Evolving coalescents

不断发展的成膜助剂

• 批准号: 221529486
• 负责人: Professor Dr. Götz Kersting
• 金额: --
• 依托单位: Fachbereich 12 - Informatik und Mathematik
• 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 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/221529486?language=en
• 关键词: Evolving; coalescents

Coalescent theory has become a topic of central importance at the interface of probability theory and population genetics. In recent years, coalescent structures evolving in time have gained particular interest, they serve as a model for the changes which genealogies of populations undergo in time. In the first funding period we have studied evolving coalescents as tree-valued processes, and analysed the asymptotic distribution of various functionals of evolving Beta coalescents. We found a method which allows to represent a rich class of functionals of Beta coalescents as stable Poisson integrals, simultaneously for the static and the evolving case. In the second funding period we will continue this line of research. We will elaborate on the method of Poisson integrals, with a particular focus on the internal length spectrum of Beta coalescents. Moreover we will zoom in on new functionals of the Bolthausen-Sznitman coalescent and extend our investigations of coalescent functionals to general Lambda-coalescents. Specifically we are interested in the external branches of extremal length and the size of the last merger. We also plan to investigate the symmetric excursion representation for genealogies under individual competition.

聚结理论已成为概率论和群体遗传学交叉领域的一个核心重要话题。近年来，随时间演变的合并结构引起了特别的兴趣，它们作为人口谱系随时间变化的模型。在第一个资助期间，我们研究了演化的聚结剂作为树值过程，并分析了演化的 Beta 聚结剂的各种泛函的渐近分布。我们找到了一种方法，可以将丰富的 Beta 聚结泛函表示为稳定的泊松积分，同时适用于静态和演化的情况。在第二个资助期内，我们将继续这方面的研究。我们将详细阐述泊松积分的方法，特别关注 Beta 聚结剂的内部长度谱。 此外，我们将重点关注 Bolthausen-Sznitman 聚结剂的新泛函，并将我们对聚结泛函的研究扩展到一般的 Lambda 聚结剂。 具体来说，我们对极值长度的外部分支和最后一次合并的大小感兴趣。 我们还计划研究个人竞赛下谱系的对称偏移表示。