Name
Abstract | ||
|---|---|---|
Statistical models of evolution are algebraic varieties in the space of joint probability distributions on the leaf colorations of a phylogenetic tree. The phylogenetic invariants of a model are the polynomials which vanish on the variety. Several widely used models for biological sequences have transition matrices that can be diagonalized by means of the Fourier transform of an abelian group. Their phylogenetic invariants form a toric ideal in the Fourier coordinates. We determine generators and Grobner bases for these toric ideals. For the Jukes-Cantor and Kimura models on a binary tree, our Grobner bases consist of certain explicitly constructed polynomials of degree at most four. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1089/cmb.2005.12.204 | JOURNAL OF COMPUTATIONAL BIOLOGY |
Keywords | Field | DocType |
binary tree,statistical model,invariants,phylogenetic tree,algebraic variety,fourier transform,probability distribution,abelian group,phylogenetics | Abelian group,Combinatorics,Phylogenetic tree,Polynomial,Binary tree,Fourier transform,Algebraic variety,Invariant (mathematics),Algebraic statistics,Mathematics | Journal |
Volume | Issue | ISSN |
12.0 | 2 | 1066-5277 |
Citations | PageRank | References |
18 | 2.24 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernd Sturmfels | 1 | 926 | 136.85 |
| Seth Sullivant | 2 | 93 | 19.17 |