Coalescent Processes and Population Models

University Of California-San Diego, La Jolla CA

Investigators

Abstract

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.