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Phylogenetic mixtures and linear invariants for equal input models
dc.contributor.author | Casanellas Rius, Marta |
dc.contributor.author | Steel, Mike |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-11-16T11:32:11Z |
dc.date.available | 2017-09-19T00:30:22Z |
dc.date.issued | 2016-09-07 |
dc.identifier.citation | Casanellas, M., Steel, M. Phylogenetic mixtures and linear invariants for equal input models. "Journal of mathematical biology", 7 Setembre 2016, p. 1-32. |
dc.identifier.issn | 0303-6812 |
dc.identifier.uri | http://hdl.handle.net/2117/96713 |
dc.description.abstract | 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). |
dc.format.extent | 32 p. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Biomathematics |
dc.subject.lcsh | Markov processes |
dc.subject.other | Phylogenetic tree |
dc.subject.other | Markov processes |
dc.subject.other | linear invariants |
dc.title | Phylogenetic mixtures and linear invariants for equal input models |
dc.type | Article |
dc.subject.lemac | Biomatemàtica |
dc.subject.lemac | Markov, Processos de |
dc.contributor.group | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
dc.identifier.doi | 10.1007/s00285-016-1055-8 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.subject.ams | Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes |
dc.subject.ams | Classificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics |
dc.relation.publisherversion | http://link.springer.com/article/10.1007%2Fs00285-016-1055-8 |
dc.rights.access | Open Access |
local.identifier.drac | 18971052 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Casanellas, M.; Steel, M. |
local.citation.publicationName | Journal of mathematical biology |
local.citation.startingPage | 1 |
local.citation.endingPage | 32 |
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