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.

💡 Research Summary

The paper investigates how much of an evolutionary tree—measured by phylogenetic diversity (PD)—is expected to survive under a simple stochastic extinction scenario. The authors adopt a generalized “field of bullets” model in which each extant species independently survives with probability (1-p) (or goes extinct with probability (p)). For a given rooted phylogenetic tree with edge lengths (\ell(e)) and a set (S) of surviving species, PD is defined as the sum of the lengths of all edges that lie on the minimal subtree connecting the members of (S).

The first major theoretical contribution is a central‑limit‑type result. By expressing the contribution of each edge as a Bernoulli‑type random variable—active if at least one descendant of the edge survives—the authors derive the edge‑wise expectation (\mathbb{E}