27th March 2007 — On the Genealogy of Large Populations

Yee Whye will discuss:

On the Genealogy of Large Populations, J. F. C. Kingman, Journal of Applied Probability, 19, 1982
The Coalescent, J. F. C. Kingman, Stochastic Systems and their Applications, 13, 1982

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.