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After having worked with Bayesian phylogenetic tree inference for some time, I am now trying out a method to infer network phylogenies. To get an idea of what it infers, I'd like to find a way of summarizing the results.

The output of the inference is a NEXUS file containing a stream of networks encoded in eXtended Newick as trees with duplicate node names, like this:

(((((((Kiraman:0.028228,Kui:0.028228)S1:0.0797301)#H4:0.35229)#H2:23.4168)#H1:15.8027,(Kamang:29.3316,#H1:5.45455[&&NHX:gamma=0.36825381342449554])S11:10.3482)S12:1.27331,((Klon:1.16727,((#H4:0.524833[&&NHX:gamma=0.33697036713230577],Kafoa:0.632791)S6:0.0615575)#H3:0.472921[&&NHX:gamma=0.6642547809404831])S2:35.6082,(#H2:22.2107[&&NHX:gamma=0.7544913491697585],((A-Petleng:0.421975,(A-Takalelang:0.168615,(A-Ulaga:0.145472,A-Atimelang:0.145472)S4:0.0231422)S5:0.253361)S7:0.902144,#H3:0.629771)S3:21.3468)S8:14.1045)S9:4.17761)S10:54.5301):0;

The network described by the Newick string above

There is no formal restriction on the shape of the network, and hybridization edges have a weight 0<γ<1. How do visually or formally summarize a stack of several thousands of these networks, and in particular the backbone tree structure plus a glimpse of the hybridization events they display?

I have played with some tree summarizing approaches and tried to first infer a summary tree and then glue some cross-edges in there, but the way I came up with did not look reasonable.

I am now considering to calculate distances between leaves and using network visualization tools like SplitsTree or NeighborNet to get a visual representation of that, but how shoud I represent the uncertainty of the distances in even a single network (not to mention thousands of them) in the input for these algorithms?

Are there any good approaches to summarize phylogenetic networks of the shape given above? Or to consistently simplify them to a shape that can be easily summarized?

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Firstly you treat this as two separate independent calculations.

  1. The traditional approach is simply to produce a consensus phylogeny using your Bayesian method and assess the equivocal bootstraps/Bayesian probability.
  2. Feed your data set (not the trees) into NeighborNet within SplitsTrees. There are statistics that classify the level of departure from a bifurcating phylogeny.

Examine both outputs for orthogonal support for incongruence.

Note Phylogenetic network statistics are a relatively soft area of phylogeny (they are not used as hard evidence).

Networks from Bayesian trees

The final approach (which is what you are asking about), is to feed your Bayesian trees into Dendroscope, this is a GUI that represents the uncertainty between different bifurcating phylogenies as networks and you can use it to understand the incongruence between different trees within your Bayesian MCMC, because the phylogenetic networks directly corresponds to the level of incongruence.

Dendroscope is a nice Java API and is very easy to use.

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