Stochastic Processes in the development of a genealogy
by
Nicoleen Cloete
University of Auckland

A rooted binary tree can represent the genealogy of a finite set of organisms. The stochastic process of development of such a genealogy can be modeled by the Kingman n-coalescent. The n-coalescent is a jump process which can be used as a prior distribution in Bayesian inference. The likelihood is defined by a process of gene mutation which transforms the root genome into the descendant genomes associated with the leaves. Given the leaf genomes as data, parameters that can be infer red are the mutation rate and the time to the most recent common ancestor. However, this model does not take natural selection into account.

On the other hand, Neuhauser and Krone proposed a stochastic model to construct the genealogy of a natural population incorporating selection. This model defines a selection parameter. The Kingman coalescent may be regarded as a special case of the N-K model, since it is obtained when the selection parameter of the N-K model is set to zero.

I will discuss estimation of the selection parameter of the N-K model from genome data.

Date received: October 11, 2001