Phylogenetic ideals and varieties for the general Markov model
| dc.creator | Allman, Elizabeth S. | |
| dc.creator | Rhodes, John A. | |
| dc.date | 2004-10-28 | |
| dc.date | 2006-10-06 | |
| dc.date.accessioned | 2026-07-07T08:06:34Z | |
| dc.date.available | 2026-07-07T08:06:34Z | |
| dc.description | The general Markov model of the evolution of biological sequences along a tree leads to a parameterization of an algebraic variety. Understanding this variety and the polynomials, called phylogenetic invariants, which vanish on it, is a problem within the broader area of Algebraic Statistics. For an arbitrary trivalent tree, we determine the full ideal of invariants for the 2-state model, establishing a conjecture of Pachter-Sturmfels. For the $κ$-state model, we reduce the problem of determining a defining set of polynomials to that of determining a defining set for a 3-leaved tree. Along the way, we prove several new cases of a conjecture of Garcia-Stillman-Sturmfels on certain statistical models on star trees, and reduce their conjecture to a family of subcases. | |
| dc.description | 5 figures; Minor changes, including renumbering, to reflect final publication form | |
| dc.identifier | https://arxiv.org/abs/math/0410604 | |
| dc.identifier | http://arxiv.org/abs/math/0410604 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130652 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Statistics Theory | |
| dc.subject | Populations and Evolution | |
| dc.subject | 92D15; 14J99; 60J20 | |
| dc.title | Phylogenetic ideals and varieties for the general Markov model | |
| dc.type | text |