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

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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