Phylogenetic invariants for group-based models

  • Maria Donten-Bury Author University: University of Warsaw Author Department: Mathematics Institute
  • Mateusz Michalek Author University: Polish Academy of Sciences Author Department: Mathematics Institute
Keywords: phylogenetic tree, group-based model, phylogenetic invariant

Abstract

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 (rst) 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.

References

Published Year: 2012
Volume: 3
Number: 1
Page Numbers: 44-63
Published
2012-04-30