Low degree equations for phylogenetic group-based models

Motivated by phylogenetics, our aim is to obtain a system of low degree equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group G , we prov...

Full description

Saved in:
Bibliographic Details
Published in:Collectanea mathematica (Barcelona) Vol. 66; no. 2; pp. 203 - 225
Main Authors: Casanellas, Marta, Fernández-Sánchez, Jesús, Michałek, Mateusz
Format: Journal Article Publication
Language:English
Published: Milan Springer Milan 01.05.2015
Subjects:
14 Algebraic geometry
14H Curves
60 Probability theory and stochastic processes
60J Markov processes
92 Biology and other natural sciences
92D Genetics and population dynamics
Algebra
Analysis
Applications of Mathematics
Biomatemàtica
Biomathematics
Classificació AMS
Geometry
Matemàtiques i estadística
Mathematics
Mathematics and Statistics
Àrees temàtiques de la UPC
60J20
92D15
14H10
ISSN:0010-0757, 2038-4815
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Motivated by phylogenetics, our aim is to obtain a system of low degree equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group G , we provide an explicit construction of codim X polynomial equations (phylogenetic invariants) of degree at most | G | that define the variety X on a Zariski open set U . The set U contains all biologically meaningful points when G is the group of the Kimura 3-parameter model. In particular, our main result confirms (Michałek, Toric varieties: phylogenetics and derived categories, PhD thesis, Conjecture 7.9, 2012 ) and, on the set U , Conjectures 29 and 30 of Sturmfels and Sullivant (J Comput Biol 12:204–228, 2005 ).
ISSN:0010-0757
2038-4815
DOI:10.1007/s13348-014-0120-0