The extent to which phylogenetic diversity (PD) captures feature diversity (FD) is a topical and controversial question in biodiversity conservation. In this short paper, we formalise this question and establish a precise mathematical condition for FD (based on discrete characters) to coincide with PD. In this way, we make explicit the two main reasons why the two diversity measures might disagree for given data; namely, the presence of certain patterns of feature evolution and loss, and using temporal branch lengths for PD in settings that may not be appropriate (e.g. due to rapid evolution of certain features over short periods of time). Our paper also explores the relationship between the 'Fair Proportion' index of PD and a simple index of FD (both of which correspond to Shapley values in cooperative game theory). In a second mathematical result, we show that the two indices can take identical values for any phylogenetic tree, provided the branch lengths in the tree are chosen appropriately.

中文翻译：

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特征多样性和系统发育多样性之间的正式联系

系统发育多样性 (PD) 捕获特征多样性 (FD) 的程度是生物多样性保护中的一个热门和有争议的问题。在这篇简短的论文中，我们将这个问题形式化，并为 FD（基于离散字符）与 PD 重合建立了精确的数学条件。通过这种方式，我们明确了两种多样性措施对于给定数据可能不一致的两个主​​要原因；即，某些特征演化和丢失模式的存在，以及在可能不合适的设置中使用 PD 的时间分支长度（例如，由于某些特征在短时间内快速演化）。我们的论文还探讨了 PD 的“公平比例”指数与 FD 的简单指数（两者都对应于合作博弈论中的 Shapley 值）之间的关系。