Enhancing Phylogenetic Methods and Theory via Algebraic Perspectives

该项目带来了代数和代数几何技术，以解决遗传学中出现的问题，研究物种（或其他生物类群，如属或种群）之间的进化关系。 虽然概率和组合方法已成功地应用于这一领域的生物学，代数几何的工具产生新的见解，并帮助研究人员获得更好地了解许多潜在的数学问题。 这个项目的目标是开发新的算法搜索树空间，开发一个新的统计措施，支持本地功能的系统发育树，并开发，形式化，并研究新的数学模型的序列进化。 通过加速树空间的启发式搜索来改进系统发育方法将在实际的遗传学中具有重要价值，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大学费尔班克斯进行，并涉及与北极生物学研究所有联系的研究人员。从序列数据进行系统发育推断在整个生物科学中得到广泛应用，方法和理论理解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，序列水平上进化过程的生物学解释也越来越好，理解描述工作过程的更复杂的模型对于开发有效和有效的统计推断方法是必要的。 这项工作开发了代数几何和数学生物学领域之间的新兴联系，并带来了更广泛的影响，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.