Mixture Model of Mutagenetic Trees and Application in Evolutionary Biology

Date of Award

2007

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Keywords

Algebraic Statistics, Algebraic Geometry, Math Bio, HIV Drug Resistance, Mutagenetic Tree

Area of Concentration

Mathematics

Abstract

Acquired drug resistance for known human pathogens presents a serious challenge to treatment of these pathogens. Acquired drug resistance has proved particularly intractable in the case of HIV. This thesis concerns a class of graphical models, mutagenetic tree models, and linear combinations of such models, mutagenetic tree mixture models, which were developed to study the accumulative evolutionary processes undergoing permanent genetic changes, and the evolution of drug resistance in the HIV genome in particular. Using methods from algebraic statistics, we compute the dimension of all two-tree mixture models where each tree has 4 non-root nodes. We also compute the polynomial invariants for all these models which are used in Frequentist methods for model selection. The information is compiled in a database that can aid biologists and statisticians working in model selection.

Rights

This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

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