Properties of Normal Phylogenetic Networks
- 96 Downloads
A phylogenetic network is a rooted acyclic digraph with vertices corresponding to taxa. Let X denote a set of vertices containing the root, the leaves, and all vertices of outdegree 1. Regard X as the set of vertices on which measurements such as DNA can be made. A vertex is called normal if it has one parent, and hybrid if it has more than one parent. The network is called normal if it has no redundant arcs and also from every vertex there is a directed path to a member of X such that all vertices after the first are normal. This paper studies properties of normal networks.
Under a simple model of inheritance that allows homoplasies only at hybrid vertices, there is essentially unique determination of the genomes at all vertices by the genomes at members of X if and only if the network is normal. This model is a limiting case of more standard models of inheritance when the substitution rate is sufficiently low.
Various mathematical properties of normal networks are described. These properties include that the number of vertices grows at most quadratically with the number of leaves and that the number of hybrid vertices grows at most linearly with the number of leaves.
KeywordsNormal network Hybrid Recombination Speciation Genome Ancestral reconstruction
Unable to display preview. Download preview PDF.
- Cardona, G., Rosselló, F., Valiente, G., 2007. Comparison of tree-child phylogenetic networks. To appear in IEEE/ACM Trans. Comput. Biol. Bioinform. doi: 10.1109/TCBB.2007.70270
- Nakhleh, L., Warnow, T., Linder, C.R., 2004. Reconstructing reticulate evolution in species-theory and practice. In: Bourne, P.E., Gusfield, D. (Eds.), Proceedings of the Eighth Annual International Conference on Computational Molecular Biology, RECOMB ’04, March 27–31, 2004, San Diego, California, pp. 337–346. ACM, New York. Google Scholar
- van Iersel, L., Keijsper, J., Kelk, S., Stougie, L., 2007. Constructing level-2 phylogenetic networks from triplets. arXiv:0707.2890v1 [q-bio.PE].