Combinatoric and probabilistic properties regarding the topology of genealogical trees and application in population genetics

谱系树拓扑的组合和概率特性及其在群体遗传学中的应用

• 批准号: 221524226
• 负责人: Professor Dr. Thomas Wiehe
• 金额: --
• 依托单位: Institut für Genetik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/221524226?language=en
• 关键词: Combinatoric; probabilistic; properties; regarding; topology

Bifurcating trees have extensively and succesfully been used as tools to model evolutionary dynamics. The genealogical tree of a set of alleles, genes, or species can be considered as a single realization of the evolutionary process. Yet, in models and their applications - for instance the coalescent model and the neutrality tests derived from it - it is typically assumed that samples are obtained under long-term average conditions. However, this assumption may not be appropriate when interpreting experimental data, and overlooking this important point may lead to severe mis-interpretations and mis-inferences. In order to gain a clearer understanding it is critically important to investigate the conditional sampling distribution of the tree properties. A comprehensive theory is however still missing. One goal of this proposal is to bridge this gap. We build on the results obtained during the first funding period, but emphasis will shift from combinatoric to probabilistic properties and from static to evolving trees. In particular, we will investigate how strongly a given population genealogy impinges on the genealogical properties of samples by studying the conditional sub-sampling distribution of tree properties, such as height, length and tree balance. Furthermore, we will study how strongly the contingent tree topology of a population leads to a bias in neutrality tests when applied to experimental data. Another key aspect is to integrate the fundamental evolutionary mechanism of recombination in this framework. We will use the ancestral recombination graph as a model of the spatial coalescent and study tree balance of samples and sub-samples as a stochastic process along the chromosome. Since recombination can be silent, i.e. not altering tree topology, it is essential to define topologically relevant recombination events and to quantify their rates. Complementing the spatial view, we will investigate tree balance as a process in time using the classical Moran model. In evolving trees lineages split or die and, as a consequence, tree balance changes over time. Critical times are those when the root jumps to younger tree nodes: in these events history is erased and new evolutionary episodes start. We will study the effect of this process on the sampling and conditional sub-sampling distributions of tree properties. Of particular interest are the rate of change and persistence times relative to generation time. Finally, on a slightly different tack, we will extend work from the first funding period and use tree topology and combinatoric properties of ordered trees to investigate the evolutionary mechanisms behind the distribution of large gene families along chromosomes. We will apply our theoretical results to the analysis of experimental data and their interpretation in the light of neutral vs. adaptive evolution.

分岔树已被广泛和成功地用作模拟进化动力学的工具。一组等位基因、基因或物种的谱系树可以被认为是进化过程的单一实现。然而，在模型及其应用中——例如聚结模型及其衍生的中性检验——通常假定样本是在长期平均条件下获得的。然而，在解释实验数据时，这种假设可能不合适，忽视这一点可能会导致严重的误解和错误推断。为了获得更清晰的理解，研究树属性的条件抽样分布是至关重要的。然而，一个全面的理论仍然缺失。这项提议的目标之一就是弥合这一差距。我们以第一个资助期获得的结果为基础，但重点将从组合属性转移到概率属性，从静态树转移到进化树。特别是，我们将通过研究树属性（如高度，长度和树平衡）的条件子抽样分布来研究给定种群谱系对样本谱系属性的影响有多强。此外，我们将研究群体的偶然树拓扑在应用于实验数据时导致中立性测试偏差的强烈程度。另一个关键方面是在这个框架中整合重组的基本进化机制。我们将使用祖先重组图作为空间聚合的模型，并研究样本和子样本的树平衡作为沿染色体的随机过程。由于重组可以是无声的，即不改变树的拓扑结构，因此有必要定义拓扑相关的重组事件并量化它们的速率。作为空间观点的补充，我们将使用经典的Moran模型来研究树木平衡作为一个时间过程。在进化的树木中，血统分裂或死亡，因此，树木的平衡随着时间的推移而改变。关键时刻是根跳转到更年轻的树节点的时刻：在这些事件中，历史被抹去，新的进化事件开始了。我们将研究这一过程对树性质的抽样和条件子抽样分布的影响。特别令人感兴趣的是相对于生成时间的变化率和持续时间。最后，在一个稍微不同的策略上，我们将从第一个资助期开始扩展工作，并使用树的拓扑结构和有序树的组合特性来研究大基因家族沿染色体分布背后的进化机制。我们将把我们的理论结果应用于实验数据的分析，并在中性与适应性进化的光下解释它们。