A new universal system of tree shape indices.
A new universal system of tree shape indices.
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一种新的通用树形指数系统。
DOI：
10.1101/2023.07.17.549219
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Verity,Kimberley
中科院分区：
文献类型：
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作者：
Noble,Robert;Verity,Kimberley
树形图的比较和分类是生物学、语言学、计算机科学等领域的基础，但目前应用于描述树形的索引存在着严重的缺陷，使得它们的解释变得复杂，限制了它们的范围。在这里，我们引入了一个新的指标体系，没有这样的缺点。我们的索引考虑了节点大小和分支长度，并且对这两个属性中的任何一个的微小变化都是健壮的。与当前流行的系统发育多样性、系统发育熵和树平衡指数不同，我们的定义为所有有根的树分配了可解释的值，并允许对任何一对树进行有意义的比较。我们的自洽定义进一步统一了一个连贯系统中的多样性、丰富度、平衡性、对称性、有效高度、有效外度和有效分枝数的度量，并推导出这些指数之间的许多简单关系。我们的指数的主要实用优势是：1)量化非超尺度树的多样性；2)评估具有不同分枝长度或节点大小的树的平衡；3)比较具有不同叶数或离散度的树的平衡；4)获得对采样误差和推理误差具有鲁棒性的一致的、通用的、多维的树木形状量化。我们通过比较代表HIV和乌拉尔语进化的树的形状，以及由肿瘤进化的计算模型生成的树的形状来说明这些特征。鉴于树结构的普遍存在，我们确定了跨不同领域的广泛应用。
The comparison and categorization of tree diagrams is fundamental to large parts of biology, linguistics, computer science, and other fields, yet the indices currently applied to describing tree shape have important flaws that complicate their interpretation and limit their scope. Here we introduce a new system of indices with no such shortcomings. Our indices account for node sizes and branch lengths and are robust to small changes in either attribute. Unlike currently popular phylogenetic diversity, phylogenetic entropy, and tree balance indices, our definitions assign interpretable values to all rooted trees and enable meaningful comparison of any pair of trees. Our self-consistent definitions further unite measures of diversity, richness, balance, symmetry, effective height, effective outdegree, and effective branch count in a coherent system, and we derive numerous simple relationships between these indices. The main practical advantages of our indices are in 1) quantifying diversity in non-ultrametric trees; 2) assessing the balance of trees that have non-uniform branch lengths or node sizes; 3) comparing the balance of trees with different leaf counts or outdegrees; 4) obtaining a coherent, generic, multidimensional quantification of tree shape that is robust to sampling error and inferential error. We illustrate these features by comparing the shapes of trees representing the evolution of HIV and of Uralic languages, and trees generated by computational models of tumour evolution. Given the ubiquity of tree structures, we identify a wide range of applications across diverse domains.