Reconstructing Phylogenetic Trees

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Hagedorn0077851 The investigator seeks advances in the reconstruction ofphylogenetic, or evolutionary, trees in biology by improving theutility of the method of phylogenetic invariants, one of severaldifferent methods of tree reconstruction. It would be extremelyuseful to have an accurate, computationally efficient method ofphylogenetic analysis, but no such method is yet known. Themethod of phylogenetic invariants theoretically has theseadvantages. Modern phylogenetic methods analyze the mathematicaland statistical similarities between the nucleotide sequences ofdifferent species. By modeling the evolution of the sequence fora proposed evolutionary tree T as a Markov model, one can obtainpolynomials specifying the frequencies with which certainpatterns should occur in observed sequence data. Thesepolynomials parameterize a high-dimensional real algebraicvariety X. Finding the equations that implicitly define X istheoretically equivalent to knowing how to determine whether T isthe "true" evolutionary tree. These equations have beenpreviously found for special evolutionary models such as theKimura 3-parameter model. The investigator studies theinvariants for the most general Markov model of nucleotidesequences and uses a combination of combinatorics and non-abelianFourier analysis to find a complete set of invariants. He alsoexplores ways to reduce the method's sensitivity to evolutionarynoise and raising its accuracy. Advances on these issues areessential to make implementations of the invariant methodpractical for phylogenetic analysis. The investigator develops better methods to constructbiological trees explaining the evolutionary relationshipsbetween species. Understanding evolutionary relationships is animportant biological question, whose applications range fromaiding the discovery of the origin of life to helping the medicalcommunity research possible vaccines and treatments for pathogenssuch as the H.I.V. virus. It would be extremely useful to havean accurate and computationally efficient method of phylogenetic(or evolutionary) analysis, but no method is currently known topossess both qualities. The project seeks to improve theaccuracy of the tree reconstruction method using phylogeneticinvariants. The method of invariants is a computationallyefficient method, which is known to theoretically give correctanswers. However, in practice, the method is very susceptible tothe presence of noise in the data. The investigator aims tominimize this problem by eliminating several assumptions thatcurrently must be met to use the method of invariants.