  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.
