A phylogenetic network is any

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

used to visualize evolutionary relationships (either abstractly or explicitly) between nucleotide sequences,

gene In biology, the word gene (from , ; "... Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a b ...

chromosome A chromosome is a long DNA molecule with part or all of the genetic material of an organism. In most chromosomes the very long thin DNA fibers are coated with packaging proteins; in eukaryotic cells the most important of these proteins ar ...

genome In the fields of molecular biology and genetics, a genome is all the genetic information of an organism. It consists of nucleotide sequences of DNA (or RNA in RNA viruses). The nuclear genome includes protein-coding genes and non-coding ...

s, or

species In biology, a species is the basic unit of Taxonomy (biology), classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of ...

. They are employed when reticulation events such as hybridization,

horizontal gene transfer Horizontal gene transfer (HGT) or lateral gene transfer (LGT) is the movement of genetic material between unicellular and/or multicellular organisms other than by the ("vertical") transmission of DNA from parent to offspring ( reproduction). ...

, recombination, or gene duplication and loss are believed to be involved. They differ from phylogenetic trees by the explicit modeling of richly linked networks, by means of the addition of hybrid nodes (nodes with two parents) instead of only tree nodes (a hierarchy of nodes, each with only one parent). Phylogenetic trees are a subset of

phylogenetic In biology, phylogenetics (; from Greek φυλή/ φῦλον [] "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary history and relationships among or within groups o ...

networks. Phylogenetic networks can be inferred and visualised with software such as SplitsTree, the R-package, phangorn, 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, ancestral recombination graphs (ARGs) from binary sequences, median networks from a set of splits, optimal realizations and reticulograms from a

distance matrix In mathematics, computer science and especially graph theory, a distance matrix is a square matrix In mathematics, a square matrix is a matrix with the same number of rows and columns. An ''n''-by-''n'' matrix is known as a square matrix of orde ...

), or restrictions to get computationally tractable problems (galled trees, and their generalizations level-k phylogenetic networks, tree-child or tree-sibling phylogenetic networks).

Microevolution

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

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 In biology, a taxon ( back-formation from '' taxonomy''; plural taxa) is a group of one or more populations of an organism or organisms seen by taxonomists to form a unit. Although neither is required, a taxon is usually known by a particular n ...

. 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. In most cases, such networks only depict relations between taxa, without giving information about the evolutionary history. Although some methods produce unrooted networks that can be interpreted as undirected versions of rooted networks, which do represent a phylogeny. ;Rooted phylogenetic network :Let X be a set of taxa. A rooted phylogenetic network N on X is a rooted directed acyclic graph where the set of leaves is bijectively labeled by the taxa in X. Rooted phylogenetic networks, like rooted phylogenetic trees, give explicit representations of evolutionary history. This means that they visualize the order in which the species diverged (speciated), converged (hybridized), and transferred genetic material (horizontal gene transfer).

Classes of networks

For computational purposes, studies often restrict their attention to classes of networks: subsets of all networks with certain properties. Although computational simplicity is the main goal, most of these classes have a biological justification as well. Some prominent classes currently used in the mathematical phylogenetics literature are tree-child networks, tree-based networks, and level-k networks

Software to compute phylogenetic networks

PhyloNet
A Java-based software package that builds phylogenetic networks taking ILS, HGT etc. into consideration.
PhyloNetworks

Julia
package for the manipulation, visualization, inference of phylogenetic networks, and their use for trait evolution.

Free Phylogenetic Network Software. Network generates evolutionary trees and networks from genetic, linguistic, and other data.

some of which compute phylogenetic networks
List of programs for phylogenetic network reconstruction, evaluation, visualization, etc.
* SplitsTree * Dendroscope
Network inferring on the T-REX serverTCS
Phylogenetic networks from DNA sequences or nucleotide distances using statistical parsimony.
NetTest
Characterization of phylogenetic networks.

SimPlot++
Sequence similarity network analysis.

Microevolution

Rooted vs unrooted

Classes of networks

Software to compute phylogenetic networks

References

Further reading