Mathematical Phylogenetics

North Carolina State University, Raleigh NC

Investigators

Abstract

Phylogenetics is the branch of mathematical biology concerned with reconstructing evolutionary relationships among species. While phylogenetic analyses are widely used throughout the biological sciences, there remain fundamental questions about how to reconstruct trees most effectively under a host of increasingly complex data scenarios. This project addresses fundamental scientific challenges in phylogenetics using a range of mathematics tools from probability, combinatorics, and geometry. One main goal of the project will be to develop better methods for reconstructing evolutionary histories. The project will further develop STEM infrastructure by training graduate students in mathematical methods in biology. This research develops tools from probability, combinatorics, and geometry to solve problems in phylogenetics, that area of mathematical biology concerned with reconstructing evolutionary histories between collections of species. The particular problems to be addressed include the development of new algorithms for alignment free phylogenetic tree reconstruction, the study of the distribution of maximum agreement subtrees for random trees, and the development of geometric tools to better deploy distance-based phylogenetic algorithms. The implementation assuming alignment free phylogenetic tree reconstruction will be the first statistically consistent method that takes into account both substitution and insertion/deletion processes. The project on maximum agreement subtrees makes connections to longest increasing subsequences and related tools from combinatorial probability. The project on distance-based methods will use tools from polyhedral combinatorics and tropical geometry to better understand the comparison between greedy algorithms procedures and the underlying approximate optimization procedures.