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Low degree equations for phylogenetic group-based models
Casanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusz
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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
Àrees temàtiques de la UPC::Matemàtiques i estadística
Biomathematics
Biomatemàtica
Classificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics
Classificació AMS::14 Algebraic geometry::14H Curves
Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
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