On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees

Choi, Kwok Pui, Kaur, Gursharn and Wu, Taoyang (2021) On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees. Journal of Mathematical Biology, 83 (4). ISSN 0303-6812

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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
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Depositing User: LivePure Connector
Date Deposited: 10 Sep 2021 00:23
Last Modified: 06 Jan 2022 01:14
URI: https://ueaeprints.uea.ac.uk/id/eprint/81352
DOI: 10.1007/s00285-021-01667-2

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