Linear Models over the Space of Phylogenetic Trees.

发现不同生物群体之间的进化关系和重建祖先关系的应用包括预测快速进化物种的进化，如HIV，生命树计划，不同物种之间的协同进化和人类进化历史。这些方法可以应用于COVID-19的进化历史，以分析它们是如何突变的，以便科学家能够开发有效的疫苗，并研究它是如何传播的。该提案旨在为全基因组系统发育分析（Genome-wide Phylogenomics）开发新的强大的机器学习模型。进化假说为生物和医学科学提供了重要的基础，需要对生物体（包括寄生微生物）之间的进化关系进行全面的全基因组理解，以测试和完善这些假说。理论和经验证据清楚地表明，不同基因（基因座）的同源（树）不应该显示精确匹配的拓扑结构。这种系统发育不一致的主要原因是由于真核生物中减数分裂的有性重组或原核生物中遗传物质的水平转移导致的大多数物种的网状进化历史。然而，大多数基因在多维树空间中应该表现出拓扑相关的亲缘关系，并且应该分成一个或多个簇（对于遗传杂种）。随着遗传学的发展，对齐的基因序列被用来重建物种之间的进化历史（系统发育树），这导致了一种数学和算法方法来重建树。我们的目标是在所有系统发育树的空间上开发统计方法，并研究它们相对于经典方法的优势。在这个项目中，我们开发符合热带几何的统计方法。该项目将首先考虑热带逻辑回归将基因树分类到某些物种，通过提供系统发育MLE树估计中MCMC收敛的标准，并通过创建具有连续响应变量的热带线性回归。与海军研究生院合作。

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.