Mass extinctions can be modelled as a pruning process on the extant species of a phylogenetic tree; the current rapid extinction of species leads not only to the loss millions of years of unique evolutionary history, but to the loss of unique features possessed by species. Phylogenetic diversity (PD) is a commonly used proxy for estimating the feature diversity (FD) of a set of species. However there remains considerable debate in the biological literature as to the adequacy of using PD as a proxy for FD. In this thesis we consider three types of data for estimating the relative loss of FD after a rapid \ eld of bullets" style extinction event at the present. We rst consider a general case where the features assigned to a set of species is xed without reference to an underlying phylogeny. We then extend this model by allowing a stochastic model of feature evolution along the branches of an underlying phylogenetic tree generate the feature assignment on the species observed at the leaves of the tree. Finally, we apply this stochastic model of feature evolution to random birth-death trees. For each of these cases we relate the expected loss of feature diversity to established results for PD loss, providing the conditions under which PD predicts FD loss, or when FD is better predicted by another measure of biodiversity.