Distribution of phylogenetic diversity under random extinction

Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the unknown subset of current species that will still be present at some future time, then this 'future phylogenetic diversity' provides a measure of the impact of various extinction scenarios in biodiversity conservation. In this paper, we study the distribution of future phylogenetic diversity under a simple model of extinction (a generalized 'field of bullets' model). We show that the distribution of future phylogenetic diversity converges to a normal distribution as the number of species grows, under mild conditions, which are necessary. We also describe an algorithm to compute the distribution efficiently, provided the edge lengths are integral, and briefly outline the significance of our findings for biodiversity conservation.