1 research outputs found
Generating Normal Networks via Leaf Insertion and Nearest Neighbor Interchange
Galled trees are studied as a recombination model in theoretic population
genetics. This class of phylogenetic networks has been generalized to
tree-child networks, normal networks and tree-based networks by relaxing a
structural condition. Although these networks are simple, their topological
structures have yet to be fully understood. It is well-known that all
phylogenetic trees on taxa can be generated by the insertion of the -th
taxa to each edge of all the phylogenetic trees on taxa. We prove that
all tree-child networks with reticulate nodes on taxa can be uniquely
generated via three operations from all the tree-child networks with or
reticulate nodes on taxa . An application of this result is found in
counting tree-child networks and normal networks. In particular, a simple
formula is given for the number of rooted phylogenetic networks with one
reticulate node.Comment: 4 figures and 13 page