Sumner, JG and Jarvis, PD and Holland, BR, A tensorial approach to the inversion of group-based phylogenetic models, BMC Evolutionary Biology, 14 Article 236. ISSN 1471-2148 (2014) [Refereed Article]
Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0) http://creativecommons.org/licenses/by/4.0/
Background: Hadamard conjugation is part of the standard mathematical armoury in the analysis of molecular phylogenetic methods. For group-based models, the approach provides a one-to-one correspondence between the so-called "edge length" and "sequence" spectrum on a phylogenetic tree. The Hadamard conjugation has been used in diverse phylogenetic applications not only for inference but also as an important conceptual tool for thinking about molecular data leading to generalizations beyond strictly tree-like evolutionary modelling.
Results: For general group-based models of phylogenetic branching processes, we reformulate the problem of constructing a one-one correspondence between pattern probabilities and edge parameters. This takes a classic result previously shown through use of Fourier analysis and presents it in the language of tensors and group representation theory. This derivation makes it clear why the inversion is possible, because, under their usual definition, group-based models are defined for abelian groups only.
Conclusion: We provide an inversion of group-based phylogenetic models that can implemented using matrix multiplication between rectangular matrices indexed by ordered-partitions of varying sizes. Our approach provides additional context for the construction of phylogenetic probability distributions on network structures, and highlights the potential limitations of restricting to group-based models in this setting.
|Item Type:||Refereed Article|
|Keywords:||groups, representation theory, symmetry, Markov chains|
|Research Division:||Mathematical Sciences|
|Research Group:||Applied Mathematics|
|Research Field:||Biological Mathematics|
|Objective Division:||Expanding Knowledge|
|Objective Group:||Expanding Knowledge|
|Objective Field:||Expanding Knowledge in the Mathematical Sciences|
|Author:||Sumner, JG (Dr Jeremy Sumner)|
|Author:||Jarvis, PD (Dr Peter Jarvis)|
|Author:||Holland, BR (Associate Professor Barbara Holland)|
|Funding Support:||Australian Research Council (FT100100031)|
|Deposited By:||Mathematics and Physics|
|Downloads:||231 View Download Statistics|
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