##### Department of Mathematics,

University of California San Diego

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### Math 196/296 - Student Colloquium

## Jason Schweinsberg

#### UCSD

## Modeling the effect of beneficial mutations on the genealogy of a population

##### Abstract:

The solutions of many important problems in population genetics require tools from probability theory because the evolution of a population over time is modeled as a random process. In this talk, we focus on the question of how to describe the effect that beneficial mutations have on the genealogy of a population. We present two approximations. The first, which involves coin tossing, is simple but not very accurate. The second, which is based on a stick-breaking construction, leads to much more accurate results.

### October 11, 2007

### 12:00 PM

### AP&M B402A

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