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Incorporating compositional heterogeneity into Lie Markov models for phylogenetic inference

Lookup NU author(s): Naomi Hannaford, Dr Sarah Heaps, Dr Tom Nye, Professor T. Martin Embley FMedSci FRS

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This is the authors' accepted manuscript of an article that has been published in its final definitive form by Institute of Mathematical Statistics, 2020.

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Abstract

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees. Substitutions in sequences are modelled through a continuous-time Markov process, characterised by an instantaneous rate matrix, which standard models assume is time-reversible and stationary. These assumptions are biologically questionable and induce a likelihood function which is invariant to a tree's root position. This hampers inference because a tree's biological interpretation depends critically on where it is rooted. Relaxing both assumptions, we introduce a model whose likelihood can distinguish between rooted trees. The model is non-stationary, with step changes in the instantaneous rate matrix at each speciation event. Exploiting recent theoretical work, each rate matrix belongs to a non-reversible family of Lie Markov models. These models are closed under matrix multiplication, so our extension offers the conceptually appealing property that a tree and all its sub-trees could have arisen from the same family of non-stationary models.We adopt a Bayesian approach, describe an MCMC algorithm for posterior inference and provide software. The biological insight that our model can provide is illustrated through an analysis in which non-reversible but stationary, and non-stationary but reversible models cannot identify a plausible root.


Publication metadata

Author(s): Hannaford NE, Heaps SE, Nye TMW, Williams TA, Embley TM

Publication type: Article

Publication status: Published

Journal: The Annals of Applied Statistics

Year: 2020

Volume: 14

Issue: 4

Pages: 1964-1983

Online publication date: 19/12/2020

Acceptance date: 02/07/2020

Date deposited: 17/07/2020

ISSN (print): 1932-6157

ISSN (electronic): 1941-7330

Publisher: Institute of Mathematical Statistics

URL: https://doi.org/10.1214/20-AOAS1369

DOI: 10.1214/20-AOAS1369


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