Phylogenetic diversity: from combinatorics to ecology

The phylogenetic diversity (P D) of a set of taxa contained within a phylogenetic tree is a measure of the biodiversity of that set. P D has been widely used for prioritizing taxa for conservation and is the basis of the 'Noah's Ark Problem' in biodiversity management. In this chapter we describe some new and recent algorithmic, mathematical, and stochastic results concerning PD. Our results highlight the importance of considering time scales and survival probabilities when making conservation decisions. The loss of P D under a simple extinction process is also described for any given tree-this provides contrasting results depending on whether extinction is measured as function of time or of the number of lost species. Lastly we explore a very different application of P D, its use for reconstructing trees and the associated mathematical properties. The wide range of applications in this chapter shows the usefulness of P D for exploring phylogenetic tree structure with further applications sure to follow.