Phylogenetic diversity rankings in the face of extinctions: The robustness of the fair proportion index

Planning for the protection of species often involves difficult choices
about which species to prioritize, given constrained resources. One way of
prioritizing species is to consider their  "evolutionary
distinctiveness'', i.e. their relative evolutionary isolation on
a phylogenetic tree. Several evolutionary isolation metrics or
phylogenetic diversity indices have been introduced in the literature,
among them the so-called Fair Proportion index (also known as
the  "evolutionary distinctiveness" score).
This index apportions the total diversity of a tree among all leaves,
thereby providing a simple prioritization criterion for
conservation.  Here, we focus on the prioritization order
obtained from the Fair Proportion index and analyze the effects of species
extinction on this ranking. More precisely, we analyze the extent to which
the ranking order may change when some species go extinct and the Fair
Proportion index is re-computed for the remaining taxa. We show that for
each phylogenetic tree, there are edge lengths such that the extinction of
one leaf per cherry completely reverses the ranking. Moreover, we show
that even if only the lowest ranked species goes extinct, the ranking
order may drastically change.  We end by analyzing the effects of
these two extinction scenarios (extinction of the lowest ranked species
and extinction of one leaf per cherry) for a collection of empirical and
simulated trees. In both cases, we can observe significant changes in the
prioritization orders, highlighting the empirical relevance of our
theoretical findings.