Simulation of ancestral histories of genes
Seminar Room 1, Newton Institute
An empirical distribution of the stochastic history of a sample of genes, conditional on their types, can be found by an advanced simulation technique of sequential importance sampling (SIS) on coalescent histories. If the sample data are DNA sequences, then the pattern of mutations provides information about the ancestral tree of the data. For example, empirical distributions of the time to the most recent common ancestor of the genes and ages of mutations, conditional on the tree topology, can be found. Coalescent processes looking back in time are dual processes to diffusion process models of how gene frequencies evolve forward in time. Proposal distributions for SIS in coalescent histories can be constructed from the generator of the diffusion process. This talk will sketch the SIS technique and present examples of ancestral inference.