ArticleJournal of mathematical biology2021
On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees.
Article in Journal of mathematical biology, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Inference of chromosome selection parameters and missegregation rate in cancer from DNA-sequencing data.Scientific reports · 2024Article
- Network representation and analysis of energy coupling mechanisms in cellular metabolism by a graph-theoretical approach.Theory in biosciences = Theorie in den Biowissenschaften · 2022Article
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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.
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