##### Department of Mathematics,

University of California San Diego

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### Stochastic Systems

## Jason Schweinsberg

#### UCSD

## Mutation patterns in populations with large family sizes

##### Abstract:

Suppose we take a sample of size $n$ from a population and follow the ancestral lines backwards in time until the most recent common ancestor. Under standard assumptions, this process can be approximated by Kingman's coalescent, in which two lineages merge at rate one. Mutations that have occurred since the time of the most recent common ancestor will lead to segregating sites, which are positions in the DNA at which not all individuals in the sample are the same. If we denote by $M_k$ the number of mutations that affect k individuals in the sample, then the sequence $M_1, ... , M_{n-1}$, is called the site frequency spectrum. We will explain how the site frequency spectrum would be affected if some individuals have large numbers of offspring, so that the coalescent process that describes the genealogy of the population can have multiple mergers of ancestral lines. This model may be realistic for certain marine species. This is joint work with Julien Berestycki and Nathanael Berestycki.

Host:

### March 8, 2006

### 2:00 PM

### AP&M 6218

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