Mathematical Sciences: Stochastic Processes in Genetics and Statistics

首席研究员的研究包括两个主要部分，这两个部分都是在理论群体遗传学领域。这个领域的兴趣是通过数学建模来理解进化的过程。首先，埃塞尔将利用他最近的想法，通过扩散理论包括等位基因的年龄和谱系。他正在努力统一这一主题，通过展示年龄和谱系的更传统的方法，如凝聚过程，可以从一个适当的平稳扩散模型中推导出来，这个模型通常被认为是群体遗传学的基本随机模型。其次，他将继续研究双轨迹扩散模型，重点研究这些过程的理论方面，特别是重组的影响。

The principal investigator's research consists of two main parts, both of which are in the field of theoretical population genetics. This field is interested in understanding the process of evolution through mathematical modeling. First, Ethier will exploit his recent ideas of including an allele's age and genealogy via diffusion theory. He is working towards unifying the subject by showing that the more conventional approaches to ages and genealogies, such as coalescent processes, can be derived from an appropriate stationary diffusion model, which is often regarded as the basic stochastic model in population genetics. Second, he will continue working on two-locus diffusions models, with emphasis on theoretical aspects of such processes, especially the effect of recombination.