27th March 2007 — On the Genealogy of Large Populations
Yee Whye will discuss:
On the Genealogy of Large Populations, J. F. C. Kingman,
The Coalescent, J. F. C. Kingman,
The Dirichlet process can be derived from kingman's coalescent, which is a standard model of mathematical population genetics. Kingman's coalescent can be obtained as the continuous/infinite limit of the following process: at each time t there is a population of N individuals; each individual picks a parent at random from the previous generation of individuals, located in time t+1/N. We will try to understand this process in more detail, and also derive the DP as kingman's coalescent coupled with a separate mutation process.