  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.
