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Phylogenetic invariants for group-based models

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2012

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Donten-Bury, Maria

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https://doi.org/10.18409/jas.v3i1.15
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Journal of Algebraic Statistics. Illinois Institute of Technology. 2012, 3(1), pp. 44-63. eISSN 1309-3452. Available under: doi: 10.18409/jas.v3i1.15

Zusammenfassung

In this paper we investigate properties of algebraic varieties representing group-based phylogenetic models. We propose a method of generating many phylogenetic invariants. We prove that we obtain all invariants for any tree for the two-state Jukes-Cantor model. We conjecture that for a large class of models our method can give all phylogenetic invariants for any tree. We show that for 3-Kimura our conjecture is equivalent to the conjecture of Sturmfels and Sullivant [22, Conjecture 2]. This, combined with the results in [22], would make it possible to determine all phylogenetic invariants for any tree for 3-Kimura model, and also other phylogenetic models. Next we give the (first) examples of non-normal varieties associated to general group-based model for an abelian group. Following Kubjas [17] we prove that for many group-based models varieties associated to trees with the same number of leaves do not have to be deformation equivalent.

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510 Mathematik

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phylogenetic tree, group-based model, phylogenetic invariant

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ISO 690DONTEN-BURY, Maria, Mateusz MICHALEK, 2012. Phylogenetic invariants for group-based models. In: Journal of Algebraic Statistics. Illinois Institute of Technology. 2012, 3(1), pp. 44-63. eISSN 1309-3452. Available under: doi: 10.18409/jas.v3i1.15
BibTex
@article{DontenBury2012Phylo-53143,
  year={2012},
  doi={10.18409/jas.v3i1.15},
  title={Phylogenetic invariants for group-based models},
  number={1},
  volume={3},
  journal={Journal of Algebraic Statistics},
  pages={44--63},
  author={Donten-Bury, Maria and Michalek, Mateusz}
}
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