SplitsTree-a program for analyzing and visualizing evolutionary data

Motivation. Real evolutionary data often contains a number of different and sometimes conflicting phylogenetic signals and thus does not always clearly support a unique tree. To address this problem, H. -J. Bandelt and A.W. M. Dress developed the method of split decomposition. For ideal data, this method gives rise to a tree, whereas less ideal data is represented by a tree-like network that may indicate evidence for different and conflicting phylogenies. Results. SplitsTree is an interactive program for analyzing a n d visualizing evolutionary data, that implements this approach. It also supports a number of distances transformations, the computation of parsimony splits, spectral analysis and bootstrapping. Availability. There are two versions of SplitsTree, an interactive Macintosh version (shareware) and a command-line unix version (public domain). Both are available from: ftp://ftp.uni-bielefeld.de/pub/math/splits/splitstree2. There is a WWW version running at: http://www.bibiserv. techfak.uni-bielefeld.de/splits. I n t r o d u c t i o n Evolutionary relationships between taxa are most often represented a s phylogenetic trees, and many different algorithms for t r e e construction have been developed (Swofford et al. 1996). This is, of course, justified by the assumption that evolution is a branching o r Analyzing Evolutionary Data with SplitsTree 2 tree-like process. However, a set of real data often contains a n u m b e r of different and sometimes conflicting signals and thus does n o t always clearly support a unique tree. To address this problem, H. -J. Bandelt and A.W. M. Dress (1992a) developed the method of split decomposition. In contrast to methods such as maximum parsimony and maximum likelihood that reconstruct phylogenetic trees by optimizing certain parameters, split decomposition is a transformation-based approach. Essentially, evolutionary data is transformed or, more precisely, "canonically decomposed", into a sum of "weakly compatible splits" and t h e n represented by a so-called splits graph. For ideal data, this is a t ree , whereas less ideal data will give rise to a tree-like network that can be interpreted as possible evidence for different and conflicting phylogenies. Further, as split decomposition does not attempt to force data onto a tree, it can provide a good indication of how tree-like given data is. There exist efficient algorithms for performing split decomposition (Bandelt and Dress 1992a) and for computing splits graphs (Wetzel 1995 and D.H. Huson, in preparation). A.W. M. Dress and R. Wetzel produced a simple implementation of split decomposition (Wetzel 1995) as a investigative tool to help develop the general theory. Based on their work, a first public version was developed by R. Wetzel a n d the author (SplitsTree version 1). The program described in this p a p e r (SplitsTree version 2) is a completely new implementation. In this paper we first review the concepts of splits, splits graphs a n d the method of split decomposition, and then discuss the SplitsTree program in detail. For a number of biological applications of the split decomposition method, see e.g.: Bandelt and Dress 1992b, Dopazo et al. 1993, Dress and Wetzel 1993, Lockhart et al, 1995, Wetzel 1995, Dress et al. 1996, McLenachan et al. 1996, or P.J. Lockhart et al., i n preparation. Splits and Splits Graphs Evolutionary relationships are generally represented by a phylogenetic tree , T, that is, a tree whose leaves are labeled by a set X of taxa a n d whose remaining vertices are unlabeled and of degree at least 3. (We only consider unrooted trees in this paper.) Any edge e of T defines a split S={A,A'} of X, i.e. a partition of X into two non-empty sets A a n d A', consisting of all taxa on the one side, or the other, of the edge e. Analyzing Evolutionary Data with SplitsTree 3 Such a system Σ of splits is called compatible, if for any two splits S1={A1,A'1} and S2={A2,A'2} in Σ, one of the four intersections A1∩A2, A1∩A'2, A'1∩A2, or A'1∩A'2 is empty. Any phylogenetic tree T gives rise to a compatible split system Σ . In 1971, P. Buneman established that, vice versa, a n y compatible split system Σ corresponds to a unique phylogenetic tree T (Buneman 1971). So, tree reconstruction for a given set of taxa X is equivalent to computing a compatible system of splits Σ for X a n d determining a weight for each split S that corresponds to the length of the associated edge. Hence, to obtain more general graphs, one must consider less restricted systems of splits. Let X be a set of taxa. A system of splits Σ of X is called weakly compatible, if for any three splits S1, S2, S3 and all A i ∈ S i (i=1,2,3), at least one of the four intersections A1∩A2∩A3, A1∩A'2∩A'3, A'1∩A2∩A'3, or A'1∩A'2∩A3 is empty (Bandelt and Dress 1992a). So, in particular, any two splits are permitted to be incompatible. Intermediately, Σ is called circular , if there exists an ordering x1,x2,. ,xm of the taxa such that for every split S∈Σ there exists A∈S with A={xp(S),xp(S)+1,. ,xq(S)} and1≤p(S)≤q(S)≤m . One can prove that a circular split system is always weakly compatible and a compatible split system is always circular (Bandelt and Dress 1992a, Wetzel 1995). A splits graph representing a weakly compatible split system Σ is a graph G(Σ)=(V,E) whose vertices v∈V are labeled by the set of taxa X and whose edges e∈E are straight line segments that represent t h e splits in Σ, see Figure 1. More precisely, each split S={A,A'}∈Σ is represented by a band of parallel edges of equal length in such a w a y that deleting all edges in such a band partitions the graph into precisely two components, one containing all vertices labeled by taxa in A and the other containing all vertices labeled by taxa in A'. The length of the edges representing a given split S indicates its weight o r support and is calculated as the isolation index of S. For algorithms that compute splits graphs, see (Wetzel 1995 and D.H. Huson, i n preparation). Analyzing Evolutionary Data with SplitsTree 4 Consider a weakly compatible system of splits Σ of a set X of taxa. If Σ is compatible, then G(Σ) is a phylogenetic tree. What is the situation if Σ is merely circular? Then G(Σ) can be realized as a planar g raph (Wetzel 1995 and D.H. Huson, in preparation). Finally, if Σ is n o t circular, then in general G(Σ) will not be planar. In biological applications, the arising split systems are often either circular o r mildly non-circular.