Phylosymmetric Algebras: Mathematical Properties of a New Tool in Phylogenetics.

Bulletin of Mathematical Biology
Michael Hendriksen, Julia A. Shore

Abstract

In phylogenetics, it is of interest for rate matrix sets to satisfy closure under matrix multiplication as this makes finding the set of corresponding transition matrices possible without having to compute matrix exponentials. It is also advantageous to have a small number of free parameters as this, in applications, will result in a reduction in computation time. We explore a method of building a rate matrix set from a rooted tree structure by assigning rates to internal tree nodes and states to the leaves, then defining the rate of change between two states as the rate assigned to the most recent common ancestor of those two states. We investigate the properties of these matrix sets from both a linear algebra and a graph theory perspective and show that any rate matrix set generated this way is closed under matrix multiplication. The consequences of setting two rates assigned to internal tree nodes to be equal are then considered. This methodology could be used to develop parameterised models of amino acid substitution which have a small number of parameters but convey biological meaning.

References

Apr 1, 1996·Journal of Molecular Evolution·J Adachi, M Hasegawa
Dec 29, 1998·Molecular Biology and Evolution·Z YangM Hasegawa
Mar 28, 2008·Molecular Biology and Evolution·Si Quang Le, Olivier Gascuel
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Apr 12, 2014·Journal of Mathematical Biology·Jesús Fernández-SánchezMichael D Woodhams
Mar 31, 2015·Origins of Life and Evolution of the Biosphere : the Journal of the International Society for the Study of the Origin of Life·Peter R WillsJohn S McCaskill
Nov 12, 2016·Molecular Biology and Evolution·Beatriz MelloSudhir Kumar
Nov 30, 2019·Journal of Molecular Evolution·Julia A ShorePeter R Wills

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