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:
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?