The role of dormancy in population genetics

休眠在包括微生物在内的许多分类群中都是一种有充分证据的特征，并产生一个种子库，被认为在物种的种群遗传学中发挥着重要作用。最近，一种新的通用合并结构-种子库合并被引入，作为包括休眠的新的Wright-Fisher模型谱系的时间标度限制的倒退，以自然的方式出现。对该模型的第一次数学检验显示出与标准聚结模型(如Kingman聚结模型)的定性差异。虽然已经取得了一些初步结果，但这一新对象开辟了许多种群遗传学研究的新途径。在拟议的项目中，我们计划对种子库模型和种子库合并及其相关模型进行深入的数学和统计调查，主要研究内容如下：第一，我们将对该模型进行详细的数学分析，特别是关于它的长期行为，相应的系谱树性质，极限定理，生成的划分结构，以及普适性性质。其次，我们将在模型中加入更多的进化力量，特别是一般的突变空间、不同类型的选择、波动的种群规模或可变的环境，并扩展模型以适应启动和终止休眠的不同机制。这将有助于更好地理解休眠作为一种进化力量的作用，以及它与种群遗传学中其他力量的相互作用。第三，我们将对模型进行统计分析，考察种子库合并下的站点频谱等经典量。我们还将致力于获得(近似)抽样公式，以导出显式样本概率。我们的目标是估计模型参数，特别是种子库大小、休眠率和突变率，并开发测试(弱或强)种子库的存在，或休眠形式的突变的存在。然后，这些推理方法应该使用模拟进行评估，并最终产生一个工具箱，生物学家可以使用它来调查真实的DNA序列数据。

Dormancy is a well-documented trait in many taxa, including microorganisms, and generates a seedbank that is considered to play an important role in the population genetics of a species. Very recently, a new universal coalescent structure, the seedbank coalescent, has been introduced, arising in a natural way as the backward in time scaling limit of the genealogy of a new Wright-Fisher model that includes dormancy. A first mathematical inspection of this model exhibits qualitative differences to standard coalescent models such as the Kingman coalescent. While some preliminary results have already been obtained, this new objects opens up many new lines of research in population genetics. In the proposed project, we plan a thorough mathematical and statistical investigation of the seedbank model and the seedbank coalescent and related models, following three main lines of research: First, we will carry out a detailed mathematical analysis of the model concerning in particular its longterm behaviour, the corresponding genealogical tree properties, limit theorems, generated partition structures, and universality properties. Second, we will incorporate further evolutionary forces into the model, in particular general mutation spaces, different types of selection, fluctuating population size, or variable environments, and also extend the model to accommodate different mechanisms of initiating and terminating dormancy. This will lead to a better understanding of the role of dormancy as an evolutionary force, and its interplay with other forces in population genetics. Third, we will undertake a statistical analysis of the model, investigate classical quantities such as the site frequency spectrum, under the seedbank coalescent. We will also aim to obtain (approximate) sampling formulae to derive explicit sample likelihoods. We aim to estimate model parameters, in particular for the seedbank size, the dormancy rate, and the mutation rates, and also to develop tests for the presence of (weak or strong) seed banks, or the presence of mutation in dormant forms. These inference methods should then be assessed using simulations, and ultimately lead to a toolbox that can be used by biologists to investigate real DNA sequence data.