Branching random walks in random enviroment and their applications to population genetics

随机环境中的分支随机游走及其在群体遗传学中的应用

• 批准号: 221751432
• 负责人: Professor Dr. Wolfgang König
• 金额: --
• 依托单位: Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
• 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 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/221751432?language=en
• 关键词: Branching; random; walks; enviroment; their

We propose to study various branching random walk systems with random branching rates. The state space that we focus on is the N-dimensional hypercube, serving as a model for long gene sequences with mutations occurring by flip of a gene. We throughout consider the limit of large N, coupled with characteristic parameters such as time and sample size.The random branching rates form a fitness landscape that governs the selection. We first focus on uncorrelated landscapes and start with a population of one randomly picked gene sequence. We want to study the concentration properties of the system, the evolution of the mean fitness of the population and the aging properties. We will attack these questions both with probabilistic and analytical, i.e., spectral theoretical, methods. In another workload, we will consider Gaussian correlated fitness landscapes, namely, Sherrington-Kirkpatrick models of spin glasses. The key to the study of these models is Gaussian comparison techniques, and we shall adopt these tools for studying branching systems.Finally, we will consider theoretical models of experiments on evolution which involves a strategy of restarting the system with a part of the population at the end of some time periods. We plan to develop a thorough understanding of appropriate choices of the scales for the time lags in order to be able to deduce useful conclusions from the experiment.

我们研究了具有随机分支率的分支随机游动系统。我们关注的状态空间是N维超立方体，作为一个模型的长基因序列发生突变的基因翻转。我们始终考虑大N的限制，再加上特征参数，如时间和样本大小。随机分支率形成一个适应度景观，管理选择。我们首先关注不相关的景观，并从一个随机挑选的基因序列的人口开始。我们想研究系统的浓度性质、种群平均适应度的演化和老龄化性质。我们将用概率和分析的方法来解决这些问题，即，光谱理论方法在另一个工作负载中，我们将考虑高斯相关的适应度景观，即自旋眼镜的Sherrington-Kirkpatrick模型。研究这些模型的关键是高斯比较技术，我们将采用这些工具来研究分支系统。最后，我们将考虑进化实验的理论模型，其中涉及在某些时间段结束时用部分种群重新启动系统的策略。我们计划对时滞尺度的适当选择有一个透彻的理解，以便能够从实验中推导出有用的结论。