Mathematics of Phylogenetic Trees Seminar
L. Pachter and B. Sturmfels
Wednesdays, 3:00-5:00pm
939 Evans

Date: September 24th, 2003

Time: 4:00pm

Title: Algebraic Techniques for Phylogeny Reconstruction.

Speaker: Elizabeth Allman, University of Southern Maine

Abstract: For a Markov model of evolution of biological sequences (DNA, proteins) along a phylogenetic tree, the expected frequencies of base patterns in the leaf taxa are polynomials in the model parameters, and so define a parametrized variety. Describing this variety implicitly, by giving polynomials which vanish on it, would enable one to develop tests for whether observed frequency data from aligned DNA sequences is described well by a particular evolutionary tree. Such polynomials are called phylogenetic invariants, and until recently have been hard to find, as naive computational approaches fail when faced with the large number of variables involved.

A method of construction of these invariants will be explained that leads to both expressions of a relatively simple form and a direct connection between the polynomials and topological features of the tree. While the determination of all invariants for a tree is still open, a connection between these polynomials and recovery of model parameters indicates they provide much of the picture.

Current work, on the use of invariants in quartet methods for phylogenetic inference, invariants for more general models, and real-algebraic issues of restricting parameters to stochastically-meaningful values will be touched on.

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