Kybernetika 56 no. 6, 1154-1175, 2020

Brownian motion tree models are toric

Bernd Sturmfels, Caroline Uhler and Piotr ZwiernikDOI: 10.14736/kyb-2020-6-1154

Abstract:

Felsenstein's classical model for Gaussian distributions on a phylogenetic tree is shown to be a toric variety in the space of concentration matrices. We present an exact semialgebraic characterization of this model, and we demonstrate how the toric structure leads to exact methods for maximum likelihood estimation. Our results also give new insights into the geometry of ultrametric matrices.

Keywords:

Brownian motion tree model, ultrametric matrices, toric geometry

Classification:

62R01, 62H22, 15B48

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