Predicting the depth of the most recent common ancestor of a random sample of $k$ species: the impact of phylogenetic tree shape
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| Format: | Preprint |
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2025
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| _version_ | 1866911297286701056 |
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| author | Fuchs, Michael Steel, Mike |
| author_facet | Fuchs, Michael Steel, Mike |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Predicting the depth of the most recent common ancestor of a random sample of $k$ species: the impact of phylogenetic tree shape Fuchs, Michael Steel, Mike Populations and Evolution Combinatorics Probability 05C05, 05A16, 60C05, 92D15 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. |
| title | Predicting the depth of the most recent common ancestor of a random sample of $k$ species: the impact of phylogenetic tree shape |
| topic | Populations and Evolution Combinatorics Probability 05C05, 05A16, 60C05, 92D15 |
| url | https://arxiv.org/abs/2501.09270 |