Phylogenetic Diversity Rankings in the Face of Extinctions: The Robustness of the Fair Proportion Index

Abstract

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.

The robustness of phylogenetic diversity indices to extinctions

“…The extinction of any other leaves of T does not alter this difference as the paths from the root to x 1 and x 2 are affected identically (cf. proof of Theorem 1 in Fischer et al (2022)). Thus, for the ranking of ES index scores to reverse, it is necessary for at least one of x 1 , x 2 to become extinct.…”

“…Furthermore, we use, and repeat here, the definitions of ranking, strict , and reversible as they appear in Fischer et al (2022) (pp. 2,3).…”

“…Theorem 2 of Fischer et al (2022) shows that, absent any ultrametric constraint, the extinction of one leaf per cherry is sufficient to reverse Fair Proportion index score rankings. We call such a set of concurrent extinctions a one-per-cherry extinction event.…”

“…Specific edge weightings for reversibility. Corollary 1 ofFischer et al (2022) states that a strict and reversible ranking exists for any caterpillar tree under the Fair Proportion index. Furthermore, this reversal is caused by the extinction of the species that initially had the lowest FP index…”

“… A bstract Phylogenetic diversity indices provide a formal way to apportion evolutionary heritage amongst extant species. In this short note, we investigate some questions posed in a recent paper (Fischer et al, 2022). In that paper, it is shown that under certain extinction scenarios, the ranking of the surviving species by their Fair Proportion index scores may be the reverse of their ranking beforehand.…”