In the literature, phylogenetic trees often appear even when the paper is discussing non-tree evolutionary histories.
A case in point is the paper by: Susanne Gallus, Axel Janke, Vikas Kumar, Maria A. Nilsson (2015) Disentangling the relationship of the Australian marsupial orders using retrotransposon and evolutionary network analyses. Genome Biology and Evolution, in press.
The authors discuss the relationship between the four Australian marsupial orders, and use data from transposable element (retrotransposon) insertions for resolving the inter- and intra-ordinal relationships of the Australian and South American orders. They plot the retrotransposon presence/absence onto a tree derived from alignments of 28 nuclear gene fragments. This is shown in the first figure, with the retrotransposons indicated as dots on the internal branches.
For comparison, the next figure is a Median-Joining network based on the presence/absence of the retrotransposons.
With the exception of the Monito del monte, Shrew opossum and Western quoll, the network matches the basic tree structure. However, it emphasizes more strongly the fact that the retrotransposons do not resolve the relationships among the Marsupial orders. As the authors note:
The retrotransposon insertions support three conflicting topologies regarding Peramelemorphia, Dasyuromorphia and Notoryctemorphia, indicating that the split between the three orders may be best understood as a network ...The rapid divergences left conflicting phylogenetic information in the genome possibly generated by incomplete lineage sorting or introgressive hybridisation, leaving the relationship among Australian marsupial orders unresolvable as a bifurcating process million years later.