Enhancing Phylogenetic Methods and Theory via Algebraic Perspectives

该项目引入代数和代数几何技术来解决系统发育中出现的问题，研究物种（或其他生物分类群，如属或种群）之间的进化关系。虽然概率和组合方法已经成功地应用于这个生物学领域，但代数几何的工具产生了新的见解，并帮助研究人员更好地理解许多潜在的数学问题。该项目的目标是开发树空间搜索的新算法，开发支持系统发育树中局部特征的新统计度量，以及开发，形式化和研究序列进化的新数学模型。通过加快树空间的启发式搜索来改进系统发育方法将在实际系统发育中具有重要价值，允许对更大数据集的系统发育关系进行调查，并增加树空间搜索的彻底性。这项工作将在阿拉斯加费尔班克斯大学进行，涉及与北极生物研究所有联系的研究人员。从序列数据中推断系统发育在整个生物科学中广泛使用，方法和理论认识的改进将产生深远的影响。随着系统发育数据集变得越来越大，在序列水平上对进化过程的生物学解释越来越完善，理解描述工作过程的更复杂的模型对于开发有效的统计推断方法是必要的。这项工作发展了代数几何和数学生物学领域之间的新兴联系，并带来了重大的广泛影响，从学生的跨学科培训和软件传播到与阿拉斯加以外的研究人员的合作。

This project brings techniques in algebra and algebraic geometry to address questions arising in phylogenetics, the study of evolutionary relationships between species (or other biological taxa such as genera, or populations). While probabilistic and combinatorial methods have been applied successfully in this field of biology, the tools of algebraic geometry yield new insight and help researchers to gain a better understanding of many of the underlying mathematical issues. The goals of this project are to develop new algorithms for the search of tree space, develop a new statistical measure of support for local features in a phylogenetic tree, and to develop, formalize, and study new mathematical models of sequence evolution. Improving phylogenetic methods by speeding up heuristic searches of tree space will have significant value in practical phylogenetics, allowing the investigation of phylogenetic relationships for larger data sets and for increased thoroughness in the search of tree space. The work will be carried out at the University of Alaska Fairbanks and involves researchers with connections to the Institute of Arctic Biology.Phylogenetic inference from sequence data is used widely throughout the biological sciences, and improvements in methods and theoretical understanding will have a far-reaching impact. As phylogenetic data sets become larger and biological explanations of the evolutionary process at the sequence level improve, understanding the more complicated models describing the processes at work is necessary for developing valid and effective methods of statistical inference. This work develops emerging connections between the areas of algebraic geometry and mathematical biology and brings about significant broader impacts ranging from the interdisciplinary training of students and software dissemination to collaborations with researchers outside of Alaska.