A phylogenetic network is any graph used to visualize evolutionary relationships (either abstractly or explicitly) between nucleotide sequences, genes, chromosomes, genomes, or species. They are employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved. They differ from phylogenetic trees by the explicit modeling, by means of the addition of hybrid nodes (nodes with two parents) instead of only tree nodes (nodes with only one parent). Phylogenetic trees are a subset of phylogenetic networks. Phylogenetic networks can be inferred and visualised with software such as SplitsTree and, more recently, Dendroscope. A standard format for representing phylogenetic networks is a variant of Newick format which is extended to support networks as well as trees.
Many kinds and subclasses of phylogenetic networks have been defined based on the biological phenomenon they represent or which data they are built from (hybridization networks, usually built from rooted trees, recombination networks from binary sequences, median networks from a set of splits, optimal realizations and reticulograms from a distance matrix), or restrictions to get computationally tractable problems (galled trees, and their generalizations level-k phylogenetic networks, tree-child or tree-sibling phylogenetic networks).
Phylogenetic trees also have trouble depicting microevolutionary events, for example the geographical distribution of muskrat or fish populations of a given species among river networks, because there is no species boundary to prevent gene flow between populations. Therefore, a more general phylogenetic network better depicts these situations.
 Rooted vs unrooted
- Unrooted phylogenetic network
- Let X be a set of taxa. An unrooted phylogenetic network N on X is any undirected graph whose leaves are bijectively labeled by the taxa in X. A number of different types of unrooted phylogenetic networks are in use like split networks and quasi-median networks.
- Rooted phylogenetic network
- Let X be a set of taxa. A rooted phylogenetic network N on X is a rooted DAG where the set of leaves is bijectively labeled by the taxa in X.
 Software to compute phylogenetic networks
- ^ Huson, DH and Scornavacca, C (2011). A survey of combinatorial methods for phylogenetic networks Genome Biology and Evolution, 3:23-35.
- ^ D. H. Huson, R. Rupp and C. Scornavacca, Phylogenetic Networks, Cambridge University Press (2010).
- ^ Arenas, M; Miguel Arenas, Gabriel Valiente, and David Posada (2008-10-15). "Characterization of Reticulate Networks Based on the Coalescent with Recombination". Mol Biol Evol 25 (12): 2517–2520. doi:10.1093/molbev/msn219. PMC 2582979. PMID 18927089.
- ^ D. H. Huson and D. Bryant, Application of Phylogenetic Networks in Evolutionary Studies, Mol. Biol. Evol., 23(2):254-267, 2006.
- ^ Cardona, G; Gabriel Cardona, Francesc Rosselló, and Gabriel Valiente (2008-12-15). "Extended Newick: it is time for a standard representation of phylogenetic networks". BMC Bioinformatics 9: 532. doi:10.1186/1471-2105-9-532. PMC 2621367. PMID 19077301.
- ^ Legendre, P; Makarenkov, V (Apr 2002). "Reconstruction of biogeographic and evolutionary networks using reticulograms". Systematic Biology 51 (2): 199–216. doi:10.1080/10635150252899725. ISSN 1063-5157. PMID 12028728
- ^ Arenas, M; Patricio, M; Posada, D; Valiente, G (2010) Characterization of phylogenetic networks with NetTest. BMC Bioinformatics 11: 268
 Further reading