Dimensions of Group-Based Phylogenetic Mixtures

Hector Baños, Nathaniel Bushek, Ruth Davidson, Elizabeth Gross, Pamela E. Harris, Robert Krone, Colby Long, Allen Stewart, Robert Walker

Research output: Contribution to journalArticle

Abstract

Mixtures of group-based Markov models of evolution correspond to joins of toric varieties. In this paper, we establish a large number of cases for which these phylogenetic join varieties realize their expected dimension, meaning that they are nondefective. Nondefectiveness is not only interesting from a geometric point-of-view, but has been used to establish combinatorial identifiability for several classes of phylogenetic mixture models. Our focus is on group-based models where the equivalence classes of identified parameters are orbits of a subgroup of the automorphism group of the abelian group defining the model. In particular, we show that for these group-based models, the variety corresponding to the mixture of r trees with n leaves is nondefective when n≥ 2 r+ 5. We also give improved bounds for claw trees and give computational evidence that 2-tree and 3-tree mixtures are nondefective for small n.

Original languageEnglish (US)
Pages (from-to)316-336
Number of pages21
JournalBulletin of mathematical biology
Volume81
Issue number2
DOIs
StatePublished - Feb 15 2019

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Phylogenetics
phylogenetics
Join
phylogeny
Claw
R-tree
Hoof and Claw
Toric Varieties
Identifiability
Orbit
Equivalence class
Mixture Model
Automorphism Group
Markov Model
Abelian group
Leaves
Equivalence classes
Subgroup
Model
orbits

PubMed: MeSH publication types

  • Journal Article
  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, Non-P.H.S.
  • Research Support, Non-U.S. Gov't

Cite this

Baños, H., Bushek, N., Davidson, R., Gross, E., Harris, P. E., Krone, R., ... Walker, R. (2019). Dimensions of Group-Based Phylogenetic Mixtures. Bulletin of mathematical biology, 81(2), 316-336. https://doi.org/10.1007/s11538-018-0489-0

Dimensions of Group-Based Phylogenetic Mixtures. / Baños, Hector; Bushek, Nathaniel; Davidson, Ruth; Gross, Elizabeth; Harris, Pamela E.; Krone, Robert; Long, Colby; Stewart, Allen; Walker, Robert.

In: Bulletin of mathematical biology, Vol. 81, No. 2, 15.02.2019, p. 316-336.

Research output: Contribution to journalArticle

Baños, H, Bushek, N, Davidson, R, Gross, E, Harris, PE, Krone, R, Long, C, Stewart, A & Walker, R 2019, 'Dimensions of Group-Based Phylogenetic Mixtures', Bulletin of mathematical biology, vol. 81, no. 2, pp. 316-336. https://doi.org/10.1007/s11538-018-0489-0
Baños H, Bushek N, Davidson R, Gross E, Harris PE, Krone R et al. Dimensions of Group-Based Phylogenetic Mixtures. Bulletin of mathematical biology. 2019 Feb 15;81(2):316-336. https://doi.org/10.1007/s11538-018-0489-0
Baños, Hector ; Bushek, Nathaniel ; Davidson, Ruth ; Gross, Elizabeth ; Harris, Pamela E. ; Krone, Robert ; Long, Colby ; Stewart, Allen ; Walker, Robert. / Dimensions of Group-Based Phylogenetic Mixtures. In: Bulletin of mathematical biology. 2019 ; Vol. 81, No. 2. pp. 316-336.
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