Phylogenetic mixtures and linear invariants for equal input models

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely...

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Detalles Bibliográficos
Autores: Casanellas Rius, Marta|||0000-0002-1724-8358, Steel, Mike
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/96713
Acceso en línea:https://hdl.handle.net/2117/96713
https://dx.doi.org/10.1007/s00285-016-1055-8
Access Level:acceso abierto
Palabra clave:Biomathematics
Markov processes
Phylogenetic tree
linear invariants
Biomatemàtica
Markov, Processos de
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes
Classificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling Phylogenetic mixtures and linear invariants for equal input modelsCasanellas Rius, Marta|||0000-0002-1724-8358Steel, MikeBiomathematicsMarkov processesPhylogenetic treeMarkov processeslinear invariantsBiomatemàticaMarkov, Processos deClassificació AMS::05 Combinatorics::05C Graph theoryClassificació AMS::60 Probability theory and stochastic processes::60J Markov processesClassificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamicsÀrees temàtiques de la UPC::Matemàtiques i estadísticaThe reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the ‘equal input model’. This model generalizes the ‘Felsenstein 1981’ model (and thereby the Jukes–Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a ‘random cluster’ process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees—the so called ‘model invariants’), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of n=4 leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167–191, 1987).Peer Reviewed20162016-09-0720162016-11-16journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/96713https://dx.doi.org/10.1007/s00285-016-1055-8reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/967132026-05-27T15:37:01Z
dc.title.none.fl_str_mv Phylogenetic mixtures and linear invariants for equal input models
title Phylogenetic mixtures and linear invariants for equal input models
spellingShingle Phylogenetic mixtures and linear invariants for equal input models
Casanellas Rius, Marta|||0000-0002-1724-8358
Biomathematics
Markov processes
Phylogenetic tree
Markov processes
linear invariants
Biomatemàtica
Markov, Processos de
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes
Classificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Phylogenetic mixtures and linear invariants for equal input models
title_full Phylogenetic mixtures and linear invariants for equal input models
title_fullStr Phylogenetic mixtures and linear invariants for equal input models
title_full_unstemmed Phylogenetic mixtures and linear invariants for equal input models
title_sort Phylogenetic mixtures and linear invariants for equal input models
dc.creator.none.fl_str_mv Casanellas Rius, Marta|||0000-0002-1724-8358
Steel, Mike
author Casanellas Rius, Marta|||0000-0002-1724-8358
author_facet Casanellas Rius, Marta|||0000-0002-1724-8358
Steel, Mike
author_role author
author2 Steel, Mike
author2_role author
dc.subject.none.fl_str_mv Biomathematics
Markov processes
Phylogenetic tree
Markov processes
linear invariants
Biomatemàtica
Markov, Processos de
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes
Classificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Biomathematics
Markov processes
Phylogenetic tree
Markov processes
linear invariants
Biomatemàtica
Markov, Processos de
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes
Classificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics
Àrees temàtiques de la UPC::Matemàtiques i estadística
description The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the ‘equal input model’. This model generalizes the ‘Felsenstein 1981’ model (and thereby the Jukes–Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a ‘random cluster’ process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees—the so called ‘model invariants’), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of n=4 leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167–191, 1987).
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-09-07
2016
2016-11-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/96713
https://dx.doi.org/10.1007/s00285-016-1055-8
url https://hdl.handle.net/2117/96713
https://dx.doi.org/10.1007/s00285-016-1055-8
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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