Low degree equations for phylogenetic group-based models

descriptionPublicationkeyboard_double_arrow_right Article 03 Aug 2014 English Publisher:Springer Science and Business Media LLCJournal:Collectanea Mathematica, volume 66, pages 203-225 (issn: 0010-0757, eissn: 2038-4815,

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Authors: Casanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusz;

doi: 10.1007/s13348-014-0120-0

handle: 2117/26029

Low degree equations for phylogenetic group-based models

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Abstract

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 codimX 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 (Michalek, 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). Peer Reviewed

Related Organizations

Universitat Politècnica de Catalunya
Spain
Polish Academy of Learning
Poland
Universitat Polite`cnica de Catalunya
Spain

Keywords

Biomathematics, Àrees temàtiques de la UPC::Matemàtiques i estadística, Biomatemàtica, phylogenetic variety, Applications of graph theory, :Matemàtiques i estadística [Àrees temàtiques de la UPC], :92 Biology and other natural sciences::92D Genetics and population dynamics [Classificació AMS], Zariski open set, abelian group, Curves in algebraic geometry, Classificació AMS::14 Algebraic geometry::14H Curves, phylogenetics, Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes, Classificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics, :14 Algebraic geometry::14H Curves [Classificació AMS], Problems related to evolution, group-based models, :60 Probability theory and stochastic processes::60J Markov processes [Classificació AMS], Abelian groups

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