Computer Software

Conservation planning software like Marxan (Ball et al. 2009) and Zonation (Moilanen et al. 2009) mainly focus on species richness. However, both programs can indirectly account for phylogenetic diversity (see also Silvano, Valdujo and Colli, chapter “Priorities for Conservation of the Evolutionary History of Amphibians in the Cerrado” and Arponen and Zupan, chapter “Representing Hotspots of Evolutionary History in Systematic Conservation Planning for European Mammals”). Only a few programs explicitly allow to compute phylogenetic diversity (Webb et al. 2008; Kembel et al. 2010). In the following we describe two programs relevant for the SD analysis.

SplitsTree

SplitsTree (Huson and Bryant 2006) is a user-friendly and leading software to reconstruct and visualize phylogenetic networks from multiple sequence alignments, distance matrices, or sets of trees. SplitsTree implements a wide range of split network inference methods such as split decomposition (Bandelt and Dress 1992b) and neighbor-net (Bryant and Moulton 2004). SplisTree has a limited ability to compute PD and SD. It works for all major platforms including Windows, Mac OS X, and Unix. More information about SplitsTree is available at splitstree.org.

PDA: Phylogenetic Diversity Analyzer

PDA (Minh et al. 2009) is a software tool that computes and maximizes species richness, PD, and SD given a variety of user-defined constraints including budget, ecological, and geographical constraints. PDA can be used in conjunction with SplitsTree to work with SD. It solves all Problems 1–5 by greedy algorithms, dynamic programming, and integer programming methods. Moreover, it supports weighted dependency networks for viable taxon selection and spatial reserve selection problems (Chernomor et al. 2015). Among other features is the computation of PD/SD endemism and complementarity (Faith et al. 2004). PDA is available as a command-line program for Windows, Mac OS X, and Unix as well as an online web service. More information about PDA is available at cibiv.at/software/pda.

Conclusions and Perspectives

In this chapter we have presented the concept of split diversity, a generalization of PD to account for contradicting phylogenetic information in biodiversity optimization. We demonstrated the new concept with a small pheasant data set. We note that this example is not realistic because neither genera are vulnerable nor the selection of entire countries is reasonable. Moreover, genetic data for galliforms are available for more genera and genomic loci (Wang et al. 2013) and the methodology developed here is well applicable to this new data.

We then presented computational tools to perform the analysis under the SD framework. Both greedy algorithms and IP can be generally applied to solve the same conservation questions, where the former quickly computes a solution and the latter ensures optimal solutions. Moreover, IP works well for data set sizes usually encountered in real data. For example, we have recently applied IP to solve the viable taxon selection (Problem 3) for 242 marine species of Caribbean coral community and the budgeted reserve selection (Problem 5) for the Cape of South Africa with 735 plant genera (Chernomor et al. 2015). IP always returned optimal sets of taxa and areas within seconds to a few minutes.

SD can be extended to include species extinction risks as developed for PD (Weitzman 1992; Witting and Loeschcke 1995). Such a “probabilistic” PD approach (see chapters “The Value of Phylogenetic Diversity” and “Reconsidering the Loss of Evolutionary History: How Does Non-random Extinction Prune the Tree-of-Life?”) predicts future diversity given the fact that some species might become extinct in, say, 20 years. The problem, previously coined the Noah's Ark Problem (NAP; Weitzman 1998), is then to maximize future PD given limited budgets. The same concept can be applied to SD as follows. One first computes “survival probabilities” for each split in split networks in the same fashion as for branches in phylogenetic trees. The future SD is then defined as the dot product of the split weights and split survival probabilities. This definition of future SD consistently generalizes that of future PD.

From a computational view point, solving the extended NAP under future SD is NP-hard as proven for PD (Hartmann and Steel 2006). Dynamic programming algorithms (DPA) optimally solve the NAP under future PD in a special scenario, where the species extinction probability becomes 0 if it is given enough resources (Pardi and Goldman 2007). For general scenarios Hickey et al. (2008) devised such a DPA that gives an approximation ratio of nearly 1 compared to the optimal solution. More recently, Billionnet (2013) presented an IP approach for the NAP that runs within a few minutes for simulated 4,000-taxon cases and provides near-optimal solutions, which are only 1.2 % away from the optimal solution. It will be interesting to investigate how such DPA and IP approaches can be adapted to solve the NAP under the more general SD framework.

Acknowledgments The authors thank Tung Lam Nguyen for developing PDA web service. The authors also thank Roseli Pellens and Philippe Grandcolas for inviting us to write this chapter and three anonymous reviewers for constructive comments. This work was supported by University of Vienna (Initiativkolleg I059-N) to O.C. and the Austrian Science Fund – FWF (I760-B17) to

B.Q.M. and A.v.H.

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