2021/01/19 by Kwok Pui Choi, Choi, Kwok Pui, Gursharn Kaur +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Earth and Planetary Sciences · #Bayesian Methods and Mixture Models #Evolution and Paleontology Studies #FOS: Mathematics #Genomics and Phylogenetic Studies #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2101.07488
openalex publication_date 2021/01/19 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
Tree shape statistics provide valuable quantitative insights into evolutionary mechanisms underpinning phylogenetic trees, a commonly used graph representation of evolution systems ranging from viruses to species. By developing limit theorems for a version of extended Pólya urn models in which negative entries are permitted for their replacement matrices, we present strong laws of large numbers and central limit theorems for asymptotic joint distributions of two subtree counting statistics, the number of cherries and that 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. Our results indicate that the limiting behaviour of these two statistics, when appropriately scaled, are independent of the initial trees used in the tree generating process.