The evolutionary relationships among organisms have traditionally been represented using
rooted phylogenetic trees. However, due to reticulate processes such as hybridization or …

Rooted acyclic graphs appear naturally when the phylogenetic relationship of a set X of taxa
involves not only speciations but also recombination, horizontal transfer, or hybridization that …

Inference of network-like evolutionary relationships between species from genomic data
must address the interwoven signals from both gene flow and incomplete lineage sorting …

We show that many topological features of level-1 species networks are identifiable from the
distribution of the gene tree quartets under the network multi-species coalescent model. In …

Phylogenetic networks generalize phylogenetic trees, and have been introduced in order to
describe evolution in the case of transfer of genetic material between coexisting species …

Phylogenetic networks provide a means of describing the evolutionary history of sets of
species believed to have undergone hybridization or gene flow during their evolution. The …

Rooted triples, rooted binary phylogenetic trees on three leaves, are sufficient to encode
rooted binary phylogenetic trees. That is, if T and T′ are rooted binary phylogenetic X-trees …

The modular decomposition of a graph G is a natural construction to capture key features of
G in terms of a labeled tree (T, t) whose vertices are labeled as “series”(1),“parallel”(0) or …

Phylogenetic networks are a generalization of evolutionary trees that can be used to
represent reticulate processes such as hybridization and recombination. Here, we introduce …

Motivation Reticulate evolutionary histories, such as those arising in the presence of
hybridization, are best modeled as phylogenetic networks. Recently developed methods …