Coalescent Processes and Population Models

PI研究了与聚结过程和种群模型有关的几个问题。凝聚过程是一种随机过程，它模拟了一个粒子系统，随着时间的推移，粒子系统开始分离并合并成簇。这些过程可以用来描述一个群体的家谱，因为如果从一个群体中取一个样本，沿着祖先的谱系向后追溯，那么祖先的谱系就会融合在一起。其中一个目标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还研究来自群体遗传学的聚结理论中的问题，涉及到群体规模或大家庭规模的增加如何影响聚结过程，以及可能在群体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的突变所需的时间分布。聚并的随机模型在生物学、物理化学和天文学等其他科学领域有着广泛的应用。对理解进化感兴趣的生物学家关注的是一个种群中一个样本的祖先谱系的合并。应该有可能利用融合的数学理论来进一步了解大家庭规模、不断增长的人口规模和自然选择是如何影响这一过程的。另一个项目包括确定种群中一个个体经历几个突变所需的时间。这个项目的动机是癌症模型，假设一个细胞只有在几个有害的突变发生后才会癌变。

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.