Details:
Speaker: John Rhodes (U. Alaska, Fairbanks)
Title: The Geometry and Algebra of Evolution: Developing a new tool for phylogenetic analysis of genomic data
Abstract: Using DNA sequences as a basis for inferring evolutionary relationships between organisms has become routine over the past 30 years. However, as sequence datasets grow from single genes to entire genomes, new tools are needed and novel mathematical approaches continue to be investigated.
After explaining the basic probabilistic models of sequence evolution on trees, this talk will present a non-standard way of viewing them, as high-dimensional geometric objects with algebraic descriptions (algebraic varieties). This perspective motivates the purely mathematical problem of finding an explicit algebraic description of the models, whose answer in turn leads to a new practical tool for biological data analysis, the Split Score. This score is a statistically consistent measure of support in a data set for a single edge
within a tree, without regard to the rest of the tree branching pattern. Pleasantly, it can be implemented using highly-developed scientific computation packages, and an analysis of a full chromosome typically requires only minutes. Several examples of its use on biological datasets will be shown.
The intended audience spans mathematics, statistics, and biology. Familiarity with any of the fields, and a willingness to take a journey passing through the others, is all that is required.
Faculty host: Luke Oeding
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