Tools
Tools
Choi, Kwok Pui, Kaur, Gursharn and Wu, Taoyang 
ORCID: https://orcid.org/0000-0002-2663-2001
(2021)
On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees.
Journal of Mathematical Biology, 83 (4).
ISSN 0303-6812
Preview |
PDF (Published_Version)
- Published Version
Available under License Creative Commons Attribution. Download (670kB) | Preview |
Abstract
Tree shape statistics provide valuable quantitative insights into evolutionary mechanisms underpinning phylogenetic trees, a commonly used graph representation of evolutionary relationships among taxonomic units ranging from viruses to species. We study two subtree counting statistics, the number of cherries and the number of pitchforks, for random phylogenetic trees generated by two widely used null tree models: the proportional to distinguishable arrangements (PDA) and the Yule-Harding-Kingman (YHK) models. By developing limit theorems for a version of extended Pólya urn models in which negative entries are permitted for their replacement matrices, we deduce the strong laws of large numbers and the central limit theorems for the joint distributions of these two counting statistics for the PDA and the YHK models. Our results indicate that the limiting behaviour of these two statistics, when appropriately scaled using the number of leaves in the underlying trees, is independent of the initial tree used in the tree generating process.
| Item Type: | Article |
|---|---|
| Additional Information: | Funding Information: K.P. Choi acknowledges the support of Singapore Ministry of Education Academic Research Fund R-155-000-188-114. The work of Gursharn Kaur was supported by NUS Research Grant R-155-000-198-114. |
| Uncontrolled Keywords: | joint subtree distributions,limit distributions,pda model,pólya urn model,tree shape,yule-harding-kingman model,modelling and simulation,agricultural and biological sciences (miscellaneous),applied mathematics ,/dk/atira/pure/subjectarea/asjc/2600/2611 |
| Faculty \ School: | Faculty of Science > School of Computing Sciences |
| UEA Research Groups: | Faculty of Science > Research Groups > Computational Biology Faculty of Science > Research Centres > Centre for Ecology, Evolution and Conservation Faculty of Science > Research Groups > Data Science and AI |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 10 Sep 2021 00:23 |
| Last Modified: | 10 Dec 2024 01:37 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/81352 |
| DOI: | 10.1007/s00285-021-01667-2 |
Downloads
Downloads per month over past year
Actions (login required)
 |
View Item |