  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.
