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The probabilities of rooted tree-shapes generated by random bifurcation
Abstract
The set of rooted trees, generated by random bifurcation at the terminal nodes, is considered with the aims of enumerating it and of determining its probability distribution. The account of enumeration collates much previous work and attempts a complete perspective of the problems and their solutions. Asymptotic and numerical results are given, and some unsolved problems are pointed out. The problem of ascertaining the probability distribution is solved by obtaining its governing recurrence equation, and numerical results are given. The difficult problem of determining the most probable tree-shape of given size is considered, and for labelled trees a conjecture at its solution is offered. For unlabelled shapes the problem remains open. These mathematical problems arise in attempting to reconstruct evolutionary trees by the statistical approach of Cavalli-Sforza and Edwards.
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Cited by
Ultrafast Approximation for Phylogenetic Bootstrap
Minh, B. Q., Nguyen, M. A. T., & von Haeseler, A. (2013) · Molecular Biology and Evolution · doi:10.1093/molbev/mst024 · Cited by 4,844
Mapping Phylogenetic Trees to Reveal Distinct Patterns of Evolution
Kendall, M., & Colijn, C. (2016) · Molecular Biology and Evolution · doi:10.1093/molbev/msw124 · Cited by 134
Metadata
- Authors
- Harding, E.
- Venue
- Advances in Applied Probability
- Publisher
- Cambridge University Press
- Published
- 1971-01-01
- Volume
- 3
- Issue
- 01
- Pages
- 44-77
- ISSN
- 0001-8678 (ISSN-L)
- OpenAlex
- W2130727968
- Cited by
- 317
- References
- 0
- FWCI
- 1.67
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
