  Phylogenetic diversity is a popular measure for quantifying the biodiversity
of a collection $Y$ of species, while phylogenetic diversity indices provide a
way to apportion phylogenetic diversity to individual species. Typically, for
some specific diversity index, the phylogenetic diversity of $Y$ is not equal
to the sum of the diversity indices of the species in $Y.$ In this paper, we
investigate the extent of this difference for two commonly-used indices: Fair
Proportion and Equal Splits. In particular, we determine the maximum value of
this difference under various instances including when the associated rooted
phylogenetic tree is allowed to vary across all root phylogenetic trees with
the same leaf set and whose edge lengths are constrained by either their total
sum or their maximum value.
