Reconstructing Phylogenetic Trees

Hagedorn0077851研究人员通过改进系统发育不变量方法的实用性，寻求在生物学中重建系统发育或进化树的进展，系统发育不变量方法是树重建的几种不同方法之一。拥有一种准确的、计算高效的系统发育分析方法将是非常有用的，但目前还没有这样的方法。从理论上讲，系统发育不变量方法具有这些优点。现代系统发育学方法分析不同物种之间的核苷酸序列在数学和统计上的相似性。通过将所提出的进化树T的序列的演化建模为马尔可夫模型，可以获得多项式，该多项式指定某些模式在观察到的序列数据中应该出现的频率。这些多项式将高维实代数簇X参数化。找到隐含地定义X的方程在理论上等同于知道如何确定T是否是“真正的”进化树。这些方程以前已经在特殊的进化模型中找到过，比如木村三参数模型。研究者研究了核苷酸序列的最一般马尔可夫模型的不变量，并使用组合学和非简明傅立叶分析相结合的方法来寻找完整的不变量集。他还探索了降低该方法对进化噪声的敏感性并提高其精度的方法。在这些问题上的进展对于实现不变量方法在系统发育分析中的实用是至关重要的。研究人员开发了更好的方法来构建生物树，解释物种之间的进化关系。了解进化关系是一个重要的生物学问题，其应用范围从发现生命起源到帮助医学界研究可能的疫苗和针对艾滋病毒等病原体的治疗方法。拥有一种准确和计算高效的系统发育(或进化)分析方法将是非常有用的，但目前还没有一种方法兼具这两种特性。该项目寻求使用系统发育不变量来提高树重建方法的准确性。不变量法是一种计算效率很高的方法，在理论上给出了正确的答案。然而，在实际应用中，该方法对数据中存在的噪声非常敏感。研究人员的目标是通过消除目前使用不变量方法必须满足的几个假设来简化这个问题。

Hagedorn0077851 The investigator seeks advances in the reconstruction ofphylogenetic, or evolutionary, trees in biology by improving theutility of the method of phylogenetic invariants, one of severaldifferent methods of tree reconstruction. It would be extremelyuseful to have an accurate, computationally efficient method ofphylogenetic analysis, but no such method is yet known. Themethod of phylogenetic invariants theoretically has theseadvantages. Modern phylogenetic methods analyze the mathematicaland statistical similarities between the nucleotide sequences ofdifferent species. By modeling the evolution of the sequence fora proposed evolutionary tree T as a Markov model, one can obtainpolynomials specifying the frequencies with which certainpatterns should occur in observed sequence data. Thesepolynomials parameterize a high-dimensional real algebraicvariety X. Finding the equations that implicitly define X istheoretically equivalent to knowing how to determine whether T isthe "true" evolutionary tree. These equations have beenpreviously found for special evolutionary models such as theKimura 3-parameter model. The investigator studies theinvariants for the most general Markov model of nucleotidesequences and uses a combination of combinatorics and non-abelianFourier analysis to find a complete set of invariants. He alsoexplores ways to reduce the method's sensitivity to evolutionarynoise and raising its accuracy. Advances on these issues areessential to make implementations of the invariant methodpractical for phylogenetic analysis. The investigator develops better methods to constructbiological trees explaining the evolutionary relationshipsbetween species. Understanding evolutionary relationships is animportant biological question, whose applications range fromaiding the discovery of the origin of life to helping the medicalcommunity research possible vaccines and treatments for pathogenssuch as the H.I.V. virus. It would be extremely useful to havean accurate and computationally efficient method of phylogenetic(or evolutionary) analysis, but no method is currently known topossess both qualities. The project seeks to improve theaccuracy of the tree reconstruction method using phylogeneticinvariants. The method of invariants is a computationallyefficient method, which is known to theoretically give correctanswers. However, in practice, the method is very susceptible tothe presence of noise in the data. The investigator aims tominimize this problem by eliminating several assumptions thatcurrently must be met to use the method of invariants.