Coalescent Processes and Population Models

PI研究了与聚结过程和种群模型相关的几个问题。 聚结过程是模拟粒子系统的随机过程，这些粒子开始分离并随着时间的推移合并成簇。 这些过程可以用来描述一个种群的系谱，因为如果从一个种群中抽取样本，沿着祖先的谱系追溯过去，祖先的谱系就会合并，目的之一是更深入地了解自然选择对这一过程的影响。 这个问题的数学方面与分支布朗运动、FKPP方程和自旋玻璃理论有关。 PI还研究了来自群体遗传学的合并理论中的问题，涉及人口规模或大家庭规模如何影响合并过程，以及因此可能在人口样本中观察到的突变模式。 第三个项目是确定种群中一个个体经历特定数量突变所需的时间分布。聚结的随机模型在其他科学领域如生物学、物理化学和天文学中有广泛的应用。 对理解进化感兴趣的生物学家关心的是来自种群样本的祖先系的合并。 应该有可能使用数学理论的聚结，以获得进一步了解如何大家庭规模，不断增加的人口规模和自然选择影响这一过程。 另一个项目涉及确定群体中一个个体经历几次突变所需的时间，该项目的动机是癌症模型，其中假设细胞只有在发生几次有害突变后才会癌变。

The PI studies several problems related to coalescent processes and population models. Coalescent processes are stochastic processes that model a system of particles which start out separated and merge into clusters as time goes forward. These processes can be used to describe the genealogy of a population because if one takes a sample from a population and follows the ancestral lines backwards in time, the ancestral lines will coalesce.One goal is to gain more insight into the effect that natural selection has on this process. The mathematical aspects of this question are related to branching Brownian motion, the FKPP equation, and the theory of spin glasses. The PI also studies problems in coalescent theory that come from population genetics, related to how increasing population sizes or large family sizes affect the coalescent process, and therefore the patterns of mutations that are likely to be observed in a sample from the population. A third project is to determine the distribution of the time that it takes for one individual in a population to experience a specified number of mutations.Stochastic models of coalescence have a wide range of applications in other fields of science such as biology, physical chemistry, and astronomy. Biologists interested in understanding evolution are concerned with the merging of the ancestral lines of a sample from a population. It should be possible to use the mathematical theory of coalescence to gain further insight into how large family sizes, increasing population sizes, and natural selection impact this process. An additional project involves determining the amount of time that it takes for one individual in a population to experience several mutations.This project is motivated by models of cancer in which it is assumed that a cell becomes cancerous only after several harmful mutations take place.