ArticlePhilosophical transactions of the Royal Society of London. Series B, Biological sciences2025
Labelled histories with multifurcation and simultaneity.
Article in Philosophical transactions of the Royal Society of London. Series B, Biological sciences, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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4 citing papers in PubMed.
- "A mathematical theory of evolution": phylogenetic models dating back 100 years.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2025Article
- Reading tree leaves: inferring speciation anfd extinction processes using phylogenies.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2025Review
- Tree balance in phylogenetic models.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2025Article
- Shape parameters of evolutionary trees in theoretical computer science.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2025Review
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Abstract
In mathematical models of phylogenetic trees evolving in time, a labelled history for a rooted labelled bifurcating tree is a temporal sequence of the branchings that give rise to the tree. That is, given a leaf-labelled tree with [Formula: see text] leaves and [Formula: see text] internal nodes, a labelled history is an identification between the internal nodes and the set [Formula: see text], such that the label assigned to a given node is strictly greater than the labels assigned to its descendants. We generalize the concept of labelled histories to [Formula: see text]-furcating trees. Consider a rooted labelled tree in which each internal node has exactly [Formula: see text] children, [Formula: see text]. We first generalize the enumeration of labelled histories for a bifurcating tree ([Formula: see text]) to enumerate labelled histories for an [Formula: see text]-furcating tree with arbitrary [Formula: see text]. We formulate a conjecture for the rooted unlabelled [Formula: see text]-furcating tree shape on [Formula: see text] internal nodes whose labelled topologies have the most labelled histories. Finally, we enumerate labelled histories for [Formula: see text]-furcating trees in a setting that allows for simultaneous branchings. These results advance mathematical phylogenetic modelling by extending computations concerning fundamental features of bifurcating phylogenetic trees to a more general class of multifurcating trees.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.
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