3 citing papers in PubMed.

  1. Counting Spinal Phylogenetic Networks.Bulletin of mathematical biology · 2026
    Article
  2. Counting Rankings of Tree-Child Networks.Bulletin of mathematical biology · 2026
    Article
  3. Article
4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

3 authors.

Michael FuchsDepartment of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan.ORCID https://orcid.org/0000-0001-8891-6897
Mike SteelBiomathematics Research Centre, University of Canterbury, Christchurch, New Zealand. mike.steel@canterbury.ac.nz.ORCID http://orcid.org/0000-0001-7015-4644
Qiang ZhangBiomathematics Research Centre, University of Canterbury, Christchurch, New Zealand.

Funding

Marsden Fund 23-UOC-003National Science and Technology Council NSTC-113-2115-M-004-004-MY3National Science and Technology Council NSTC-113-2918-I-004-001
6 · The paper itself

Abstract

Phylogenetic networks provide a more general description of evolutionary relationships than rooted phylogenetic trees. One way to produce a phylogenetic network is to randomly place k arcs between the edges of a rooted binary phylogenetic tree with n leaves. The resulting directed graph may fail to be a phylogenetic network, and even when it is it may fail to be a tree-child or normal network. In this paper, we first show that if k is fixed, the proportion of arc placements that result in a normal network tends to 1 as n grows. From this result, the asymptotic enumeration of normal networks becomes straightforward and provides a transparent meaning to the combinatorial terms that arise. Moreover, the approach extends to allow k to grow with n (at the rate

Indexed as

Hybridization, GeneticModels, GeneticPhylogenyMathematical ConceptsAsymptotic enumerationGenerating functionPhylogenetic networkTrees

Identifiers

PMID40332676
PMCPMC12058904

What OpenQuestion holds

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Registered trials

None linked

Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.