标题： 预测随机样本中$k$个物种最近共同祖先的深度：系统发生树形状的影响 显示英文标题

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

摘要： 我们考虑以下问题：在系统发育树中，从树的末端随机抽取的$k$个物种的最近共同祖先，离祖先根有多近？ 对于由 Yule-Harding 模型预测形状的树，已知最近共同祖先很可能接近（或等于）整个树的根，即使$n$变得很大（对于$k$固定）。 然而，这一结果并不适用于更贴近进化生物学中遇到的系统发育的树形模型。 我们研究了树形（通过 Aldous$\beta-$分裂模型）对预测随机抽取的$k$个末端物种的最近共同祖先和它们所来自的父树根之间分离的边数的影响。 给出了精确和渐近的结果。 我们还简要地考虑了抽样末端物种数量为随机数的过程。 显示英文摘要

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 $\beta-$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.