比较从两个biodiversity指数获得的排名：公平比例指数和Shapley值
Comparing the rankings obtained from two biodiversity indices: the Fair Proportion Index and the Shapley Value
摘要：
系统发育树的Shapley值和公平比例指数是保护生物学中常用的排序工具。这两个指数排名物种根据其对总系统发育多样性的贡献，允许一个简单的保护标准。虽然这两个指数都有其特定的优点和缺点，但最近的研究表明，这两个值是密切相关的。然而，由于不同的作者使用不同的Shapley值定义，相关性的具体程度取决于Shapley值的具体版本-它的范围从高相关指数到指数相等。在本说明中，我们首先概述了不同的指数。然后，我们将注意力转向由任何一个指数提供的纯粹的排名顺序。我们比较从不同版本的Shapley值的欧洲两栖动物的系统发育树的排名，并说明他们的差异。然后，我们对模拟数据进行进一步分析，并表明即使两个排名完全相同的机会（当从不同版本的Shapley值获得时）随着分类群数量的增加而减少，但两个排名之间的距离收敛到零，即，排名越来越相似了。此外，我们介绍我们的免费软件包FairShapley，这是在Perl中实现的，所有的计算都已执行。
英文摘要：
The Shapley Value and the Fair Proportion Index of phylogenetic trees have been frequently discussed as prioritization tools in conservation biology. Both indices rank species according to their contribution to total phylogenetic diversity, allowing for a simple conservation criterion. While both indices have their specific advantages and drawbacks, it has recently been shown that both values are closely related. However, as different authors use different definitions of the Shapley Value, the specific degree of relatedness depends on the specific version of the Shapley Value - it ranges from a high correlation index to equality of the indices. In this note, we first give an overview of the different indices. Then we turn our attention to the mere ranking order provided by either of the indices. We compare the rankings obtained from different versions of the Shapley Value for a phylogenetic tree of European amphibians and illustrate their differences. We then undertake further analyses on simulated data and show that even though the chance of two rankings being exactly identical (when obtained from different versions of the Shapley Value) decreases with an increasing number of taxa, the distance between the two rankings converges to zero, i.e., the rankings are becoming more and more alike. Moreover, we introduce our freely available software package FairShapley, which was implemented in Perl and with which all calculations have been performed.
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