Phylogenetic trees are often constructed by using a metric on the set of taxa that label the leaves of the tree. While there are a number of methods for constructing a tree using a given metric, such trees will only display the metric if it satisfies the so-called "four point condition", established by Buneman in 1971. While this condition guarantees that a unique tree will display the metric, meaning that the distance between any two leaves can be found by adding the distances on arcs in the path between the leaves, it doesn't exclude the possibility that a phylogenetic network might also display the metric. This possibility was recently pointed out and "tree-metrized" networks - that display a tree metric - with a single reticulation were characterized. In this paper, we show that in the case of HGT (horizontal gene transfer) networks, in fact there are tree-metrized networks containing many reticulations.

中文翻译：

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树形HGT网络。

系统发育树通常是通过在一组分类单元上使用度量来构建的，该度量标记树的叶子。尽管有许多种方法可以使用给定的度量标准来构建树，但只有满足1971年Buneman建立的所谓“四点条件”时，此类树才会显示该度量。尽管这种条件可以保证唯一的树将显示度量，这意味着可以通过在叶子之间的路径中的弧上加上距离来找到任意两个叶子之间的距离，但这并不排除系统进化网络也可以显示该度量的可能性。最近指出了这种可能性，并且表征了具有树状度量的具有单个网状结构的“树状”网络。在本文中，