Evolutionary isolation and phylogenetic diversity loss under random extinction events.

The extinction of species at the present leads to the loss of 'phylogenetic diversity' (PD) from the evolutionary tree in which these species lie. Prior to extinction, the total PD present can be divided up among the species in various ways using measures of evolutionary isolation (such as 'fair proportion' and 'equal splits'). However, the loss of PD when certain combinations of species become extinct can be either larger or smaller than the cumulative loss of the isolation values associated with the extinct species. In this paper, we show that for trees generated under neutral evolutionary models, the loss of PD under a null model of random extinction at the present can be predicted from the loss of the cumulative isolation values, by applying a non-linear transformation that is independent of the tree. Moreover, the error in the prediction provably converges to zero as the size of the tree grows, with simulations showing good agreement even for moderate sized trees (n=64).