eMB: Collaborative Research: Advancing Inference of Phylogenetic Trees and Networks under Multispecies Coalescent with Hybridization and Gene Flow

每个有机体的DNA都保留了其进化谱系的痕迹，随着DNA的复制，新的遗传变异也被引入。研究人员分析DNA序列中的模式，以拼凑生物的进化史，对这些关系的估计有不同的应用。例如，描述转移性结直肠癌的进化模式或确定不同病毒株之间的关系。进化历史通常由系统发育树来表示，该树显示了生物之间的祖先和血统关系；然而，遗传信息并不总是垂直传递的，在这种情况下，这些关系应该用网络来表示。例如，两个病毒基因组可以共同感染同一宿主细胞，导致基因片段的交换，称为重组，从而促进它们的多样性。此外，生物进化发生在两个不同的水平：个体基因水平和物种水平，这限制了个体基因的历史。进化树和进化网络的准确估计是数学和统计推理中的一个主要问题，因为它们的估计的精度直接影响到流行病学、法医学、生物安全和癌症生物学等领域。该项目的主要目标是提高当前方法的可扩展性和准确性，并开发新的方法来推断系统发育物种网络。该项目是美国大学和佛罗里达大学的合作项目，提供了宝贵的教育和推广机会。具体地说，作为这一过程的一部分，研究生和本科生将接受系统学方法方面的培训，从而实现知识的垂直转移。根据多基因比对推断物种水平关系的工作特定于同时解释由于不完整的谱系排序、基因流动、杂交和重组等过程而导致的个体基因历史的可变性的模型。重点放在基于站点的物种方法上，目标是(1)改进四重组物种推理和可扩展性；(2)从有根的三元组中实现有根物种树的推理；(3)开发更有效的基于站点的方法来识别杂交物种或重组事件，而不需要外群；以及(4)从四重组和四分类单元网络中实现基于站点的物种网络推理。为了实现这些目标，PI将把多个数学思想从单基因树环境中的马尔可夫模型扩展到合并和基因流动下的模型，例如树叶变换和基于准线性距离的度量，这些到目前为止还没有在物种树模型下正式描述、测试或实现。与目前在网络上寻找零多项式的代数方法不同，杂交物种识别的方法是基于导出函数，其比值接近于混合参数的比值。因此，这项工作对数学、统计和生物科学做出了贡献，并有可能在理论和计算领域引发新的讨论。我们基于现场的物种水平推断方法的完整软件包将免费提供给经验系统发育学社区。该项目由数学科学部的数学生物学计划和环境生物学部的系统和生物多样性科学集群共同资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The DNA of every organism retains a trace of its evolutionary lineage, and as the DNA is copied, new genetic variations are introduced. Researchers analyze patterns in DNA sequences to piece together organisms' evolutionary histories, and the estimation of these relationships has diverse applications. Examples include characterizing the evolutionary patterns of metastatic colorectal cancer or determining the relationship between different viral strains. The evolutionary history is often represented by a phylogenetic tree that displays the ancestry and descent relationships among organisms; however, genetic information is not always transferred vertically, and in these cases, the relationships should be represented by a network. For example, two viral genomes can co-infect the same host cell, leading to the exchange of genetic segments, called recombination, and thus contributing to their diversity. Additionally, organismal evolution occurs at two distinct levels: at the level of individual genes and at the level of species, which constrains the histories of the individual genes. Accurate estimation of evolutionary trees and networks is a major problem in mathematical and statistical inference since the precision of their estimation has a direct impact on fields such as epidemiology, forensic medicine, biosecurity, and cancer biology. The main objective of this project is to improve the scalability and accuracy of current methods and develop new methods for inferring phylogenetic species networks. The project is a collaboration between the American University and University of Florida and offers valuable educational and outreach opportunities. Specifically, graduate and undergraduate students will be trained in phylogenetic methodologies as part of the process, resulting in a vertical transfer of knowledge. The work for inferring species-level relationships from multigene alignments are specific to models that simultaneously account for variability in individual gene histories due to processes such as incomplete lineage sorting, gene flow, hybridization, and recombination. The focus is on site-based species methodologies, with the goals of (1) improving quartet species inference and scalability; (2) implementing inference of rooted species trees from rooted triples; (3) developing more efficient site-based methods for identifying hybrid species or recombination events without the need for an outgroup; and (4) implementing site-based species network inference from quartets and 4-taxon networks. To achieve these goals, the PIs will extend multiple mathematical ideas from Markov models in the single gene tree setting to models under coalescent and gene flow, such as leaf transformations and a measure based on paralinear distance, which so far have not been formally described, tested, or implemented under the species tree model. The method for hybrid species identification is based on deriving functions whose ratio approaches the ratio of the mixing parameter, which is distinct from current algebraic methods that look for vanishing polynomials over networks. As a result, this work contributes to the mathematical, statistical, and biological sciences, and has the potential to spark new discussions in the theoretical and computational communities. A complete software package implementing our site-based species-level inference methods will be freely available to the empirical phylogenetics community.This project is jointly funded by the Mathematical Biology Program in the Division of Mathematical Sciences and Systematic and Biodiversity Science Cluster in the Division of Environmental Biology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.