Phylogenetic diversity indices provide a formal way to apportion 'evolutionary heritage' across species. Two natural diversity indices are Fair Proportion (FP) and Equal Splits (ES). FP is also called 'evolutionary distinctiveness' and, for rooted trees, is identical to the Shapley Value (SV), which arises from cooperative game theory. In this paper, we investigate the extent to which FP and ES can differ, characterise tree shapes on which the indices are identical, and study the equivalence of FP and SV and its implications in more detail. We also define and investigate analogues of these indices on unrooted trees (where SV was originally defined), including an index that is closely related to the Pauplin representation of phylogenetic diversity.

中文翻译：

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系统发育多样性指数的组合特性。

系统发育多样性指数提供了一种在物种间分配“进化遗产”的正式方法。两个自然多样性指数是公平比例（FP）和均等分割（ES）。FP也被称为“进化独特性”，对于有根的树木，它与合作博弈论中产生的Shapley值（SV）相同。在本文中，我们研究了FP和ES的差异程度，描述了索引相同的树形特征，并更详细地研究了FP和SV的等效性及其含义。我们还定义和研究了这些指数在无根树上的类似物（最初定义SV的地方），包括与Pauplin代表的系统发育多样性密切相关的指数。