树桶与系统发育树对的重建
Tree Buckets and the Reconstruction of Pairs of Phylogenetic Trees
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中文总结 AI 辅助
该研究针对系统发育组合学中从部分信息恢复树的问题，提出k-桶概念，确定了系统发育树对在不同条件下可从子树中恢复的精确情形，还明确带标记叶子的树对可在子树交换下恢复。
中文摘要 AI 辅助
系统发育树在进化生物学中用于代表一组分类单元的进化历史。由于我们对任何进化历史的信息都不完整，从部分信息中恢复树是系统发育组合学的一个研究重点。然而，在某些情况下，可用数据并未描述单个系统发育树。我们考虑从带有k个叶子的组合子树中恢复系统发育树对，将其称为k-桶。我们确定了两种情况下这些树对可从移除单个叶子后的子树中恢复的精确情形：一种是仅考虑树的结构，另一种是额外考虑叶子上的分类单元集合。我们还考虑了带有标记叶子的树对从其有根子三元组中的恢复，并确定它们可在一系列子树交换下被恢复。
英文摘要
Phylogenetic trees are used in evolutionary biology to represent the evolutionary history of a collection of taxa. As we have incomplete information about any evolutionary history, recovering trees from partial information is a focus of phylogenetic combinatorics. However, in some cases the available data does not describe a single phylogenetic tree. We consider recovery of pairs of phylogenetic trees from their combined subtrees with $k$ leaves, which we call a $k$-bucket. We establish the exact cases in which these pairs of trees are recoverable from their subtrees with a single leaf removed, both when just considering the structure of the trees, and when additionally considering the set of taxa on the leaves. We also consider recovery of pairs of trees with labelled leaves from their rooted triples, and establish that they are recoverable up to a sequence of subtree swaps.
