The robustness of phylogenetic diversity indices to extinctions

Abstract

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. Here, we provide a necessary condition for such reversals to occur on phylogenetic trees whose edge lengths obey the ultrametric constraint. Secondly, we show that while a direct analogue of their reversal result does not hold when using the Equal-Splits (ES) diversity index, nonetheless just two extinctions can lead to a complete ES-ranking reversal on caterpillar trees.