What is a phylogenetic network?

Adapted from South Park - When Mrs Garrison explains evolution with reticulations
The Theory of Evolution can be
summed up by this level-3
phylogenetic network
according to
Mrs Garrison in South Park S10E12.
The classical mathematical model to represent evolution (of some species, or genes) is the phylogenetic tree. But trees are unable to represent horizontal gene transfer, recombination or hybridization events: in those cases, some branches of the tree combine into a reticulation node, and the tree becomes a network.

The main question about phylogenetic networks is how to reconstruct them from available data. This data can be of different kinds: sequences (sometimes binary sequences), distances between those sequences, rooted or unrooted trees, triplets (rooted trees on three leaves), quartets (unrooted trees on four leaves), splits (bipartitions of the set of leaves), clusters (subset of leaves which should appear together in the network), multilabeled trees (in the context of duplications), or even networks (to get a consensus network from the input).

This question gave rise to some other ones: how to visualize phylogenetic networks (which is linked with graph drawing, except in phylogeny the lengths of the branches may be constrained), or how to compare them in the context of evaluation of the reconstruction methods. These problematics give rise to many theoretical problems, some of which are polynomial, but many of which are NP-complete. Fixed-parameter tractable, approximation algorithms, or heuristics have thus been developed to solve them. Depending on the problem adressed, and its complexity, the network used in the analysis may be an explicit phylogenetic network if it describes biological events, or an abstract phylogenetic network if its edges may not be interpreted biologically. A popular example of abstract network in the literature is the split network which can be used as a visualization of a set of incompatible phylogenetic trees, therefore giving some understanding on the conflicts present in the data.

Inclusion of phylogenetic network classes

This ISGCI-like hierarchy is under construction...

An arrow pointing from a class A to B represents that A contains B (beware, no arrow doesn't mean that the classes are disjoint, they may overlap!). Here phylogenetic networks are considered as combinatorial objects with graph properties, if you want to see a hierarchy which classifies some existing kinds of networks according to the context in which they are used, you can refer to Figure 1 in [HusonBryant2006].

A hierarchy of restrictions on phylogenetic networks

More details about these figures will be available in my PhD thesis.

More information on these classes of phylogenetic networks: abstract network, block realization, explicit network, galled-tree, galled-network, level-f phylogenetic network, normal network, pyramid, regular network, reticulogram, tree-child network, tree-sibling network, split network, unicyclic network, weak hierarchy, weakly compatible set of splits...

See also