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The Shapley Value and the Fair Proportion Index of phylogenetic trees havebeen frequently discussed as prioritization tools in conservation biology. Bothindices rank species according to their contribution to total phylogeneticdiversity, allowing for a simple conservation criterion. While both indiceshave their specific advantages and drawbacks, it has recently been shown thatboth values are closely related. However, as different authors use differentdefinitions of the Shapley Value, the specific degree of relatedness depends onthe specific version of the Shapley Value - it ranges from a high correlationindex to equality of the indices. In this note, we first give an overview ofthe different indices. Then we turn our attention to the mere ranking orderprovided by either of the indices. We compare the rankings obtained fromdifferent versions of the Shapley Value for a phylogenetic tree of Europeanamphibians and illustrate their differences. We then undertake further analyseson simulated data and show that even though the chance of two rankings beingexactly identical (when obtained from different versions of the Shapley Value)decreases with an increasing number of taxa, the distance between the tworankings converges to zero, i.e., the rankings are becoming more and morealike. Moreover, we introduce our freely available software packageFairShapley, which was implemented in Perl and with which all calculations havebeen performed.

Comparing the rankings obtained from two biodiversity indices: the Fair Proportion Index and the Shapley Value