Coalescent Processes and Population Models

PI研究了与聚合过程和种群模型相关的几个问题。聚结过程是对粒子系统进行建模的随机过程，这些粒子系统一开始是分离的，然后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谱系，因为如果一个人从一个种群中提取样本，并在时间上追溯祖先的血统，祖先的血统就会融合。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涉及到分支布朗运动、FKPP方程和自旋玻璃理论。PI还研究来自群体遗传学的合并理论中的问题，涉及到不断增加的人口规模或大家庭规模如何影响合并过程，从而研究从群体样本中可能观察到的突变模式。第三个项目是确定种群中的一个个体经历特定数量的突变所需时间的分布。聚合的随机模型在其他科学领域有广泛的应用，如生物学、物理化学和天文学。对了解进化感兴趣的生物学家关心的是种群样本的祖先谱系的合并。应该有可能利用结合的数学理论来进一步洞察大家庭规模、不断增加的人口规模和自然选择如何影响这一过程。另一个项目涉及确定一个群体中的一个人经历几次突变所需的时间。这个项目是由癌症模型推动的，在该模型中，假设一个细胞只有在发生几次有害的突变后才会变成癌细胞。

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.