10.1371/journal.pone.0069187PLoS ONE87-POLN

Anuj Pahwa

B Pakendorf

B Singer

C Sheffield

D Barr

D Penny

G Elfving

GA Doerge

Gavin A. Huttley

GS Goodman

H Frydman

H Lindsay

H Song

HW Schranz

J Geweke

J Sumner

JFC Kingman

JT Chang

JT Runnenberg

K Tamura

Klara L. Verbyla

Konrad Scheffler

L Bofkin

LS Jermiin

M Kallersjo

M Kanehisa

M Oscamou

M Wolf

MJD Powell

N Galtier

N Lartillot

NGC Smith

P Carette

PA Goloboff

PG Foster

PJ Lockhart

R Bevan

R Hardison

R Knight

S Johansen

SYW Ho

V Jayaswal

Von Bing Yap

WL Goffe

XH Xia

Yunli Shao

Z Yang

PLoS ONE

PubMed

<div><p>Continuous-time Markov processes are often used to model the complex natural phenomenon of sequence evolution. To make the process of sequence evolution tractable, simplifying assumptions are often made about the sequence properties and the underlying process. The validity of one such assumption, time-homogeneity, has never been explored. Violations of this assumption can be found by identifying non-embeddability. A process is non-embeddable if it can not be embedded in a continuous time-homogeneous Markov process. In this study, non-embeddability was demonstrated to exist when modelling sequence evolution with Markov models. Evidence of non-embeddability was found primarily at the third codon position, possibly resulting from changes in mutation rate over time. Outgroup edges and those with a deeper time depth were found to have an increased probability of the underlying process being non-embeddable. Overall, low levels of non-embeddability were detected when examining individual edges of triads across a diverse set of alignments. Subsequent phylogenetic reconstruction analyses demonstrated that non-embeddability could impact on the correct prediction of phylogenies, but at extremely low levels. Despite the existence of non-embeddability, there is minimal evidence of violations of the local time homogeneity assumption and consequently the impact is likely to be minor.</p></div

Klara L. Verbyla (439460)

Von Bing Yap (439461)

Anuj Pahwa (439462)

Yunli Shao (439463)

Gavin A. Huttley (423627)

The Francis Crick Institute

The Embedding Problem for Markov Models of Nucleotide Substitution

Verbyla Klara L.

Yap Von Bing

Pahwa Anuj

Shao Yunli

Huttley Gavin A.

Public Library of Science (PLOS)

Continuous-time Markov processes are often used to model the complex natural phenomenon of sequence evolution. To make the process of sequence evolution tractable, simplifying assumptions are often made about the sequence properties and the underlying process. The validity of one such assumption, time-homogeneity, has never been explored. Violations of this assumption can be found by identifying non-embeddability. A process is non-embeddable if it can not be embedded in a continuous time-homogeneous Markov process. In this study, non-embeddability was demonstrated to exist when modelling sequence evolution with Markov models. Evidence of non-embeddability was found primarily at the third codon position, possibly resulting from changes in mutation rate over time. Outgroup edges and those with a deeper time depth were found to have an increased probability of the underlying process being non-embeddable. Overall, low levels of non-embeddability were detected when examining individual edges of triads across a diverse set of alignments. Subsequent phylogenetic reconstruction analyses demonstrated that non-embeddability could impact on the correct prediction of phylogenies, but at extremely low levels. Despite the existence of non-embeddability, there is minimal evidence of violations of the local time homogeneity assumption and consequently the impact is likely to be minor.Research was funded by an ARC grant (Australian Research Council – http://www.arc.gov.au/) awarded to GAH and VBY. The funders had no role in
study design, data collection and analysis, decision to publish, or preparation of the manuscrip

Verbyla, Klara L.

Yap, Von Bing

Pahwa, Anuj

Shao, Yunli

Huttley, Gavin A.

The Australian National University

English

Crossref

Continuous-time Markov processes are often used to model the complex natural phenomenon of sequence evolution. To make the process of sequence evolution tractable, simplifying assumptions are often made about the sequence properties and the underlying process. The validity of one such assumption, time-homogeneity, has never been explored. Violations of this assumption can be found by identifying non-embeddability. A process is non-embeddable if it can not be embedded in a continuous time-homogeneous Markov process. In this study, non-embeddability was demonstrated to exist when modelling sequence evolution with Markov models. Evidence of non-embeddability was found primarily at the third codon position, possibly resulting from changes in mutation rate over time. Outgroup edges and those with a deeper time depth were found to have an increased probability of the underlying process being non-embeddable. Overall, low levels of non-embeddability were detected when examining individual edges of triads across a diverse set of alignments. Subsequent phylogenetic reconstruction analyses demonstrated that non-embeddability could impact on the correct prediction of phylogenies, but at extremely low levels. Despite the existence of non-embeddability, there is minimal evidence of violations of the local time homogeneity assumption and consequently the impact is likely to be minor

Klara L Verbyla

Gavin A Huttley

Directory of Open Access Journals

The embedding problem for markov models of nucleotide substitution.

file:///data/core-remote/dit/data/public_library_of_science/pdf/702/ZnRwOi8vZnRwLm5jYmkubmxtLm5paC5nb3YvcHViL3BtYy9vYV9wYWNrYWdlLzg0LzdmL1BNQzM3MjgzMDMudGFyLmd6.pdf

The Embedding Problem for Markov Models of Nucleotide Substitution

Abstract

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The Francis Crick Institute

Public Library of Science (PLOS)

The Australian National University

Crossref

Directory of Open Access Journals