General coalescent trees and subtrees in evolutionary population genetics

The coalescent process of Kingman (1982) in evolutionary genetics describes the ancestry of a sample of genes back in time. In the simplest formulation the coalescence rate while k ancestors is $\left(\begin{array}{}k\\ 2\end{array}\right)$, a rate of 1 for each unordered pair of edges in the tree. There is a connection with classical population genetics models and many earlier results can be rederived from a coalescent model, rather than from diffusion processes. This talk will describe recent research on general binary exchangeable coalescent trees and subtrees where times between coalescences have an arbitary distribution. Included are results about the age of mutations in gene trees, the distribution of mutations on trees and the characteristics of subtrees under a mutation.