Reconstructing Phylogenetic Trees

The College Of New Jersey, Ewing NJ

Investigators

Abstract

Hagedorn 0077851 The investigator seeks advances in the reconstruction of phylogenetic, or evolutionary, trees in biology by improving the utility of the method of phylogenetic invariants, one of several different methods of tree reconstruction. It would be extremely useful to have an accurate, computationally efficient method of phylogenetic analysis, but no such method is yet known. The method of phylogenetic invariants theoretically has these advantages. Modern phylogenetic methods analyze the mathematical and statistical similarities between the nucleotide sequences of different species. By modeling the evolution of the sequence for a proposed evolutionary tree T as a Markov model, one can obtain polynomials specifying the frequencies with which certain patterns should occur in observed sequence data. These polynomials parameterize a high-dimensional real algebraic variety X. Finding the equations that implicitly define X is theoretically equivalent to knowing how to determine whether T is the "true" evolutionary tree. These equations have been previously found for special evolutionary models such as the Kimura 3-parameter model. The investigator studies the invariants for the most general Markov model of nucleotide sequences and uses a combination of combinatorics and non-abelian Fourier analysis to find a complete set of invariants. He also explores ways to reduce the method's sensitivity to evolutionary noise and raising its accuracy. Advances on these issues are essential to make implementations of the invariant method practical for phylogenetic analysis. The investigator develops better methods to construct biological trees explaining the evolutionary relationships between species. Understanding evolutionary relationships is an important biological question, whose applications range from aiding the discovery of the origin of life to helping the medical community research possible vaccines and treatments for pathogens such as the H.I.V. virus. It would be extremely useful to have an accurate and computationally efficient method of phylogenetic (or evolutionary) analysis, but no method is currently known to possess both qualities. The project seeks to improve the accuracy of the tree reconstruction method using phylogenetic invariants. The method of invariants is a computationally efficient method, which is known to theoretically give correct answers. However, in practice, the method is very susceptible to the presence of noise in the data. The investigator aims to minimize this problem by eliminating several assumptions that currently must be met to use the method of invariants.