A metric phylogenetic tree relating a collection of taxa induces weighted rooted triples and weighted quartets for all subsets of three and four taxa, respectively. New intertaxon distances are defined that can be calculated from these weights, and shown to exactly fit the same tree topology, but with edge weights rescaled by certain factors dependent on the associated split size. These distances are analogs for metric trees of similar ones recently introduced for topological trees that are based on induced unweighted rooted triples and quartets. The distances introduced here lead to new statistically consistent methods of inferring a metric species tree from a collection of topological gene trees generated under the multispecies coalescent model of incomplete lineage sorting. Simulations provide insight into their potential.

中文翻译：

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通过类群间距离从加权四重奏推断度量树

与分类群集合相关的度量系统发育树分别为三个和四个分类群的所有子集诱导加权根三元组和加权四元组。定义了新的分类单元间距离，可以从这些权重计算，并显示完全适合相同的树拓扑，但​​边缘权重由依赖于相关拆分大小的某些因素重新缩放。这些距离是度量树的类似物，最近为基于诱导未加权根三元组和四重组的拓扑树引入了类似的度量树。这里引入的距离导致了新的统计一致的方法，可以从在不完全谱系排序的多物种合并模型下生成的拓扑基因树集合中推断出度量物种树。模拟可以深入了解它们的潜力。