Tree-average distances on certain phylogenetic networks have their weights uniquely determined.

Algorithms for Molecular Biology : AMB
Stephen J Willson

Abstract

A phylogenetic network N has vertices corresponding to species and arcs corresponding to direct genetic inheritance from the species at the tail to the species at the head. Measurements of DNA are often made on species in the leaf set, and one seeks to infer properties of the network, possibly including the graph itself. In the case of phylogenetic trees, distances between extant species are frequently used to infer the phylogenetic trees by methods such as neighbor-joining. This paper proposes a tree-average distance for networks more general than trees. The notion requires a weight on each arc measuring the genetic change along the arc. For each displayed tree the distance between two leaves is the sum of the weights along the path joining them. At a hybrid vertex, each character is inherited from one of its parents. We will assume that for each hybrid there is a probability that the inheritance of a character is from a specified parent. Assume that the inheritance events at different hybrids are independent. Then for each displayed tree there will be a probability that the inheritance of a given character follows the tree; this probability may be interpreted as the probability of the tree. The tree-average distance between t...Continue Reading

References

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Oct 20, 2006·IEEE/ACM Transactions on Computational Biology and Bioinformatics·Bernard M E MoretRuth Timme
Oct 1, 2009·Bulletin of Mathematical Biology·Stephen J Willson
Oct 31, 2009·IEEE/ACM Transactions on Computational Biology and Bioinformatics·Gabriel CardonaGabriel Valiente
Oct 31, 2009·IEEE/ACM Transactions on Computational Biology and Bioinformatics·Leo van IerselTeun Boekhout

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Citations

May 18, 2013·Journal of Mathematical Biology·Leo van Iersel, Vincent Moulton
Aug 31, 2014·Interdisciplinary Sciences, Computational Life Sciences·Rinku Mathur, Neeru Adlakha
Dec 17, 2015·Journal of Mathematical Biology·Magnus Bordewich, Charles Semple
Jul 19, 2013·Bulletin of Mathematical Biology·Stephen J Willson
Sep 24, 2014·Bulletin of Mathematical Biology·Paul CordueCharles Semple
Dec 3, 2014·Mathematical Biosciences·Andrew R Francis, Mike Steel
Feb 27, 2018·Journal of Mathematical Biology·Magnus BordewichCharles Semple

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