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<p>We consider the following question: how close to the ancestral root of a phylogenetic tree is the most recent common ancestor of <i>k</i> 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 <i>n</i> becomes large (for <i>k</i> 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta -\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>β</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>splitting model) to predict the number of edges that separate the most recent common ancestor of a random sample of <i>k</i> 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.</p>

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Predicting the depth of the most recent common ancestor of a random sample of k species: the impact of phylogenetic tree shape

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Michael Fuchs,
  • Mike Steel

摘要

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 \(\beta -\) 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.