Quasi-median networks

Last updated May 03, 2019

The concept of a quasi-median network is a generalization of the concept of a median network that was introduced to represent multistate characters. Note that, unlike median networks, quasi-median networks are not split networks. A quasi-median network is defined as a phylogenetic network, the node set of which is given by the quasi-median closure of the condensed version of M (let M be a multiple sequence alignment of DNA sequences on X) and in which any two nodes are joined by an edge if and only if the sequences associated with the nodes differ in exactly one position. The quasi-median closure is defined as the set of all sequences that can be obtained by repeatedly taking the quasi-median of any three sequences in the set and then adding the result to the set.^[1]^[2]

For a given set of taxa like X, and a set of splits S on X, usually together with a non-negative weighting, which may represent character changes distance, or may also have a more abstract interpretation, if the set of splits S is compatible, then it can be represented by an unrooted phylogenetic tree and each edge in the tree corresponds to exactly one of the splits. More generally, S can always be represented by a split network, which is an unrooted phylogenetic network with the property that every split s in S is represented by an array of parallel edges in the network.

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References

↑ Huson, Daniel H.; Scornavacca, Celine (2011). "A survey of combinatorial methods for phylogenetic networks". Genome Biology and Evolution. 3: 23–35. doi:10.1093/gbe/evq077.
↑ Huson, Daniel H.; Rupp, Regula; Scornavacca, Celine (2011). Phylogenetic Networks: Concepts, Algorithms and Applications. Cambridge University Press. ISBN 978-0521755962.

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[1] Huson, Daniel H.; Scornavacca, Celine (2011). "A survey of combinatorial methods for phylogenetic networks". Genome Biology and Evolution. 3: 23–35. doi:10.1093/gbe/evq077.

[2] Huson, Daniel H.; Rupp, Regula; Scornavacca, Celine (2011). Phylogenetic Networks: Concepts, Algorithms and Applications. Cambridge University Press. ISBN 978-0521755962.