Equality of Shapley value and fair proportion index in phylogenetic trees
Equality of Shapley value and fair proportion index in phylogenetic trees
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DOI：
10.1007/s00285-014-0853-0
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发表时间：
2015-11-01
影响因子：
1.9
通讯作者：
Jin, Emma Yu
中科院分区：
文献类型：
--
作者：
Fuchs, Michael;Jin, Emma Yu
Shapley值和系统发育树的公平比例指数是近年来在遗传学中用于保护性决策的两个重要指标。此外，也是最近，Hartmann（J Math Biol 67：1163-1170，2013）已经呈现了数据，其显示在Shapley值的稍微修改的版本（我们称之为修改的Shapley值）和公平比例指数之间存在强相关性。他给了一个解释这种相关性表明，这两个指数的贡献，以一个边缘的树成为相同的数量的类群趋于无穷大。本文证明了Shapley值和公平比例指数实际上是相同的。此外，我们还考虑了修改后的Shapley值，并表明它与公平比例指数的协方差在随机系统发育树下的Yule-Harding模型和均匀模型确实接近1。
The Shapley value and the fair proportion index of phylogenetic trees have been introduced recently for the purpose of making conservation decisions in genetics. Moreover, also very recently, Hartmann (J Math Biol 67:1163-1170, 2013) has presented data which shows that there is a strong correlation between a slightly modified version of the Shapley value (which we call the modified Shapley value) and the fair proportion index. He gave an explanation of this correlation by showing that the contribution of both indices to an edge of the tree becomes identical as the number of taxa tends to infinity. In this note, we show that the Shapley value and the fair proportion index are in fact the same. Moreover, we also consider the modified Shapley value and show that its covariance with the fair proportion index in random phylogenetic trees under the Yule-Harding model and uniform model is indeed close to one.