 On cherry and pitchfork distributions of random rooted and unrooted phylogenetic treesKwok Pui Choi, Ariadne Thompson and Taoyang Wu Theoretical Population Biology, 2020, vol. 132, issue C, 92-104 Abstract: Tree shape statistics are important for investigating evolutionary mechanisms mediating phylogenetic trees. As a step towards bridging shape statistics between rooted and unrooted trees, we present a comparison study on two subtree statistics known as numbers of cherries and pitchforks for the proportional to distinguishable arrangements (PDA) and the Yule–Harding–Kingman (YHK) models. Based on recursive formulas on the joint distribution of the number of cherries and that of pitchforks, it is shown that cherry distributions are log-concave for both rooted and unrooted trees under these two models. Furthermore, the mean number of cherries and that of pitchforks for unrooted trees converge respectively to those for rooted trees under the YHK model while there exists a limiting gap of 1∕4 for the PDA model. Finally, the total variation distances between the cherry distributions of rooted and those of unrooted trees converge for both models. Our results indicate that caution is required for conducting statistical analysis for tree shapes involving both rooted and unrooted trees. Keywords: Tree shape; Subtree distribution; Yule–Harding–Kingman model; PDA model; Total variation distance (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:132:y:2020:i:c:p:92-104 DOI: 10.1016/j.tpb.2020.02.001 Access Statistics for this article Theoretical Population Biology is currently edited by Jeremy Van Cleve More articles in Theoretical Population Biology from Elsevier |
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