Scalable Coalescent Inference for Large Data Sets

基因谱系的数学和统计建模-反映样本间祖先关系的树 分子序列是许多生物学领域的核心，包括群体遗传学，传染病的传播动力学， 疾病、古基因组学、遗传学和癌症基因组学。金曼的n-合并是基因的随机过程 参数依赖于进化模型的谱系。然后，模型参数的推断有助于 对导致这些序列的现象的理解。尽管许多复杂的方法 发展到今天，主要的统计和计算挑战仍然存在，因为系谱的状态空间增长 与样本数成超指数关系。我们不再受数据限制，而是缺乏计算能力， 用于分析大规模新兴基因组数据集的统计方法。研究人员的长期目标是 开发统计上一致和计算上有效的合并方法，用于精确推断进化 下一代测序数据集的参数。本研究的目的是应用 金曼的n-聚结的成块性，以解决聚结方法的状态空间爆炸问题。基本 的想法是建立一个粗略的解决方案的基础系谱和减少基数的隐藏状态空间。 这些较粗的聚结模型包括Tajima聚结模型和纯死亡过程聚结模型。具体目标 包括：（1）证明聚结模型定理，并提供理论和实践工具来解决 当对金曼聚结剂的不同分辨率或“团块”进行建模时的计算挑战;（2）开发 使用不同的聚结模型推断演化参数的可扩展方法;（3）理论上和 从经验上验证推理方法，将其应用于模拟和感染性病毒的分子序列中， 寨卡病毒等疾病，以及来自北美野牛和古代和现代人类的古代DNA样本， 样本;（4）在开放源码软件中实现新方法，确保方法的快速传播 在研究人员中。这项研究在许多不同的方面都是创新的。首先，田岛的聚结剂还没有 尽管基于更小的状态空间的潜力，但仍被用于推断。第二，这里开发的方法将 允许从之前由于计算限制而未被利用的数据集进行推断。三是 我们不仅将提供一套可供应用的工具，而且还将提供统计结果， 实现方式的我们提出的家谱树可扩展建模的研究将是有意义的，在许多eJf 领域，包括进化树理论，人口遗传学和遗传学的统计推断， 传染病和古代DNA的分子序列分析。

Mathematical and statistical modeling of gene genealogies-trees that reflect ancestral relationships among sampled molecular sequences-is central to many biological fields, including population genetics, phylodynamics of infectious disease, paleogenomics, phylogenetics, and cancer genomics. Kingman's n-coalescent is a stochastic process of gene genealogies whose parameters depend on an evolutionary model. Inference of model parameters then contributes to an understanding of the phenomena that have given rise to the sequences. Though many sophisticated methods have been developed to date, major statistical and computational challenges remain because the state space of genealogies grows superexponentially with the number of samples. We are no longer data-limited but instead, we lack computational and statistical methods for analysis of large scale emerging genomic data sets. The long-term goal of the researchers is to develop statistically consistent and computationally efficient coalescent methods for exact inference of evolutionary parameters from next-generation sequencing datasets. The objective of this research is to apply the notion of lumpability of Kingman's n-coalescent to address the state-space explosion problem of coalescent methods. The basic idea is to model a coarser resolution of the underlying genealogy and reduce the cardinality of the hidden state space. These coarser coalescent models include Tajima's coalescent and the pure-death process coalescent. The specific aims include (1) prove theorems for coalescent models and provide theoretical and practical tools for addressing computational challenges when modeling different resolutions or "lumpings" of Kingman's coalescent; (2) develop scalable methods for inference of evolutionary parameters using different coalescent models; (3) theoretically and empirically validate the inference methods, applying them in simulations and in molecular sequences from infectious diseases such as Zika, as well as ancient DNA samples from bison in North America and ancient and modern human samples; (4) implement the novel methods in open source software, ensuring fast dissemination of the methodology among researchers. The research is innovative in many distinct ways. First, Tajima's coalescent has not yet been exploited for inference despite the potential based on the smaller state space. Second, the methods developed here will allow inference from data sets that have not been exploited before because of computational limitations. Third, we will not only provide a suite of tools ready for application but we will also provide statistical results supporting our implementations. Our proposed research on scalable modeling of genealogical trees will be significant in a number eJf fields, including the theory of evolutionary trees, statistical inference in population genetics and phylogenetics, and the analysis of molecular sequences from infectious disease and ancient DNA.