A limitation of turning splits graphs into reticulate networks

Splits graphs are a useful way of displaying contradictory information within evolutionary datasets, either incompatible characters (ie. those that cannot fit onto a single tree) or incompatible trees. Since the graphs are unrooted, they are usually treated as a form of multivariate data display, rather than interpreted as depicting evolutionary history.

However, it is possible to turn a splits graph into a evolutionary network (sometimes called a reticulation network) once a root is specified (Huson and Klöpper 2007). This is true irrespective of whether the splits are derived from character data (Huson and Kloepper 2005), in which case it usually called a recombination network, or whether they come from a set of trees (Huson et al. 2005), in which case it is usually called a hybridization network.

The SplitsTree4 program (Huson and Bryant 2006) carries out the relevant calculations under algorithms entitled Reticulation Network, Recombination Network or Hybridization Network, although these all produce the same outcome once the set of splits has been determined. These options are no longer available from the menu system (in the current release of the program), but they can still be effected via the Configure Pipeline menu option.

The point of this post is to point out that the calculations are affected by the same limitation that has been pointed out before under other circumstances (see the post A fundamental limitation of hybridization networks?). That is, reticulation cycles with three or fewer outgoing arcs are not uniquely defined with respect to rooted splits — there are three equally optimal mathematical solutions. In practice, this means that in a situation where two taxa are involved in producing a third taxon we cannot decide from the splits alone which is the reticulate taxon and which are the two "parents" (eg. which one is the hybrid).

An example

I will illustrate this point with a simple example. The data are taken from Wendel et al. (1991). The data consist of the presence-absence of 76 nuclear allozyme loci and 13 nuclear restriction sites, for five plant taxa, one of which is the outgroup. The first graph shows the splits graph using the default options in SplitsTree4 — both the NeighborNet and the ParsimonySplits analyses produce the same graph, which identifies a single reticulation.

In SplitsTree4, the outgroup for rooting the splits graph must be the first taxon in the datafile, which in this case is Gossypium robinsonii. The following three graphs are the result of then choosing the ReticulateNetwork analysis. They differ by having, respectively, Gossypium bickii as the final taxon in the dataset, Gossypium sturtianum as the final taxon, and Gossypium australe + Gossypium nelsonii as the final two taxa. Note that the ReticulateNetwork algorithm always identifies the dataset's final taxon as the reticulate one.

So, the hybrid taxon is indeterminable from the data given, and the algorithm simply makes a (consistent) choice from among the three possibilities. [That is, the algorithm chooses as the reticulate arc whichever of the three outgoing arcs is latest in the dataset.]

The original authors suggest that the nuclear and other data "indicate a biphyletic ancestry of G. bickii. Our preferred hypothesis involves an ancient hybridization, in which G. sturtianum, or a similar species, served as the maternal parent with a paternal donor from the lineage leading to G. australe and G. nelsoni." This doesn't quite match any of the three rooted networks shown above.

References

Huson DH, Bryant D (2006) Application of phylogenetic networks in evolutionary studies. Molecular Biology and Evolution 23: 254-267.

Huson DH, Kloepper TH (2005) Computing recombination networks from binary sequences. Bioinformatics 21: ii159-ii165.

Huson DH, Klöpper TH (2007) Beyond galled trees – decomposition and computation of galled networks. Lecture Notes in Bioinformatics 4453: 211-225.

Huson DH, Klöpper T, Lockhart PJ, Steel MA (2005) Reconstruction of reticulate networks from gene trees. Lecture Notes in Bioinformatics 3500: 233-249.

Wendel JF, Stewart JM, Rettig JH (1991) Molecular evidence for homoploid reticulate evolution among Australian species of Gossypium. Evolution 45: 694-711.