  In biodiversity conservation it is often necessary to prioritize the species
to conserve. Existing approaches to prioritization, e.g. the Fair Proportion
Index and the Shapley Value, are based on phylogenetic trees and rank species
according to their contribution to overall phylogenetic diversity. However, in
many cases evolution is not treelike and thus, phylogenetic networks have come
to the fore as a generalization of phylogenetic trees, allowing for the
representation of non-treelike evolutionary events, such as horizontal gene
transfer or hybridization. Here, we extend the concepts of phylogenetic
diversity and phylogenetic diversity indices from phylogenetic trees to
phylogenetic networks. On the one hand, we consider the treelike content of a
phylogenetic network, e.g. the (multi)set of phylogenetic trees displayed by a
network and the LSA tree associated with it. On the other hand, we derive the
phylogenetic diversity of subsets of taxa and biodiversity indices directly
from the internal structure of the network. Furthermore, we introduce our
software package NetDiversity, which was implemented in Perl and allows for the
calculation of all generalized measures of phylogenetic diversity and
generalized phylogenetic diversity indices established in this note that are
independent of inheritance probabilities. We apply our methods to a phylogentic
network representing the evolutionary relationships among swordtails and
platyfishes (Xiphophorus: Poeciliidae), a group of species characterized by
widespread hybridization.
