2025/01/16 by Michael Fuchs, Fuchs, Michael, Mike Steel +1
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · #05A16 #05C05 #60C05 #92D15 #Combinatorics (math.CO) #Evolution and Paleontology Studies #FOS: Biological sciences #FOS: Mathematics #Genetic diversity and population structure #Genomics and Phylogenetic Studies #Populations and Evolution (q-bio.PE) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2501.09270
openalex publication_date 2025/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the following question: how close to the ancestral root of a phylogenetic tree is the most recent common ancestor of k species randomly sampled from the tips of the tree? For trees having shapes predicted by the Yule-Harding model, it is known that the most recent common ancestor is likely to be close to (or equal to) the root of the full tree, even as n becomes large (for k fixed). However, this result does not extend to models of tree shape that more closely describe phylogenies encountered in evolutionary biology. We investigate the impact of tree shape (via the Aldous β-splitting model) to predict the number of edges that separate the most recent common ancestor of a random sample of k tip species and the root of the parent tree they are sampled from. Both exact and asymptotic results are presented. We also briefly consider a variation of the process in which a random number of tip species are sampled.