Finite phylogenetic complexity and combinatorics of tables

Abstract

In algebraic statistics, Jukes–Cantor and Kimura models are of great importance. Sturmfels and Sullivant generalized these models by associating to any finite abelian group $G$ a family of toric varieties $X\left(G,K_{1,n}\right)$. We investigate the generators of their ideals. We show that for any finite abelian group $G$ there exists a constant $\varphi$, depending only on $G$, such that the ideals of $X\left(G,K_{1,n}\right)$ are generated in degree at most $\varphi$.