Linear Models over the Space of Phylogenetic Trees.

点击翻译按钮获取中文摘要

Discovering evolutionary relationship among various groups of organisms and econstruction of ancestral relationships have applications including predicting evolution of fast evolution species, such as HIV, the tree of life project, coevolutions among different species and human evolutionary history. These methodologies can be applied to the evolutionary history of COVID-19 to analyze how they mutate so that scientists can develop effective vaccinations and they can also study how it spreads. This proposal aims to develop new and powerful machine learning models for genome-wide phylogenetic analysis (phylogenomics). Evolutionary hypotheses provide important underpinnings of biological & medical sciences and comprehensive genome-wide understanding of evolutionary relationships among organisms, including parasitic microbes, are needed to test and refine such hypotheses. Theory and empirical evidence clearly indicate that phylogenies (trees) of different genes (loci) should not display precisely matched topologies. The main reason for such phylogenetic incongruence is reticulated evolutionary history of most species due to meiotic sexual recombination in eukaryotes, or horizontal transfers of genetic material in prokaryotes. Nevertheless, most genes should display topologically related phylogenies and should group into one or more (for genetic hybrids) clusters in poly-dimensional tree space.With the development of genetics, aligned gene sequences are used to reconstruct evolutionary history between species (phylogenetic tree), which has led to a mathematical and algorithmic approach to tree reconstruction. Our goal is to develop statistical methods over the space of all phylogenetic trees and investigate their strengths over classical methods. In this project we develop statistical methods that conform to tropical geometry. The project will start off by considering tropical logistic regression to classify gene trees to certain species, by providing a criterion for MCMC convergence in phylogenetic MLE tree estimation, and by creating a tropical linear regression with continuous response variables. In partnership with Naval Postgraduate School.