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Phylogenetic networks can represent evolutionary events that cannot bedescribed by phylogenetic trees. These networks are able to incorporatereticulate evolutionary events such as hybridization, introgression, andlateral gene transfer. Recently, network-based Markov models of DNA sequenceevolution have been introduced along with model-based methods forreconstructing phylogenetic networks. For these methods to be consistent, thenetwork parameter needs to be identifiable from data generated under the model.Here, we show that the semi-directed network parameter of a triangle-free,level-1 network model with any fixed number of reticulation vertices isgenerically identifiable under the Jukes-Cantor, Kimura 2-parameter, or Kimura3-parameter constraints.

Distinguishing level-1 phylogenetic networks on the basis of data generated by Markov processes