On the ideals of phylogenetic tree models

Joint work with Jochen Kuttler (Edmonton)

Lecturer: Jan Draisma

We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group based models in phylogenetics. We focus on the ideals of such models. We show how the ideals for general trees can be determined from the ideals for stars, i.e. trees with diameter at most 2. The main novelty is our proof that this procedure yields the entire ideal of the model, that is, it yields all polynomials vanishing on the model. A corollary of theoretical importance is that the ideal for a general tree is generated by the ideals of its flattenings at vertices.

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