Fourier transform inequalities for phylogenetic trees
| dc.creator | Matsen, Frederick A. | |
| dc.date | 2007-11-21 | |
| dc.date | 2008-05-28 | |
| dc.date.accessioned | 2026-07-07T09:40:59Z | |
| dc.date.available | 2026-07-07T09:40:59Z | |
| dc.description | Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints ``edge-parameter inequalities.'' In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to \emph{bona fide} trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form ``monomial $\leq 1$,'' each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties. | |
| dc.identifier | https://arxiv.org/abs/0711.3492 | |
| dc.identifier | http://arxiv.org/abs/0711.3492 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161673 | |
| dc.subject | Populations and Evolution | |
| dc.title | Fourier transform inequalities for phylogenetic trees | |
| dc.type | text |